in Medicine. By specifics is not meant such as infallibly and in all patients produce falutary effects. Such medicines are not to be expected, because the operations and effects of remedies are not formally inherent in them, but depend upon the mutual action and reaction of the body and medicine upon each other; hence the various effects of the same medicine in the same kind of disorders in different patients, and in the same patient at different times. By specific medicines we understand such medicines as are found to be more uniform in their effects than others in any particular disorder.

SPECIFIC Gravity, is a term much employed in the discussions of modern physics. It expresses the weight of any particular kind of matter, as compared with the weight of the same bulk of some other body of which the weight is supposed to be familiarly known, and is therefore taken for the standard of comparison. The body generally made use of for this purpose is pure water.

The specific gravity of bodies is a very interesting question both to the philosopher and to the man of business. The philosopher considers the weights of bodies as measures of the number of material atoms, or the quantity of matter which they contain. This he does on the supposition that every atom of matter is of the same weight, whatever may be its sensible form. This supposition, however, is made by him with caution, and he has recourse to specific gravity for ascertaining its truth in various ways. This shall be considered by and by. The man of business entertains no doubt of the matter, and proceeds on it as a sure guide in his most interesting transactions. We measure commodities of various kinds by tons, pounds, and ounces, in the same manner as we measure them by yards, feet, and inches, or by bushels, gallons, and pints; nay, we do this with much greater confidence, and prefer this measurement to all others, whenever we are much interested to know the exact proportions of matter that bodies contain. The weight of a quantity of grain is allowed to inform us much more exactly of its real quantity of useful matter than the most accurate measure of its bulk. We see many circumstances which can vary the bulk of a quantity of matter, and these are frequently such as we cannot regulate or prevent; but we know very few indeed that can make any sensible change in this weight without the addition or abstraction of other matter. Even taking it to the summit of a high mountain, or from the equator to the polar region, will make no change in its weight as it is ascertained by the balance, because there is the same real diminution of weight in the pounds and ounces used in the examination.

Notwithstanding the unavoidable change which heat and cold make in the bulk of bodies, and the permanent varieties of the same kind of matter which are caused by different circumstances of growth, texture, &c. most kinds of matter have a certain conformity in the density of their particles, and therefore in the weight of a given bulk. Thus the purity of gold, and its degree of adulteration, may be inferred from its weight, it being purer in proportion as it is more dense. The density, therefore, of different kinds of tangible matter becomes characteristic of the kind, and a test of its purity; it marks a particular appearance in which matter exists, and may therefore be called, with propriety, SPECIFIC.

But this density cannot be directly observed. It is not by comparing the distances between the atoms of matter in gold and in water that we say the first is 19 times denser than the last, and that an inch of gold contains 19 times as many material atoms as an inch of water; we reckon on the equal gravitation of every atom of matter whether of gold or of water; therefore the weight of any body becomes the indication of its material density, and the weight of a given bulk becomes specific of that kind of matter, marking its kind, and even ascertaining its purity in this form.

It is evident that, in order to make this comparison of general use, the standard must be familiarly known, and must be very uniform in its density, and the comparison of bulk and density must be easy and accurate. The most obvious method would be to form, with all nicety, a piece of the standard matter of some convenient bulk, and to weigh it very exactly, and keep a note of its weight: then, to make the comparison of any other substance, it must be made into a mass of the same precise bulk, and weighed with equal care; and the most convenient way of expressing the specific gravity would be to consider the weight of the standard as unity, and then the number expressing the specific gravity is the number of times that the weight of the standard is contained in that of the other substance. This comparison is most easily and accurately made in fluids. We have only to make a vessel of known dimensions equal to that of the standard which we employ, and to weigh it when empty, and then when filled with the fluid. Nay, the most difficult part of the process, the making a vessel of the precise dimensions of the standard, may be avoided, by using some fluid substance for a standard. Any vessel will then do; and we may ensure very great accuracy by using a vessel with a slender neck, such as a phial or matraf; for when this is filled to a certain mark in the neck, any error in the estimation by the eye will bear a very small proportion to the whole. The weight of the standard fluid which fills it to this mark being carefully ascertained, is kept in remembrance. The specific gravity of any other fluid is had by weighing the contents of this vessel when filled with it, and dividing the weight by the weight of the standard. The quotient is the specific gravity of the fluid. But in all other cases this is a very difficult problem: it requires very nice hands, and an accurate eye, to make two bodies of the same bulk. An error of one hundredth part in the linear dimensions of a solid body makes an error of a 30th part in its bulk; and bodies of irregular shapes and friable substance, such as the ores of metals, cannot be brought into convenient and exact dimensions for measurement.

From all these inconveniences and difficulties we are freed by the celebrated Archimedes, who, from the principles of hydrotatics discovered or established by him, deduced the accurate and easy method which is now universally practised for discovering the specific gravity and density of bodies. (See ARCHIMEDES and HYDRODYNAMICS). Instead of measuring the bulk of the body by that of the displaced fluid (which would have been impossible for Archimedes to do with anything like the necessary precision), we have only to observe the loss of weight sustained by the solid. This can be done with great ease and exactness. Whatever may be the bulk of the body, this loss of weight is the weight of an equal bulk of the fluid; and we obtain the specific gravity of the body by simply dividing its whole weight by the weight lost: the quotient is the specific gravity when this fluid is taken for the standard, even though we should not know the absolute weight of any given bulk of this standard. It also gives us an easy and accurate method of ascertaining even this fundamental point. We have only to form any solid body into an exact cube, sphere, or prism, of known dimensions, and observe what weight it loses when immersed in this standard fluid. This is the weight of the same bulk of the standard to be kept in remembrance; and thus we obtain, by the bye, a most easy and accurate method for measuring the bulk or solid contents of any body, however irregular its shape may be. We have only to see how much weight it loses in the standard fluid; we can compute what quantity of the standard fluid will have this weight. Thus should we find that a quantity of sand, or a furze bush, loses 250 ounces when immersed in pure water, we learn by this that the solid measure of every grain of the sand, or of every twig and prickle of the furze, when added into one sum, amounts to the fourth part of a cubic foot, or to 432 cubic inches.

To all these advantages of the Archimedean method of ascertaining the specific gravity of bodies, derived from his hydrotatical doctrines and discoveries, we may add, that the immediate standard of comparison, namely, water, is, of all the substances that we know, the fittest for the purpose of an universal standard of reference. In its ordinary natural state it is sufficiently constant and uniform in its weight for every examination where the utmost mathematical accuracy is not wanted; all its variations arise from impurities, from which it may at all times be separated by the simple process of distillation: and we have every reason to think that when pure, its density, when of the same temperature, is invariable.

Water is therefore universally taken for the unit of that scale on which we measure the specific gravity of bodies, and its weight is called 1. The specific gravity of any other body is the real weight in pounds and ounces, when of the bulk of one pound or one ounce of water. It is therefore of the first importance, in all discussions respecting the specific gravity of bodies, to have the precise weight of some known bulk of pure water. We have taken some pains to examine and compare the experiments on this subject, and shall endeavour to ascertain this point with the precision which it deserves. We shall reduce all to the English cubic foot and avoirdupois ounce of the Exchequer standard, on account of a very convenient circumstance peculiar to this unit, viz. that a cubic foot contains almost precisely a thousand ounces of pure water, so that the specific gravity of bodies expresses the number of such ounces contained in a cubic foot.

We begin with a trial made before the house of commons in 1696 by Mr Everard. He weighed 2145.6 cubic inches of water by a balance, which turned sensibly with 6 grains, when there were 30 pounds in each scale. The weights employed were the troy weights, in the deposit of the Court of Exchequer, which are still preserved, and have been most scrupulously examined and compared with each other. The weight was 1131 ounces 14 pennyweights. This wants just 11 grains of a thousand avoirdupois ounces for 1728 cubic inches, or a cubic foot; and it would have amounted to that weight had it been a degree or two colder. The temperature indeed is not mentioned; but as the trial was made in a comfortable room, we may presume the temperature to have been about 55° of Fahrenheit's thermometer. The dimensions of the vessel were as accurate as the nice hand of Mr Abraham Sharp, Mr Flamstead's assistant at Greenwich, could execute, and it was made by the Exchequer standard of length.

This is confided in by the naturalists of Europe as a very accurate standard experiment, and it is confirmed by many others both private and public. The standards of weight and capacity employed in the experiment are still in existence, and publicly known, by the report of the Royal Society to parliament in 1742, and by the report of a committee of the house of commons in 1758. This gives it a superiority over all the measures which have come to our knowledge.

The first experiment, made with proper attention, that we meet with, is by the celebrated Snellius, about the year 1615, and related in his Eratophenes Batavus. He weighed a Rhinland cubic foot of distilled water, and found it 62.79 Amsterdam pounds. If this was the ordinary weight of the shops, containing 7626 English troy grains, the English cubic foot must be 62 pounds 9 ounces, only one ounce more than by Everard's experiment. If it was the Mint pound, the weight was 62 pounds 6 ounces. The only other trials which can come into competition with Mr Everard's are some made by the Academy of Sciences at Paris. Picart, in 1691, found the Paris cubic foot of the water of the fountain d'Arcueil to weigh 69.583 pounds, poids de Paris. Du Hamel obtained the very fame result; but Mr Monge, in 1783, says that filtered rain-water of the temperature 12° (Beaumur) weighs 69.3792. Both these measures are considerably below Mr Everard's, which is 62.5, the former giving 62.533, and the latter 61.868. M. Lavoisier states the Paris cubic foot at 70 pounds, which makes the English foot 62.47. But there is an insufficiency sistency among them which makes the comparison impossible. Some changes were made in 1688, by royal authority, in the national standards, both of weight and length; and the academicians are exceedingly puzzled to this day in reconciling the differences, and cannot even ascertain with perfect assurance the lineal measures which were employed in their most boasted geodetical operations.

Such variations in the measurements made by persons of reputation for judgment and accuracy engaged the writer of this article some years ago to attempt another. A vessel was made of a cylindrical form, as being more easily executed with accuracy, whose height and diameter were 6 inches, taken from a most accurate copy of the Exchequer standard. It was weighed in distilled water at the temperature 55° several times without varying 2 grains, and it lost 4280.5 grains. This gives for the cubic foot 998.74 ounces, deficient from Mr Everard's an ounce and a quarter; a difference which may be expected, since Mr Everard used the New River water without distillation.

We hope that these observations will not be thought superfluous in a matter of such continual reference, in the most interesting questions both to the philosopher and the man of business; and that the determination which we have given will be considered as sufficiently authenticated.

Let us, therefore, for the future take water for the standard, and suppose that, when of the ordinary temperature of summer, and in its state of greatest natural purity, viz. in clean rain or snow, an English cubic foot of it weighs a thousand avoirdupois ounces of 437.5 troy grains each. Divide the weight of any body by the weight of an equal bulk of water, the quotient is the specific gravity of that body; and if the three first figures of the decimal be accounted integers, the quotient is the number of avoirdupois ounces in a cubic foot of the body. Thus the specific gravity of the very finest gold which the refiner can produce is 19.365, and a cubic foot of it weighs 19365 ounces.

But an important remark must be made here. All bodies of homogeneous or unorganized texture expand by heat, and contract by cooling. The expansion and contraction by the same change of temperature is very different in different bodies. Thus water, when heated from 60° to 100°, increases its volume nearly \( \frac{1}{11} \) of its bulk, and mercury only \( \frac{1}{271} \), and many substances much less. Hence it follows, that an experiment determines the specific gravity only in that very temperature in which the bodies are examined. It will therefore be proper always to note this temperature; and it will be convenient to adopt some very useful temperature for such trials in general: perhaps about 60° of Fahrenheit's thermometer is as convenient as any. It may always be procured in these climates without inconvenience. A temperature near to freezing would have some advantages, because water changes its bulk very little between the temperature 32° and 45°. But this temperature cannot always be obtained. It will much conduce to the facility of the comparison to know the variation which heat produces on pure water. The following table, taken from the observations of Dr Blagden and Mr Gilpin (Phil. Trans. 1792) will answer this purpose.

<table> <tr> <th>Temperature of Water</th> <th>Bulk of Water.</th> <th>Specific Gravity.</th> </tr> <tr><td>30</td><td>99910</td><td>1.00090</td></tr> <tr><td>35</td><td>99970</td><td>1.00094</td></tr> <tr><td>40</td><td>99970</td><td>1.00094</td></tr> <tr><td>45</td><td>99914</td><td>1.00086</td></tr> <tr><td>50</td><td>99932</td><td>1.00068</td></tr> <tr><td>55</td><td>99962</td><td>1.00038</td></tr> <tr><td>60</td><td>100000</td><td>1.00000</td></tr> <tr><td>65</td><td>100050</td><td>0.99950</td></tr> <tr><td>70</td><td>100106</td><td>0.99804</td></tr> <tr><td>75</td><td>100171</td><td>0.99630</td></tr> <tr><td>80</td><td>100242</td><td>0.99759</td></tr> <tr><td>85</td><td>100320</td><td>0.99681</td></tr> <tr><td>90</td><td>100404</td><td>0.99598</td></tr> <tr><td>95</td><td>100501</td><td>0.99502</td></tr> <tr><td>100</td><td>100602</td><td>0.99402</td></tr> </table>

These gentlemen observed the expansion of water to be very anomalous between 32° and 45°. This is distinctly seen during the gradual cooling of water to the point of freezing. It contracts for a while, and then suddenly expands. But we seldom have occasion to measure specific gravities in such temperature.

The reader is now sufficiently acquainted with the principles of this hydrostatical method of determining the specific gravity of bodies, and can judge of the propriety of the forms which may be proposed for the experiment.

The specific gravity of a fluid may be determined either by filling with it a vessel with a narrow neck, or by weighing a solid body that is immersed in it. It is hard to say which is the best way. The last is not subject to any error in filling, because we may suspend the solid by a fine wire, which will not displace any sensible quantity of the fluid; and if the solid is but a little heavier than the fluid, the balance being loaded only with the excess, will be very sensible to the smallest want of equilibrium. But this advantage is perhaps compensated by an obstruction to the motion of the solid up or down in the fluid, arising from viscosity. When the weight in the opposite scale is yet too small, we slowly add more, and at last grain by grain, which gradually brings the beam to the level. When it is exactly level, the weight in the scale is somewhat too great; for it not only balances the preponderance of the solid, but also this viscosity of the fluid. But we may get rid of this error. Add a small quantity more; this will bring the beam over to the other side. Now put as much into the scale on the same side with the solid; this will not restore the beam to its level. We must add more till this be accomplished; and this addition is the measure of the viscosity of the fluid, and must be subtracted from the weight that was in the other scale when the beam came to a level. This effect of viscosity is not insensible, with nice apparatus, even in the purest water, and in many fluids it is very considerable—and, what is worse, it is very changeable. It is greatly diminished by heat; and this is an additional reason for making making those trials in pretty warm temperatures. But for fluids of which the viscosity is considerable, this method is by no means proper; and we must take the other, and weigh them in a vessel with a narrow neck. Mercury must also be treated in this way, because we have no solid that will sink in it but gold and platina.

It is not so easy as one would imagine to fill a vessel precisely to the same degree upon every trial. But if we do not operate on too small quantities, the unavoidable error may be made altogether insignificant, by having the neck of the vessel very small. If the vessel hold a pound of water, and the neck do not exceed a quarter of an inch (and it will not greatly retard the operation to have it half this size), the examinator must be very careless indeed to err one part in two thousand; and this is perhaps as near as we can come with a balance. We must always recollect that the capacity of the vessel changes by heat, and we must know this variation, and take it into the account. But it is affection to regard (as Mr Homberg would make us believe that he did) the diffusion of the vessel by the pressure of the fluid. His experiments of this kind have by no means the consistency with each other that should convince us that he did not commit much greater errors than what arose from diffusion.

In examining either solids or fluids, we must be careful to free their surface, or that of the vessel in which the fluid is to be weighed, from air, which frequently adheres to it in a peculiar manner, and, by forming a bubble, increases the apparent bulk of the solid, or diminishes the capacity of the vessel. The greatest part of what appears on those occasions seems to have existed in the fluid in a state of chemical union, and to be set at liberty by the superior attraction of the fluid for the contiguous solid body. These air bubbles must be carefully brushed off by hand. All greasy matters must be cleared off for the same reason: they prevent the fluid from coming into contact.

We must be no less careful that no water is imbibed by the solid, which would increase its weight without increasing its bulk. In some cases, however, a very long maceration and imbibition is necessary. Thus, in examining the specific gravity of the fibrous part of vegetables, we should err exceedingly if we imagined it as small as appears at first. We believe that in most plants it is at least as great as water, for after long maceration they sink in it.

It is almost needless to say that the nicest and most sensible balances are necessary for this examination. Balances are even constructed on purpose, and fitted with several pieces of apparatus, which make the examination easy and neat. We have described (see Balance) Mr Gravendeel's as one of the most convenient of any. His contrivance for observing the fractions of a grain is extremely ingenious and expeditions, especially for detecting the effect of viscosity.

The hydrometer, or areometer, is another instrument for ascertaining the specific gravity of fluids. This very pretty instrument is the invention of a lady, as eminent for intellectual accomplishments as she was admired for her beauty. Hypatia, the learned daughter of the celebrated mathematician Theon of Alexandria, became so eminent for her mathematical knowledge, that she was made public professor of the science in the first school in the world. She wrote a commentary on the works of Apollonius and of Diophantus, and composed Astronomical Tables; all of which are lost. These rare accomplishments, however, could not save her from the fury of the fanatics of Alexandria, who cut her in pieces for having taken an offensive part in a dispute between the governor and patriarch.—We have described some of the most approved of these instruments in the article Hydrometer, and shall in this place make a few observations on the principles of their construction, not as they are usually made, accommodated to the examination of particular liquors, but as indicators of pure specific gravity. And we must premise, that this would, for many reasons, be the best way of constructing them. The very ingenious contrivances for accommodating them to particular purposes are unavoidably attended with many sources of error, both in their adjustment by the maker and in their use; and all that is gained by a very expensive instrument is the saving the trouble of inspecting a table. A simple scale of specific gravity would expose to no error in construction, because all the weights but one, or all the points of the scale but one, are to be obtained by calculation, which is incomparably more exact than any manual operation, and the table can always be more exact than any complex observation. But a still greater advantage is, that the instruments would by this means be fitted for examining all liquors whatever, whereas at present they are almost useless for any but the one for which they are constructed.

Hydrometers are of two kinds. The most simple and the most delicate are just a substitute for the hydrostatical balance. They consist of a ball (or rather an egg or pear-shaped vessel, which moves more easily through the fluid) A (fig. 1.) having a foot projecting down from it, terminated by another ball B, and a slender stalk or wire above, carrying a little dish C. The whole is made so light as to float in the lightest fluid we are acquainted with; such as vitriolic or muriatic ether, whose specific gravity is only 0.73. This number should be marked on the dish, indicating that this is the specific gravity of the fluid in which the instrument floats, sinking to the point D of the stem. The ball B is made heavy, and the foot is of some length, that the instrument may have stability, and swim erect, even if considerably loaded above; and, for the same reason, it must be made very round, otherwise it will lean to a side. When put into a heavier liquor, its buoyancy will cause it to float with a part of the ball above the surface. Weights are now put into the scale C, till the instrument sinks to D. The weight put into the scale, added to the weight of the instrument, is the weight of the displaced fluid. This, compared with the weight of the whole when the instrument is swimming in pure water, gives the specific gravity of the fluid. All trouble of calculation may be avoided by marking the weights with such numbers as shall indicate the specific gravity at once. Thus having loaded the instrument so as to sink it to D in pure water, call the whole weight 1000; then weigh the instrument itself, and say, "as the weight when swimming in water is to its present weight, so is 1000 to a 4th proportional." This is the specific gravity of the liquor which would float the unloaded instrument. Suppose this to be 730. The hydrometer would just float in muriatic ether, and this should be marked on the side. Now make a set of small weights, weights, and mark them, not by their weights in grains, but in such units that 270 of them shall be equal to the weight which fits the instrument for pure water.

Suppose that, in order to float this instrument in a certain brandy, there are required 186 in these small weights. This added to 732 gives 918 for the specific gravity, and shows it to be precisely excise proof spirit. Nine weights, viz. 256, 128, 64, 32, 16, 8, 4, 2, 1, will suffice for all liquors from ether to the strongest worts. And that the trouble in changing the weights may be greatly lessened, let a few circles \(a, b, c, d, e\), be marked on the top of the ball. When we see it float unloaded at the circle C for instance, we know it will require at least 128 to sink it to D on the stem.

If the weights to be added above are considerable, it raises the centre of gravity so much, that a small want of equilibrium, by laying the weights on one side, will produce a great inclination of the instrument, which is unsightly. Instead therefore of making them loose weights, it is proper to make them round plates, with a small hole in the middle, to go on a pin in the middle of the scale. This will keep the instrument always upright. But unless the hydrometer is of a considerable size, it can hardly be made so as to extend from the lightest to the heaviest fluid which we may have occasion to examine, even though we except mercury. Some of the mineral acids are considerably more than twice the weight of ether. When there is such a load at top, the hydrometer is very apt to overfet, and inclines with the smallest want of equilibrium. Great size is inconvenient even to the philosopher, because it is not always in his power to operate on a quantity of fluid sufficient to float the instrument. Therefore two, or perhaps three, are necessary for general examination. One may reach from ether to water; another may serve for all liquors of a specific gravity between one and one and a half; and the third, for the mineral acids, may reach from this to two. If each of these be about two solid inches in capacity, we may easily and expeditiously determine the specific gravity within one ten thousandth part of the truth: and this is precision enough for most purposes of science or business.

The chief questions are, 1. To ascertain the specific gravity of an unknown fluid. This needs no farther explanation. 2. To ascertain the proportion of two fluids which are known to be in a mixture. This is done by discovering the specific gravity of the mixture by means of the hydrometer, and then deducing the proportion from a comparison of this with the specific gravities of the ingredients.

In this mode of examination the bulk is always the same; for the hydrometer is immersed in the different fluids to the same depth. Now if an inch, for example, of this bulk is made up of the heaviest fluid, there is an inch wanting of the lightest; and the change made in the weight of the mixture is the difference between the weight of an inch of the heaviest, and of an inch of the lightest ingredients. The number of inches therefore of the heaviest fluid is proportional to the addition made to the weight of the mixture. Therefore let B and b be the bulks of the heaviest and lightest fluids in the bulk \(b\) of the mixture; and let D, d, and \(\delta\) be the densities, or the weights, or the specific gravities (for they are in one ratio) of the heavy fluid, the light fluid, and the mixture (their bulk being that of the hydrometer). We have \(\beta = B + b\). The addition which would have been made to the bulk \(b\), if the lightest fluid were changed entirely for the heaviest, would be \(D - d\); and the change which is really made is \(\delta - d\). Therefore \(\beta : b = D : d ; \delta : d\). For similar reasons we should have \(\beta : B = D : d ; D : \delta\); or, in words, "the difference between the specific gravities of the two fluids, is to the difference between the specific gravities of the mixture and of the lightest fluid, as the bulk of the whole to the bulk of the heaviest contained in the mixture?" and "the difference of the specific gravities of the two fluids, is to the difference of the specific gravities of the mixture and of the heaviest fluids, as the bulk of the whole to that of the lightest contained in the mixture." This is the form in which the ordinary business of life requires the answer to be expressed, because we generally reckon the quantity of liquors by bulk, in gallons, pints, quarts. But it would have been equally easy to have obtained the answer in pounds and ounces; or it may be had from their bulk, since we know their specific gravities.

The hydrometer more commonly used is the ancient one of Hypatia, consisting of a ball A (fig. 2.) made steady by an addition B, below it like the former, but having a long stem CF above. It is so loaded that it sinks to the top F of the stem in the lightest of all the fluids which we propose to measure with it, and to sink only to C in the heaviest. In a fluid of intermediate specific gravity it will sink to some point between C and F.

In this form of the hydrometer the weight is always the same, and the immediate information given by the instrument is that of different bulks with equal weight. Because the instrument sinks till the bulk of the displaced fluid equals it in weight, and the additions to the displaced fluid are all made by the stem, it is evident that equal bulks of the stem indicate equal additions of volume. Thus the stem becomes a scale of bulks to the same weight.

The only form in which the stem can be made with sufficient accuracy is cylindrical or prismatical. Such a stem may be made in the most accurate manner by wire-drawing, that is, passing it through a hole made in a hardened steel plate. If such a stem be divided into equal parts, it becomes a scale of bulks in arithmetical progression. This is the easiest and most natural division of the scale; but it will not indicate densities, specific gravities, or weights of the same bulk in arithmetical progression. The specific gravity is as the weight divided by the bulk. Now a series of divisors (the bulks), in arithmetical progression, applied to the same dividend (the bulk and weight of the hydrometer as it floats in water), will not give a series of quotients (the specific gravities) in arithmetical progression: they will be in what is called harmonic progression, their differences continually diminishing. This will appear even when physically considered. When the hydrometer sinks a tenth of an inch near the top of the stem, it displaces one tenth of an inch of a light fluid, compared with that displaced by it when it is floating with all the stem above the surface. In order therefore that the divisions of the stem may indicate equal changes of specific gravity, they must be in a series of harmonic progressions increasing. The point at which the instrument floats in pure water should be marked 1000, and those above it 999, 998, 997, &c.; and SPINNING MACHINERY.

PLATE CCCCXCIX.

Fig. 1. Fig. 2.

SPIRITUOUS LIQUORS

Fig. 1. Fig. 2.

Engraved by W. & P. Lizars Edinburgh. those below the water mark must be numbered 1001, 1002, 1003, &c. Such a scale will be a very apposite picture of the densities of fluids, for the density or vicinity of the divisions will be precisely similar to the density of the fluids. Each interval is a bulk of fluid of the same weight. If the whole instrument were drawn out into wire of the size of the stem, the length from the water mark would be 1000.

Such are the rules by which the scale must be divided. But there must be some points of it determined by experiment, and it will be proper to take them as remote from each other as possible. For this purpose let the instrument be accurately marked at the point where it stands, in two fluids, differing as much in specific gravity as the instrument will admit. Let it also be marked where it stands in water. Then determine with the utmost precision the specific gravities of these fluids, and put their values at the corresponding points of the scale. Then the intermediate points of the scale must be computed for the different intervening specific gravities, or it must be divided from a pattern scale of harmonic progressions in a way well known to the mathematical instrument-makers. If the specific gravities have been accurately determined, the value 1000 will be found to fall precisely in the water mark. If we attempt the division entirely by experiment, by making a number of fluids of different specific gravities, and marking the stem as it stands in them, we shall find the divisions turn out very anomalous. This is however the way usually practised; and there are few hydrometers, even from the best maker, that hold true to a single division or two. Yet the method by computation is not more troublesome; and one scale of harmonic progressions will serve to divide every stem that offers. We may make use of a scale of equal parts for the stem, with the assistance of two little tables. One of these contains the specific gravities in harmonic progression, corresponding to the arithmetical scale of bulks on the stem of the hydrometer; the other contains the divisions and fractions of a division of the scale of bulks, which correspond to an arithmetical scale of specific gravities. We believe this to be the best method of all. The scale of equal parts on the stem is so easily made, and the little table is so easily inspected, that it has every advantage of accuracy and dispatch, and it gives, by the way, an amusing view of the relation of the bulks and densities.

We have hitherto supposed a scale extending from the lightest to the heaviest fluid. But unless it be of a very inconvenient length, the divisions must be very minute. Moreover, when the bulk of the stem bears a great proportion to that of the body, the instrument does not swim steady; it is therefore proper to limit the range of the instrument in the same manner as those of the first kind. A range from the density of ether to that of water may be very well executed in an instrument of very moderate size, and two others will do for all the heavier liquors; or an equal range in any other densities as may suit the usual occupations of the experimenter.

To avoid the inconveniences of a hydrometer with a very long and slender stem, or the necessity of having a series of them, a third fort has been contrived, in which the principles of both are combined. Suppose a hydrometer with a stem, whose bulk is \( \frac{1}{70} \)th of that of the ball, and that it sinks in ether to the top of the stem; it is evident that in a fluid which is \( \frac{1}{70} \)th heavier, the whole stem will emerge; for the bulk of the displaced fluid is now \( \frac{1}{70} \)th of the whole lest, and the weight is the same as before, and therefore the specific gravity is \( \frac{1}{70} \)th greater.

Thus we have obtained a hydrometer which will indicate, by means of divisions marked on the stem, all specific gravities from 0.73 to 0.803; for 0.83 is \( \frac{1}{70} \)th greater than 0.73. These divisions must be made in harmonic progression, as before directed for an entire scale, placing 0.73 at the top of the stem and 0.803 at the bottom.

When it floats at the lowest division, a weight may be put on the top of the stem, which will again sink it to the top. This weight must evidently be 0.073, or \( \frac{1}{70} \)th of the weight of the fluid displaced by the unloaded instrument. The hydrometer, thus loaded, indicates the same specific gravity, by the top of the stem, that the unloaded instrument indicates by the lowest division. Therefore, when loaded, it will indicate another series of specific gravities, from 0.803 to 0.8833 (\( =0.803 + 0.0833 \)), and will float in a liquor of the specific gravity 0.8833 with the whole stem above the surface.

In like manner, if we take off this weight, and put on \( =0.0833 \), it will sink the hydrometer to the top of the stem; and with this new weight it will indicate another series of specific gravities from 0.8833 to 0.97163 (\( =0.8833 + 0.08833 \)). And, in the same manner, a third weight \( =0.8833 \) will again sink it to the top of the stem, and fit it for another series of specific gravities up to 1.068793. And thus, with three weights, we have procured a hydrometer fitted for all liquors from ether to a wort for a malt liquor of two barrels per quarter. Another weight, in the same progression, will extend the instrument to the strongest wort that is brewed.

This is a very commodious form of the instrument, and is now in very general use for examining spirituous liquors, worts, ales, brines, and many such articles of commerce. But the divisions of the scale are generally adapted to the questions which naturally occur in the business. Thus, in the commerce of strong liquors, it is usual to estimate the article by the quantity of spirit of a certain strength which the liquor contains.—This we have been accustomed to call proof spirit, and it is such that a wine gallon weighs 7 pounds 12 ounces; and it is by this strength that the excise duties are levied. Therefore the divisions on the scale, and the weights which connect the successive repetitions of the scale, are made to express at once the number of gallons or parts of a gallon of proof spirits contained in a gallon of the liquor. Such instruments save all trouble of calculation to the excise-man or dealer; but they limit the use of a very delicate and expensive instrument to a very narrow employment. It would be much better to adhere to the expression either of specific gravity or of bulk; and then a very small table, which could be comprised in the smallest case for the instrument, might render it applicable to every kind of fluid.

The reader cannot but have observed that the successive weights, by which the short scale of the instrument is extended to a great range of specific gravities, do not increase by equal quantities. Each difference is the weight of the liquor displaced by the graduated stem of the instrument when it is sunk to the top of the scale. It is a determined aliquot part of the whole weight of the instrument so loaded, (in our example it is always \( \frac{1}{7} \)th of it). It increases therefore in the same proportion with the preceding, weight of the loaded instrument. In short, both the successive additions, and the whole weights of the loaded instrument, are quantities in geometrical progression; and in like manner, the divisions on the scale, if they correspond to equal differences of specific gravity, must also be unequal.—This is not sufficiently attended to by the makers; and they commit an error here, which is very considerable when the whole range of the instrument is great. For the value of one division of the scale, when the largest weight is on, is as much greater than its value when the instrument is not loaded at all, as the full loaded instrument is heavier than the instrument unloaded. No manner whatever of dividing the scale will correspond to equal differences of specific gravity through the whole range with different weights; but if the divisions are made to indicate equal proportions of gravity when the instrument is used without a weight, they will indicate equal proportions throughout. This is evident from what we have been just now saying; for the proportion of the specific gravities corresponding to any two immediately succeeding weights is always the same.

The best way, therefore, of constructing the instrument, so that the same divisions of the scale may be accurate in all its successive repetitions with the different weights, is to make these divisions in geometrical progression. The corresponding specific gravities will also be in geometric proportion. These being all inserted in a table, we obtain them with no more trouble than by inspecting the scale which usually accompanies the hydrometer. This table is of the most easy construction; for the ratio of the successive bulks and specific gravities being all equal, the differences of the logarithms are equal.

This will be illustrated by applying it to the example already given of a hydrometer extending from 0.73 to 1.068793 with three weights. This gives four repetitions of the scale on the stem. Suppose this scale divided into 10 parts, we have 40 specific gravities.—Let these be indicated by the numbers 0, 1, 2, 3, &c. to 40. The mark o is affixed to the top of the stem, and the divisions downwards are marked 1, 2, 3, &c., the lowest being 10. These divisions are easily determined. The stem, which we may suppose 5 inches long, was supposed to be \( \frac{1}{7} \)th of the capacity of the ball. It may therefore be considered as the extremity of a rod of 11 times its length, or 55 inches, and we must find nine mean proportions between 50 and 55 inches. Subtract each of these from 55 inches, and the remainders are the distances of the points of division from o, the top of the scale. The smallest weight is marked 10, the next 20, and the third 30. If the instrument loaded with the weight 20 sinks in some liquor to the mark 7, it indicates the specific gravity 27, that is, the 27th of 40 mean proportions between 0.73 and 1.068793, or 0.944242. To obtain all these intermediate specific gravities, we have only to subtract 9.8633229, the logarithm of 0.73 from that of 1.068793, viz. 0.0288937, and take 0.0041393, the 40th part of the difference. Multiply this by 1, 2, 3, &c. and add the logarithm of 0.73 to each of the products. The sums are the logarithms of the specific gravities required. These will be found to proceed so equably, that they may be interpolated ten times by a simple table of proportional parts, without the smallest sensible error. Therefore the stem may be divided into a hundred parts very sensible to the eye (each being nearly the 20th of an inch), and 406 degrees of specific gravity obtained within the range, which is as near as we can examine this matter by any hydrometer. Thus the specific gravities corresponding to No 26, 27, 28, 29, are as follow:

<table> <tr> <th></th> <th>1st Diff.</th> <th>2d Diff.</th> </tr> <tr> <td>26</td> <td>0.93529</td> <td>895</td> </tr> <tr> <td>27</td> <td>0.94424</td> <td>904</td> </tr> <tr> <td>28</td> <td>0.95328</td> <td>913</td> </tr> <tr> <td>29</td> <td>0.96241</td> <td>9</td> </tr> </table>

Nay, the trouble of inspecting a table may be avoided, by forming on a scale the logarithms of the numbers between 7300 and 1068793, and placing along side of it a scale of the same length divided into 400 equal parts, numbered from 0 to 400. Then, looking for the mark shown by the hydrometer on this scale of equal parts, we see opposite to it the specific gravity.

We have been thus particular in the illustration of this mode of construction, because it is really a beautiful and commodious instrument, which may be of great use both to the naturalist and to the man of business.—A table may be comprised in 20 octavo pages, which will contain the specific gravities of every fluid which can interest either, and answer every question relative to their admixture with as much precision as the observations can be made. We therefore recommend it to our readers, and we recommend the very example which we have given as one of the most convenient. The instrument need not exceed eight inches in length, and may be contained in a pocket case of two inches broad and as many deep, which will also contain the scale, a thermometer, and even the table for applying it to all fluids which have been examined.

It is unfortunate that no graduated hydrometer can be made so easily for the examination of the corrosive mineral acids (A). These must be made of glass, and we cannot depend on the accurate cylindric form of any glass stem. But if any such can be procured, the construction is the same. The divided scale may either be on thin paper pasted on the inside of the stem, or it may be printed on the stem itself from a plate, with ink made of a metallic calx, which will attach itself to the glass with a very moderate heat. We would recommend common white enamel, or arsenical glass, as the fittest material for the whole instrument; and the ink used, in taking the impression of the scale, may be the same that is used for the low-priced printing on Delft ware pottery.—First form the scale on the stem. Then, having measured the solid contents of the graduated part as exactly as possible, and determined on the general shape of the ball and counterpoise below, calculate its size, so that it may be a little less than ten times that of the stem. The glass-blower can copy this very nearly, and join it to the stem. Then make two brines of other liquors, which shall have specific gravities in the ratio of 10 to 11. Load the instrument so that it may sink to 0 in the lightest. When put into the heaviest, it should rise to 10. If it does not rise so high, the immersed part is too small. Let the glass-blower enlarge the ball of the counterpoise a little. Repeat this trial till it be exact. Nothing now remains but to form the weights: And here we observe, that when the instrument is to have a very great range, as for examining all states of the vitriolic acid, it has a chance of being very tottering when loaded with the greatest weight on the top of so long a scale. To avoid this, Mr Quinn and others have added some of their weights below.—But this will not suit the present construction, because it will alter the proportion between the bulks of the stem and immersed part. Therefore let these weights consist of cylinders of metal small enough to go into the stem, and let them be foldered to the end of long wires, which will let them go to the bottom, and leave a small hook or ring at top. These can lie alongside of the instrument in its case. This is indeed the best construction for every hydrometer, because it makes it incomparably more steady. The instrument is poised by small shot or mercury. But it will be much better to do it with Newton's fusible metal (three parts of tin, five parts of lead, and eight parts of bismuth) in coarse filings. When the exact quantity has been put in, the instrument may be set in a vessel of oil, and this kept on the fire till all is completely melted. It soon freezes again, and remains fast. If this metal is not to be had, let a few bits of sealing-wax be added to the mercury or shot, to make up the counterpoise. When heated, it will float a-top, and when it freezes again it will keep all fast. Thus we shall make a very complete and cheap instrument.

There is yet another method of examining the specific gravities of fluids, first proposed by Dr Wilton, late professor of astronomy in the university of Glasgow. This is by a series of small glass bubbles, differing equally, or according to some rule, from each other in specific gravity, and each marked with its proper number. When these are thrown into a fluid which is to be examined, all those which are heavier than the fluid will fall to the bottom. Then holding the vessel in the hand, or near a fire or candle, the fluid expands, and one of the floating bubbles begins to sink. Its specific gravity, therefore, was either equal to, or a little less than, that of the fluid; and the degree of the thermometer, when it began to sink, will inform us how much it was deficient, if we know the law of expansion of the liquor. Sets of these bubbles fitted for the examination of spirituous liquors, with a little treatise showing the manner of using them, and calculating by the thermometer, are made by Mr Brown, an ingenious artist of Glasgow, and are often used by the dealers in spirits, being found both accurate and expeditious.

Also, though a bubble or two should be broken, the strength of spirits may easily be had by means of the remainder, unless two or three in immediate succession be wanting: for a liquor which answers to No 4, will sink No 2, by heating it a few degrees, and therefore No 3, may be spared. This is a great advantage in ordinary business. A nice hydrometer is not only an expensive instrument, but exceedingly delicate, being so very thin. If broken or even bruited, it is useless, and can hardly be repaired except by the very maker.

As the only question here is, to determine how many gallons of excise proof spirits is contained in a quantity of liquor, the artist has constructed this series of bubbles in the simplest manner possible, by previously making 40 or 50 mixtures of spirits and water, and then adjusting the bubbles to these mixtures. In some sets the number on each bubble is the number of gallons of proof spirits contained in 100 gallons of the liquor. In other sets the number on each bubble expresses the gallons of water which will make a liquor of this strength, if added to 14 gallons of alcohol. Thus, if a liquor answers to No 4, then 4 gallons of water added to 14 gallons of alcohol will make a liquor of this strength. The first is the best method; for we should be mistaken in supposing that 18 gallons, which answer to No 4, contains exactly 14 gallons of alcohol: it contains more than 14, for a reason to be given by and by.

By examining the specific gravity of bodies, the philosopher has made some very curious discoveries. The most remarkable of these is the change which the density of bodies suffers by mixture. It is a most reasonable expectation, that when a cubic foot of one substance is mixed any how with a cubic foot of another, the bulk of the mixture will be two cubic feet; and that 18 gallons of water joined to 18 gallons of oil will fill a vessel of 36 gallons. Accordingly this was never doubted; and even Archimedes, the most scrupulous of mathematicians, proceeded on this supposition in the solution of his famous problem, the discovery of the proportion of silver and gold in a mixture of both. He does not even mention it as a postulate that may be granted him, so much did he conceive it to be an axiom. Yet a little reflection seems sufficient to make it doubtful and to require examination. A box filled with musket-balls will receive a considerable quantity of small shot, and after this a considerable quantity of fine sand, and after this a considerable quantity of water. Something like this might happen in the admixture of bodies of porous texture. But such substances as metals, glass, and fluids, where no discontinuity of parts can be perceived, or was supposed, seem free from every chance of this kind of introduction. Lord Bacon, however, without being a naturalist or mathematician ex profeso, inferred from the mobility of fluids that they consisted of discrete particles, which must have pores interposed, whatever be their figure. And if we ascribe the different densities, or other sensible qualities, to difference in size or figure of those particles, it must frequently happen that the smaller particles will be lodged in the interstices between the larger, and thus contribute to the weight of the sensible mass without increasing its bulk. He therefore supposes that mixtures will be in general less bulky than the sum of their ingredients.

Accordingly, the examination of this question was one of the first employments of the Royal Society of London, and long before its institution had occupied the attention of the gentlemen who afterwards composed it. The register of the Society's early meetings contains many experiments on this subject, with mixtures of gold and silver, of other metals, and of various fluids, examined by the hydrostatic balance of Mr Boyle. Dr Hooke made a prodigious number, chiefly on articles of commerce, which were unfortunately lost in the fire of London.

It was soon found, however, that Lord Bacon's conjecture had been well founded, and that bodies changed their density very sensibly in many cases. In general, it was found that bodies which had a strong chemical affinity increased in density, and that their admixture was accompanied with heat.

By this discovery it is manifest that Archimedes had not solved the problem of detecting the quantity of silver mixed with the gold in King Hiero's crown, and that the physical solution of it requires experiments made on all the kinds of matter that are mixed together. We do not find that this has been done to this day, although we may affirm that there are few questions of more importance. It is a very curious fact in chemistry, and it would be most desirable to be able to reduce it to some general laws: For instance, to ascertain what is the proportion of two ingredients which produces the greatest change of density. This is important in the science of physics, because it gives us considerable information as to the mode of action of those natural powers or forces by which the particles of tangible matter are united. If this introspection, concentration, compenetration, or by whatever name it be called, were a mere reception of the particles of one substance into the interstices of those of another, it is evident that the greatest concentration would be observed when a small quantity of the recipient is mixed with, or disseminated through, a great quantity of the other. It is thus that a small quantity of fine sand will be received into the interstices of a quantity of small shot, and will increase the weight of the bagful without increasing its bulk. The case is nowife different when a piece of freestone has grown heavier by imbibing or absorbing a quantity of water. If more than a certain quantity of sand has been added to the small shot, it is no longer concealed. In like manner, various quantities of water may combine with a mass of clay, and increase its size and weight alike. All this is very conceivable, occasioning no difficulty.

But this is not the case in any of the mixtures we are now considering. In all these, the first additions of either of the two substances produce but an inconsiderable change of general density; and it is in general most remarkable, whether it be condensation or rarefaction, when the two ingredients are nearly of equal bulks. We can illustrate even this difference, by reflecting on the imbibition of water by vegetable solids, such as timber. Some kinds of wood have their weight much more increased than their bulks; other kinds of wood are more enlarged in bulk than in weight. The like happens in grains. This is curious, and shows in the most unquestionable manner that the particles of bodies are not in contact, but are kept together by forces which act at a distance. For this distance between the centres of the particles is most evidently susceptible of variation; and this variation is occasioned by the introduction of another substance, which, by acting on the particles by attraction or repulsion, diminishes or increases their mutual actions, and makes new distances necessary for bringing all things again into equilibrium. We refer the curious reader to the ingenious theory of the abbé Boscofich for an excellent illustration of this subject (Theor. Phil. Nat. § de Solutione Chemica.)

This question is no less important to the man of business. Till we know the condensation of those metals by mixture, we cannot tell the quantity of alloy in gold and silver by means of their specific gravity; nor can we tell the quantity of pure alcohol in any spirituous liquor, or that of the valuable salt in any solution of it. For want of this knowledge, the dealers in gold and silver are obliged to have recourse to the tedious and difficult test of the assay, which cannot be made in all places or by all men. It is therefore much to be wished, that some persons would institute a series of experiments in the most interesting cases: for it must be observed, that this change of density is not always a small matter; it is sometimes very considerable and paradoxical. A remarkable instance may be given of it in the mixture of brafs and tin for bells, great guns, optical speculums, &c. The specific gravity of cast brafs is nearly 8.000, and that of tin is nearly 7.363. If two parts of brafs be mixed with one of tin, the specific gravity is 8.017; whereas, if each had retained its former bulk, the sp. grav. would have been only \( \frac{2 \times 8.006 + 7.363}{3} = 7.793 \).

A mixture of equal parts should have the specific gravity 7.684; but it is 8.441. A mixture of two parts tin with one part brafs, instead of being 7.577, is 8.027.

In all these cases there is a great increase of specific gravity, and consequently a great condensation of parts or contraction of bulk. The first mixture of eight cubic inches of brafs, for instance, with four cubic inches of tin, does not produce 12 cubic inches of bell-metal, but only 10\( \frac{1}{2} \) nearly, having shrunk \( \frac{1}{3} \). It would appear that the distances of the brafs particles are most affected, or perhaps it is the brafs that receives the tin into its pores; for we find that the condensations in these mixtures are nearly proportional to the quantities of the brafs in the mixtures. It is remarkable that this mixture with the lightest of all metals has made a composition more heavy and dense than brafs can be made by any hammering.

The most remarkable instance occurs in mixing iron with platina. If ten cubic inches of iron are mixed with \( \frac{1}{4} \) of platina, the bulk of the compound is only 9\( \frac{1}{2} \) inches. The iron therefore has not simply received the platina into its pores: its own particles are brought nearer together. There are similar results in the solution of turbith mineral, and of some other salts, in water. The water, instead of rising in the neck of the vessel, when a small quantity of the salt has been added to it, sinks considerably, and the two ingredients occupy less room than the water did alone.

The same thing happens in the mixture of water with other fluids and different fluids with each other: But we are not able to trace any general rule that is observed with absolute precision. In most cases of fluids the greatest condensation happens when the bulks of the ingredients are nearly equal. Thus, in the mixture of alcohol and water, we have the greatest condensation when 16\( \frac{1}{2} \) ounces of alcohol are mixed with 20 ounces of water, and the condensation is about \( \frac{1}{3} \) of the whole bulk of the ingredients. It is extremely various in different substances, and no classification of them can be made in this respect.

A dissertation has been published on this subject by Dr Hahn of Vienna, intitled De Efficacia Mixtionis in mutandis Corporum Voluminibus, in which all the remarkable instances of the variation of density have been collected. All that we can do (as we have no directing principle) is to record such instances as are of chief importance, being articles of commerce.

The first that occurs to us is the mixtures of alcohol and water in the composition of spirituous liquors. This has been considered by many with great care. The most scrupulous examination of this, or perhaps of any mixture, has been lately made by Dr Blagden (now Sir Charles Blagden) of the Royal Society, on the requisition of the Board of Excise. He has published an account of the examination in the Philosophical Transactions of London in 1791 and 1792. We shall give an account of it under the article SPIRITUOUS LIQUORS; and at present only select one column, in order to show the condensation. The alcohol was almost the strongest that can be produced, and its specific gravity, when of the temperature 60°, was 0.825. The whole mixtures were of the same temperature.

Column 1. contains the pounds, ounces, or other measures by weight, of alcohol in the mixture. Column 2. contains the pounds or ounces of water. Column 3. is the sum of the bulks of the ingredients, the bulk of a pound or ounce of water being accounted 1. Column 4. is the observed specific gravity of the mixture, taken from Dr Blagden's dissertation. Column 5. is the specific gravity which would have been observed if the ingredients had each retained its own specific gravity. This we calculated by dividing the sum of the two numbers of the first and second columns by the corresponding number of the third. Column 6. is the difference of column 4. and column 5. and exhibits the condensation.

<table> <tr> <th>A</th> <th>W.</th> <th>Volume.</th> <th>Sp. Grav. observed.</th> <th>Sp. Grav. calculated.</th> <th>Condensation.</th> </tr> <tr><td>20</td><td>0</td><td>24.2424</td><td>0.8210</td><td>0.8250</td><td>00</td></tr> <tr><td>1</td><td>25.2424</td><td>0.8365</td><td>0.8320</td><td>40</td></tr> <tr><td>2</td><td>26.2424</td><td>0.8457</td><td>0.8385</td><td>74</td></tr> <tr><td>3</td><td>27.2424</td><td>0.8433</td><td>0.8443</td><td>100</td></tr> <tr><td>4</td><td>28.2424</td><td>0.8621</td><td>0.8598</td><td>123</td></tr> <tr><td>5</td><td>29.2424</td><td>0.8692</td><td>0.8549</td><td>143</td></tr> <tr><td>6</td><td>30.2424</td><td>0.8757</td><td>0.8597</td><td>160</td></tr> <tr><td>7</td><td>31.2424</td><td>0.8817</td><td>0.8642</td><td>175</td></tr> <tr><td>8</td><td>32.2424</td><td>0.8872</td><td>0.8684</td><td>188</td></tr> <tr><td>9</td><td>33.2424</td><td>0.8923</td><td>0.8724</td><td>199</td></tr> <tr><td>10</td><td>34.2424</td><td>0.8971</td><td>0.8761</td><td>216</td></tr> <tr><td>11</td><td>35.2424</td><td>0.9014</td><td>0.8796</td><td>218</td></tr> <tr><td>12</td><td>36.2424</td><td>0.9055</td><td>0.8820</td><td>226</td></tr> <tr><td>13</td><td>37.2424</td><td>0.9093</td><td>0.8850</td><td>233</td></tr> <tr><td>14</td><td>38.2424</td><td>0.9129</td><td>0.8891</td><td>238</td></tr> <tr><td>15</td><td>39.2424</td><td>0.9162</td><td>0.8919</td><td>243</td></tr> <tr><td>16</td><td>40.2424</td><td>0.9193</td><td>0.8946</td><td>247</td></tr> <tr><td>17</td><td>41.2424</td><td>0.9223</td><td>0.8971</td><td>252</td></tr> <tr><td>18</td><td>42.2424</td><td>0.9250</td><td>0.8996</td><td>254</td></tr> <tr><td>19</td><td>43.2424</td><td>0.9276</td><td>0.9019</td><td>257</td></tr> <tr><td>20</td><td>44.2424</td><td>0.9300</td><td>0.9041</td><td>259</td></tr> <tr><td>19</td><td>43.0303</td><td>0.9323</td><td>0.9063</td><td>262</td></tr> <tr><td>18</td><td>48.1182</td><td>0.9349</td><td>0.9087</td><td>262</td></tr> </table>

<table> <tr> <th>A.</th> <th>W.</th> <th>Volume.</th> <th>Sp. Grav. observed.</th> <th>Sp. Grav. calculated.</th> <th>Condensation.</th> </tr> <tr><td>17</td><td>20</td><td>49.6061</td><td>0.9375</td><td>0.9112</td><td>263</td></tr> <tr><td>16</td><td>20</td><td>39.3939</td><td>0.9402</td><td>0.9139</td><td>263</td></tr> <tr><td>15</td><td>20</td><td>38.1818</td><td>0.9430</td><td>0.9167</td><td>263</td></tr> <tr><td>14</td><td>20</td><td>36.9697</td><td>0.9458</td><td>0.9197</td><td>261</td></tr> <tr><td>13</td><td>20</td><td>35.7576</td><td>0.9488</td><td>0.9229</td><td>259</td></tr> <tr><td>12</td><td>20</td><td>34.5455</td><td>0.9518</td><td>0.9263</td><td>255</td></tr> <tr><td>11</td><td>20</td><td>33.3333</td><td>0.9549</td><td>0.9300</td><td>249</td></tr> <tr><td>10</td><td>20</td><td>32.1212</td><td>0.9580</td><td>0.9340</td><td>240</td></tr> <tr><td>9</td><td>20</td><td>30.9091</td><td>0.9612</td><td>0.9382</td><td>230</td></tr> <tr><td>8</td><td>20</td><td>29.6970</td><td>0.9644</td><td>0.9429</td><td>215</td></tr> <tr><td>7</td><td>20</td><td>28.4849</td><td>0.9675</td><td>0.9479</td><td>196</td></tr> <tr><td>6</td><td>20</td><td>27.2727</td><td>0.9707</td><td>0.9533</td><td>174</td></tr> <tr><td>5</td><td>20</td><td>26.0606</td><td>0.9741</td><td>0.9593</td><td>148</td></tr> <tr><td>4</td><td>20</td><td>24.8485</td><td>0.9777</td><td>0.9659</td><td>118</td></tr> <tr><td>3</td><td>20</td><td>23.6364</td><td>0.9818</td><td>0.9731</td><td>87</td></tr> <tr><td>2</td><td>20</td><td>22.4242</td><td>0.9865</td><td>0.9811</td><td>54</td></tr> <tr><td>1</td><td>20</td><td>21.2121</td><td>0.9924</td><td>0.9900</td><td>24</td></tr> <tr><td>0</td><td>20</td><td>20.0000</td><td>1.0000</td><td>1.0000</td><td></td></tr> </table>

It is to be remarked, that the condensation is greatest when 16 1/2 ounces of alcohol have been added to 20 of water, and the condensation is \( \frac{1}{3} \times \frac{1}{3} \), or nearly \( \frac{1}{9} \)th of the computed density. Since the specific gravity of alcohol is 0.825, it is evident that 16 1/2 ounces of alcohol and 20 ounces of water have equal bulks. So that the condensation is greatest when the buliances are mixed in equal volumes; and 18 gallons of alcohol mixed with 18 gallons of water will produce not 36 gallons of spirits, but 35 only.

We may also observe, that this is the mixture to which our revenue laws refer, declaring it to be one to six or one in seven under proof, and to weigh 7 pounds 13 ounces per gallon. This proportion was probably selected as the most easily composed, viz. by mixing equal measures of water and of the strongest spirit which the known processes of distillation could produce. Its specific gravity is c.930 very nearly.

We must consider this elaborate examination of the mixture of water and alcohol as a standard series of experiments, to which appeal may always be made, whether for the purposes of science or of trade. The regularity of the progression is so great, that in the column which we have examined, viz. that for temperature 60°, the greatest anomaly does not amount to one part in six thousand. The form of the series is also very judiciously chosen for the purposes of science. It would perhaps have been more directly stereometrical had the proportions of the ingredients been stated in bulks, which are more immediately connected with density. But the author has assigned a very cogent reason for his choice, viz. that the proportion of bulks varies by a change of temperature, because the water and spirits follow different laws in their expansion by heat.

This is a proper opportunity for taking notice of a mistake which is very generally made in the conclusions drawn from experiments of this kind. Equal additions of the spirit or water produce a series of specific gravities, which decrease or increase by differences continually diminishing. Hence it is inferred that there is a contraction of bulk. Even Dr Lewis, one of our most accomplished complished naturalists, advances this position, in a dissertation on the potash of America; and it considerably affects his method for estimating the strength of the potash leys. But that it is a mistake, appears plainly from this, that although we add for ever equal quantities of the spirits, we shall never produce a mixture which has as small a specific gravity as alcohol. Therefore the series of successive gravities must approximate to this without end, like the ordinates of a hyperbolic curve referred to its asymptote.

That this may appear in the most general terms, let w represent the weight of the constant quantity of water in the mixture, and let a be the weight of the small addition of spirits. Also let w represent the bulk of this quantity of water, and b the bulk of the small addition of alcohol. The weight of the mixture is \( w + a \), and its bulk is \( w + b \), and its specific gravity is \( \frac{w + a}{w + b} \).

If we now add a second equal quantity of spirits, the weight will be \( w + 2a \), and if the spirit retains its density unchanged, the bulk will be \( w + 2b \), and the specific gravity is \( \frac{w + 2a}{w + 2b} \); and after any number m of such equal additions of spirits, the specific gravity will be \( \frac{w + ma}{w + mb} \). Divide the numerator of this fraction by its denominator, and the quotient or specific gravity will be \( 1 + \frac{m(a - b)}{w + mb} \). This consists of the constant part 1, and the variable part \( \frac{m(a - b)}{w + mb} \). We need attend only to this part. If its denominator were constant, it is plain that the successive specific gravities would have equal differences, each being \( = \frac{a - b}{w + mb} \), because m increases by the continual addition of an unit, and \( a - b \) is a constant quantity. But the denominator \( w + mb \) continually increases, and therefore the value of the fraction \( \frac{a - b}{w + mb} \) continually diminishes.

Therefore the gradual diminution of the increments or decrements of specific gravity, by equal additions of one ingredient to a constant measure of the other, is not of itself an indication of a change of density of either of the ingredients; nor proves that in very diluted mixtures a greater proportion of one ingredient is absorbed or lodged in the interstices of the other, as is generally imagined. This must be ascertained by comparing each specific gravity with the gravity expressed by \( 1 + \frac{w + m(a - b)}{w + mb} \).

This series of specific gravities resembles such a numerical series as the following, 1 ; . . . . . . . ; 1.56 ; 1.163 ; 1.169 ; &c. the terms of which also consist of the constant integer 1, and the decimal fractions 0.156 ; 0.163 ; 0.169 ; &c. The fraction \( \frac{m(a - b)}{w + mb} \) expresses this decimal part. Call this d, or make \( d = \frac{m(a - b)}{w + mb} \).

This will give us \( b = \frac{ma - wd}{m(1 + d)} \). Now a is the weight of the added ingredient, and d is the variable part of the specific gravity observed; and thus we learn whether b, the bulk of the added ingredient, suffers any change. We shall have occasion by and by to resume the consideration of this question, which is of the first moment in the theory of specific gravities, and has great influence in many transactions of commerce.

This series of specific gravities is not so well fitted for commercial transactions. In these the usual question is, how many gallons of alcohol is there in a cask, or some number of gallons of spirit? and it is more directly answered by means of a table, formed by mixing the ingredients in aliquant parts of one constant bulk. The following table, constructed from the experiments of Mr Briffon of the academy of Paris, and published in the Memoirs for 1769, is therefore inserted.

<table> <tr> <th>W.</th> <th>A.</th> <th>Density observed.</th> <th>Density Computed.</th> <th>Condensation.</th> <th>Bulk of 10,000 grains.</th> </tr> <tr><td>0</td><td>16</td><td>0.8371</td><td>0.8371</td><td></td><td>1.0000</td></tr> <tr><td>1</td><td>15</td><td>0.8427</td><td>0.8473</td><td>63</td><td>0.9937</td></tr> <tr><td>2</td><td>14</td><td>0.8674</td><td>0.8775</td><td>115</td><td>0.9885</td></tr> <tr><td>3</td><td>13</td><td>0.8815</td><td>0.8677</td><td>157</td><td>0.9844</td></tr> <tr><td>4</td><td>12</td><td>0.8947</td><td>0.8778</td><td>189</td><td>0.9811</td></tr> <tr><td>5</td><td>11</td><td>0.9075</td><td>0.8880</td><td>214</td><td>0.9786</td></tr> <tr><td>6</td><td>10</td><td>0.9199</td><td>0.8982</td><td>235</td><td>0.9765</td></tr> <tr><td>7</td><td>9</td><td>0.9317</td><td>0.9084</td><td>251</td><td>0.9749</td></tr> <tr><td>8</td><td>8</td><td>0.9427</td><td>0.9186</td><td>256</td><td>0.9744</td></tr> <tr><td>9</td><td>7</td><td>0.9519</td><td>0.9287</td><td>243</td><td>0.9757</td></tr> <tr><td>10</td><td>6</td><td>0.9598</td><td>0.9380</td><td>217</td><td>0.9783</td></tr> <tr><td>11</td><td>5</td><td>0.9674</td><td>0.9491</td><td>189</td><td>0.9811</td></tr> <tr><td>12</td><td>4</td><td>0.9733</td><td>0.9593</td><td>144</td><td>0.9836</td></tr> <tr><td>13</td><td>3</td><td>0.9791</td><td>0.9695</td><td>99</td><td>0.9901</td></tr> <tr><td>14</td><td>2</td><td>0.9852</td><td>0.9796</td><td>57</td><td>0.9943</td></tr> <tr><td>15</td><td>1</td><td>0.9919</td><td>0.9898</td><td>21</td><td>0.9979</td></tr> <tr><td>16</td><td>0</td><td>1.0000</td><td>1.0000</td><td></td><td>1.0000</td></tr> </table>

In this table the whole quantity of spirituous liquor is always the same. The first column is the number of measures (gallons, pints, inches, &c.) of water in the mixture: and column 2d gives the measures of alcohol. Column 3d is the specific gravity which was observed by Mr Briffon. Column 4th is the specific gravity which would have been observed if the spirits, or water, or both, had retained their specific density unchanged. And the 5th column marks the augmentation of specific gravity or density in parts of 10,000. A 6th column is added, showing the bulk of the 16 cubic measures of the two ingredients. Each measure may be conceived as the 16th part of 10,000, or 625; and we may suppose them cubic inches, pints, gallons, or any solid measure.

This table scarcely differs from Sir Charles Blagden's; and the very small difference that may be observed, arises from Mr Briffon's having used an alcohol not so completely rectified. Its specific gravity is 9.8371, whereas the other was only 0.8250.

Here it appears more distinctly that the condensation is greatest when the two ingredients are of equal bulk.

Perhaps this series of specific gravities is as declarative as the other, whether or not there is a change of density induced in either of the ingredients. The whole bulk being always the same, it is plain that the successive equal additions to one of the ingredients is a successive equal abstraction of the other. The change produced, therefore, in the weight of the whole, is the difference between the weight of the ingredient which is taken out and the weight of the equal measure of the other which supplies its place. Therefore, if neither ingredient changes its density by mixture, the weights of the mixtures will be in arithmetical progression. If they are not, there is a variation of density in one or both the ingredients.

We see this very clearly in the mixtures of water and alcohol. The first specific gravity differs from the second by 1.56, and the last differs from the preceding by no more than 81. Had neither of the densities changed, the common difference would have been 102. We observe also, that the augmentation of specific gravity, by the successive addition of a measure of water, grows less and less till 12 measures of water is mixed with 4 of alcohol, when the augmentation is only 58, and then it increases again to 81.

It also appears, that the addition of one measure of water to a quantity of alcohol produces a greater change of density than the mixture of one measure of alcohol to a quantity of water. Hence some conclude, that the water disappears by being lodged in the interstices of the spirit. But it is more agreeable to the just notions which we can form of the internal constitution of tangible bodies, to suppose that the particles of water diminish the distances between the particles of alcohol by their strong attractions, and that this diminution (exceedingly minute in itself) becomes sensible on account of the great number of particles whose distances are thus diminished. This is merely a probability founded on this, that it would require a much greater diminution of distances if it was the particles of water which had their distances thus diminished. But the greater probability is, that the condensation takes place in both.

We have been so particular in our consideration of this mixture, because the law of variation of density has, in this instance, been ascertained with such precision by the elaborate examination of Sir Charles Blagden, so that it may serve as an example of what happens in almost every mixture of bodies. It merits a still farther discussion, because it is intimately connected with the action of the corpuscular forces; and an exact knowledge of the variations of distance between the particles will go far to ascertain the law of action of these forces. But the limits of a work like this will not permit us to dwell longer on this subject. We proceed therefore to give another useful table.

The vitriolic or sulphuric acid is of extensive use in manufactures under the name of oil of vitriol. Its value depends entirely on the saline ingredient, and the water is merely a vehicle for the acid. This, being much denser than water, affects its specific gravity, and thus gives us a method of ascertaining its strength.

The strongest oil of vitriol that can be easily manufactured contains 61 2/3 grains of dry acid, united with 387 1/3 grains of water, which cannot be separated from it by distillation, making 1000 grains of OIL OF VITRIOL. Its specific gravity in this state is 1.877.

The following table shows its specific gravity at the temperature of 55° when diluted by the successive addition of parts of water by weight.

<table> <tr> <th>Ol. Vit.</th> <th>Water.</th> <th colspan="2">Specific Gravity.</th> <th>Cond.</th> </tr> <tr> <td>10</td> <td>x</td> <td>0</td> <td>Observed.</td> <td>Calculated.</td> <td>.00</td> </tr> <tr> <td></td> <td></td> <td>4</td> <td>1.644</td> <td>1.501</td> <td>.143</td> </tr> <tr> <td></td> <td></td> <td>8</td> <td>1.474</td> <td>1.350</td> <td>.124</td> </tr> <tr> <td></td> <td></td> <td>12</td> <td>1.381</td> <td>1.269</td> <td>.112</td> </tr> <tr> <td></td> <td></td> <td>16</td> <td>1.320</td> <td>1.219</td> <td>.101</td> </tr> <tr> <td></td> <td></td> <td>20</td> <td>1.274</td> <td>1.184</td> <td>.090</td> </tr> <tr> <td></td> <td></td> <td>24</td> <td>1.243</td> <td>1.159</td> <td>.084</td> </tr> <tr> <td></td> <td></td> <td>28</td> <td>1.211</td> <td>1.140</td> <td>.071</td> </tr> <tr> <td></td> <td></td> <td>32</td> <td>1.195</td> <td>1.125</td> <td>.070</td> </tr> <tr> <td></td> <td></td> <td>36</td> <td>1.183</td> <td>1.113</td> <td>.070</td> </tr> <tr> <td></td> <td></td> <td>40</td> <td>1.172</td> <td>1.103</td> <td>.070</td> </tr> <tr> <td></td> <td></td> <td>50</td> <td>1.148</td> <td>1.084</td> <td>.064</td> </tr> <tr> <td></td> <td></td> <td>60</td> <td>1.128</td> <td>1.069</td> <td>.059</td> </tr> </table>

Here is observed a much greater condensation than in the mixture of alcohol and water. But we cannot assign the proportion of ingredients which produces the greatest condensation; because we cannot, in any case, lay what is the proportion of the saline and watery ingredients. The strongest oil of vitriol is already a watery solution; and it is by a considerable and uncertain detour that Mr Kirwan has assigned the proportion of 61 2 and 388 nearly. If this be the true ratio, it is unlike every other solution that we are acquainted with; for in all solutions of salts, the salt occupies less room in its liquid form than it did when solid; and here it would be greatly the reverse.

This solution is remarkable also for the copious emergence of heat in its dilutions with more water. This has been ascribed to the great superiority of water in its capacity of heat; but there are facts which render this very doubtful. A vessel of water, and another of oil of vitriol, being brought from a cold room into a warm one, they both imbibed heat, and rise in their temperature; and the water employs nearly the same time to attain the temperature of the room.

Aquafortis or nitrous acid is another fluid very much employed in commerce; so that it is of importance to ascertain the relation between its saline strength and its specific gravity. We owe also to Mr Kirwan a table for this purpose.

The most concentrated state into which it can easily be brought is such, that 1000 grains of it consists of 563 grains of water and 437 of dry acid. In this state its specific gravity is 1.557. Let this be called nitrous acid.

<table> <tr> <th>Nitr. Ac.</th> <th>Water.</th> <th>Observed.</th> <th>Calculated.</th> <th>Cond.</th> </tr> <tr> <td>10</td> <td>x</td> <td>0</td> <td>1.557</td> <td>1.557</td> <td></td> </tr> <tr> <td></td> <td></td> <td>1</td> <td>1.474</td> <td>1.474</td> <td></td> </tr> <tr> <td></td> <td></td> <td>6</td> <td>1.350</td> <td>1.273</td> <td>.077</td> </tr> <tr> <td></td> <td></td> <td>11</td> <td>1.269</td> <td>1.191</td> <td>.078</td> </tr> <tr> <td></td> <td></td> <td>16</td> <td>1.214</td> <td>1.147</td> <td>.067</td> </tr> <tr> <td></td> <td></td> <td>21</td> <td>1.175</td> <td>1.120</td> <td>.055</td> </tr> <tr> <td></td> <td></td> <td>26</td> <td>1.151</td> <td>1.101</td> <td>.050</td> </tr> <tr> <td></td> <td></td> <td>31</td> <td>1.127</td> <td>1.087</td> <td>.040</td> </tr> <tr> <td></td> <td></td> <td>36</td> <td>1.106</td> <td>1.077</td> <td>.029</td> </tr> <tr> <td></td> <td></td> <td>41</td> <td>1.086</td> <td>1.068</td> <td>.018</td> </tr> </table>

There is not the same uniformity in the densities of this acid in its different states of dilution. This seems owing to the variable proportion of the deleterious and vital air which compose this acid. It is more dense in proportion as it contains more of the latter ingredient.

The proportions of the aeriform ingredients of the muriatic acid are so very variable, and so little under our command, that we cannot frame tables of its specific gravity which would enable us to judge of its strength.

It is a general property of these acids, that they are more expansible by heat as they are more concentrated.

There is another class of fluids which it would be of great consequence to reduce to some rules with respect to specific gravity, namely, the solutions of salts, gums, and resins. It is interesting to the philosopher to know in what manner salts are contained in these watery solutions, and to discover the relation between their strength and density; and to the man of business it would be a most desirable thing to have a criterion of the quantity of salt in any brine, or of extractable matter in a decoction. It would be equally desirable to those who are to purchase them as to those who manufacture or employ them. Perhaps we might ascertain in this way the value of sugar, depending on the quantity of sweetening matter which it contains; a thing which at present rests on the vague determination of the eye or palate. It would therefore be doing a great service to the public, if some intelligent person would undertake a train of experiments with this view.

Accuracy alone is required; and it may be left to the philosophers to compare the facts, and draw the consequences respecting the internal arrangement of the particles.

One circumstance in the solution of salts is very general; and we are inclined, for serious reasons, to think it universal: this is a diminution of bulk. This indeed in some salts is considerable. Sedative salt, for instance, hardly shows any diminution, and might be considered as an exception, were it not the single instance. This circumstance, and some considerations connected with our notions of this kind of solution, dispose us to think that this salt differs in contraction from others only in degree, and that there is some, though it was not sensible, in the experiments hitherto made.

These experiments, indeed, have not been numerous. Those of Mr Achard of Berlin, and of Dr Richard Watson of Cambridge, are perhaps the only ones of which we have a descriptive narration, by which we can judge of the validity of the inferences drawn from them. The subject is not susceptible of much accuracy; for salts in their solid form are seldom free from cavities and shivery interstices, which do not admit the water on their first immersion, and thereby appear of greater bulk when we attempt to measure their specific gravity by weighing them in fluids which do not dissolve them, such as spirits of turpentine. They also attach to themselves, with considerable tenacity, a quantity of atmospheric air, which merely adheres, but makes no part of their composition. This escapes in the act of solution, being set at liberty by the stronger affinity of the water. Sal gem, however, and a few others, may be very accurately measured; and in these instances the degree of contraction is very constant.

The following experiments of Dr Watson appear to us the most instructive as to this circumstance. A glass vessel was used, having a slender cylindrical neck, and holding 67 ounces of pure water when filled to a certain mark. The neck above this mark had a scale of equal parts pasted on it. It was filled to the mark with water. Twenty-four pennyweights of salt were thrown into it as speedily as possible, and the bulk of the salt was measured by the elevation of the water. Every thing was attended to which could retard the immediate solution, that the error arising from the solution of the first particles, before the rest could be put in, might be as small as possible; and in order that both the absolute bulk and its variations might be obtained by some known scale, 24 pennyweights of water were put in. This raised the surface 58 parts of the scale. Now we know exactly the bulk of 24 pennyweights of pure water. It is 2.275 cubic inches; and thus we obtain every thing in absolute measures: And by comparing the bulk of each salt, both at its first immersion and after its complete solution, we obtain its specific gravity, and the change made on it in passing from a solid to a fluid form. The following table is an abstract of these experiments. The first column of numbers is the elevation of the surface immediately after immersion; the second gives the elevation when the salt is completely dissolved; and the third and fourth columns are the specific gravities of the salts in these two states.

<table> <tr> <th>Twenty-four Pennyweights.</th> <th>I.</th> <th>II.</th> <th>III.</th> <th>IV.</th> </tr> <tr> <td>Water</td> <td>58</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Glauber's salt</td> <td>42</td> <td>36</td> <td>1.380</td> <td>1.611</td> </tr> <tr> <td>Mild volatile alkali</td> <td>40</td> <td>33</td> <td>1.450</td> <td>1.787</td> </tr> <tr> <td>Sale ammoniac</td> <td>40</td> <td>39</td> <td>1.450</td> <td>1.487</td> </tr> <tr> <td>Refined white sugar</td> <td>39</td> <td>36</td> <td>1.487</td> <td>1.611</td> </tr> <tr> <td>Coarse brown sugar</td> <td>39</td> <td>36</td> <td>1.487</td> <td>1.611</td> </tr> <tr> <td>White sugarcandy</td> <td>37</td> <td>36</td> <td>1.567</td> <td>1.611</td> </tr> <tr> <td>Lymington Glauber's salt</td> <td>35</td> <td>29</td> <td>1.657</td> <td>2.000</td> </tr> <tr> <td>Terra foliata tartari</td> <td>37</td> <td>30</td> <td>1.567</td> <td>1.933</td> </tr> <tr> <td>Rochelle salt</td> <td>33</td> <td>28</td> <td>1.757</td> <td>2.071</td> </tr> <tr> <td>Alum not quite dissolved</td> <td>33</td> <td>28</td> <td>1.757</td> <td>2.061</td> </tr> <tr> <td>Borax not one half dissolved in two days</td> <td>33</td> <td>31</td> <td>1.757</td> <td></td> </tr> <tr> <td>Green vitriol</td> <td>32</td> <td>26</td> <td>1.812</td> <td>2.230</td> </tr> <tr> <td>White vitriol</td> <td>30</td> <td>24</td> <td>1.933</td> <td>2.416</td> </tr> <tr> <td>Nitre</td> <td>30</td> <td>21</td> <td>1.933</td> <td>2.766</td> </tr> <tr> <td>Sal gem from Northwich</td> <td>27</td> <td>17</td> <td>2.143</td> <td>3.411</td> </tr> <tr> <td>Blue vitriol</td> <td>26</td> <td>20</td> <td>2.230</td> <td>2.900</td> </tr> <tr> <td>Pearl ashes</td> <td>25</td> <td>10</td> <td>2.320</td> <td>5.800</td> </tr> <tr> <td>Tart. vitriolatus</td> <td>22</td> <td>11</td> <td>2.636</td> <td>5.272</td> </tr> <tr> <td>Green vitriol calcined to white</td> <td>22</td> <td>11</td> <td>2.636</td> <td>5.272</td> </tr> <tr> <td>Dry salt of tartar</td> <td>21</td> <td>13</td> <td>2.761</td> <td>4.461</td> </tr> <tr> <td>Basket sea-salt</td> <td>19</td> <td>15</td> <td>3.052</td> <td>3.866</td> </tr> <tr> <td>Corrosive sublimate</td> <td>14</td> <td>10</td> <td>4.142</td> <td>3.800</td> </tr> <tr> <td>Turbith mineral</td> <td>9</td> <td>0</td> <td>6.444</td> <td></td> </tr> </table>

The inspection of this list naturally suggests two states of the case as particularly interesting to the philosopher studying the theory of solution. The first state is when the lixivium approaches to saturation. In the very point of saturation any addition of salt retains its bulk unchanged. In diluted brines, we shall see that the den- fity of the fluid salt is greater, and gradually diminishes as we add more salt. It is an important question, Whether this diminution goes on continually, till the fluid density of the salt is the same with its solid density? or, Whether there is an abrupt passage from some degree of the one to the fixed degree of the other, as we observe in the freezing of iron, the setting of stucco, and some other instances?

The other interesting state is that of extreme dilution, when the differences between the successive densities bear a great proportion to the densities themselves, and thus enable the mathematician to ascertain with some precision the variations of corporeal force, in consequence of a variation of distance between the particles. The sketch of an investigation of this important question given by Bolzovich in his Theory of Natural Philosophy, is very promising, and should incite the philosophical chemist to the study. The first thing to be done is to compare the law of specific gravity; that is, the relation between the specific gravity and quantity of salt held in solution.

Wishing to make this work as useful as possible, we have searched for experiments, and trains of experiments, on the density of the many brines which make important articles of commerce; but we were mortified by the scantiness of the information, and disappointed in our hopes of being able to combine the detached observations, suited to the immediate views of their authors, in such a manner as to deduce from them scales (as they may be called) of their strength. We rarely found these detached observations attended with circumstances which would connect them with others; and there was frequently such a discrepancy, nay opposition, in series of experiments made for ascertaining the relation between the density and the strength, that we could not obtain general principles which enable us to construct tables of strength \( \textit{à priori} \).

Mr Lambert, one of the first mathematicians and philosophers of Europe, in a dissertation in the Berlin Memoirs (1762), gives a narration of experiments on the brines of common salt, from which he deduces a very great condensation, which he attributes to an absorption in the weak brines of the salt, or a lodgement of its particles in the interstices of the particles of water. Mr Achard of the same academy, in 1785, gives a very great list of experiments on the bulks of various brines, made in a different way, which show no such introspection; and Dr Watson thinks this confirmed by experiments which he narrates in his Chemical Essays. We see great reason, for hesitating our belief to either side, and do not think the experiments decisive. We incline to Mr Lambert's opinion; for this reason, that in the successive dilutions of oil of vitriol and aquafortis there is a most evident and remarkable condensation. Now what are these but brines, of which we have not been able to get the saline ingredient in a separate form?

The experiments of Mr Achard and Dr Watson were made in such a way that a single grain in the measurement bore too great a proportion to the whole change of specific gravity. At the same time, some of Dr Watson's are so simple in their nature that it is very difficult to withhold the assent.

In this state of uncertainty, in a subject which seems to us to be of a public importance, we thought it our duty to undertake a train of experiments to which recourse may always be had. Works like this are seldom considered as sources of original information; and it is thought sufficient when the knowledge already diffused is judiciously compiled. But a due respect for the public, and gratitude for the very honourable reception hitherto given to our labours, induce us to exert ourselves with honest zeal to merit the continuance of public favour. We assure our readers that the experiments were made with care, and on quantities sufficiently large to make the unavoidable irregularities in such cases quite insignificant. The law of density was ascertained in each substance in two ways. We dissolved different portions of salt in the same quantity of water, and examined the specific gravity of the brine by weighing it in a vessel with a narrow neck. The portions of salt were each of them one eighth of what would make a nearly saturated solution of the temperature 55°. We did not make the brine stronger, that there might be no risk of a precipitation in form of crystals. We considered the specific gravities as the ordinates of a curve, of which the abscissae were the numbers of ounces of dry salt contained in a cubic foot of the brine. Having thus obtained eight ordinates corresponding to 1, 2, 3, 4, 5, 6, 7, and 8 portions of salt, the ordinates or specific gravities for every other proportion of salt were had by the usual methods of interpolation.

The other method was, by first making a brine nearly saturated, in which the proportion of salt and water was exactly determined. We then took out one-eighth of the brine, and filled up the vessel with water, taking care that the mixture should be complete; for which purpose, besides agitation, the diluted brine was allowed to remain 24 hours before weighing. Taking out one-eighth of the brine also takes out one-eighth of the salt; so that the proportion of salt and water in the diluted brine was known. It was now weighed, and thus we determined the specific gravity for a new proportion of salt and water.

We then took out one-seventh of the brine. It is evident that this takes out one-eighth of the original quantity of salt; an abstraction equal to the former. We filled the vessel with water with the same precautions; and in the same manner we proceeded till there remained only one-eighth of the original quantity of salt.

The specific gravities by these two methods agreed extremely well. In the very deliquent salts the first method exhibited some small irregularities, arising from the unequal quantities of water which they had imbibed from the atmosphere. We therefore confided most in the experiments made with diluted brines.

That the reader may judge of the authority of the tables which we shall insert, we submit to his inspection one series of experiments.

Two thousand one hundred and eighty-eight grains of very pure and dry (but not decretipated) common salt, prepared in large crystals, were dissolved in 6562 grains of distilled water of the temperature 55°. A small matras with a narrow neck, which held 4200 grains of distilled water, was filled with this brine. Its contents weighed 5027 grains. Now 6562 + 2188 = 2188 = 5027 : 1276.75. Therefore the bottle of brine contained 1256.75 grains of salt dissolved in 3770.25 grains of water. Its specific gravity is \( \frac{5027}{4200} \), or 1.196905; and a cubic foot of brine weighs Specific Gravity. 1196.9 ounces avoirdupois. Also 5027 : 1256.75 = 1196.9 : 299.28. Therefore a cubic foot of this brine contains 299.28 ounces of perfectly dry salt.

The subsequent steps of the process are represented as follows.

<table> <tr> <th>Salt.</th> <th>Brine.</th> <th>Water.</th> <th>Wt. of<br>1th. Ft.</th> <th>Salt in<br>Cub. Ft.</th> </tr> <tr> <td>8)1256.75<br>157.1</td> <td>8)5027<br>628.4</td> <td>3770.25<br>= 1/8 of brine</td> <td>1196.9</td> <td>299.28<br>37.41 1/2</td> </tr> <tr> <td></td> <td></td> <td>4398.6<br>527.4</td> <td>Remains.<br>Water to fill it again.</td> <td></td> </tr> <tr> <td>7)1099.6<br>157.1</td> <td>7)4926.0<br>703.7</td> <td></td> <td>2d Brine.<br>1/7 taken out.</td> <td>1172.7<br>261.87<br>37.41</td> </tr> <tr> <td></td> <td></td> <td>4222.3<br>604.7</td> <td>Water added</td> <td></td> </tr> <tr> <td>942.5<br>157.1</td> <td>6)4827.0<br>804.5</td> <td></td> <td>3d Brine.<br>Taken out.</td> <td>1149.3<br>224.46</td> </tr> <tr> <td></td> <td></td> <td>4022.5<br>706.5</td> <td>Remains.<br>Water added</td> <td></td> </tr> <tr> <td>785.4<br>157.1</td> <td>5)4729.0<br>946</td> <td></td> <td>4th Brine.<br>Taken out.</td> <td>1125.9<br>187.05</td> </tr> <tr> <td></td> <td></td> <td>3783<br>847</td> <td>Remains.<br>Water added</td> <td></td> </tr> <tr> <td>628.3<br>157.1</td> <td>4)4630<br>1157.5</td> <td></td> <td>5th Brine.<br>Taken out.</td> <td>1102.3<br>149.64</td> </tr> <tr> <td></td> <td></td> <td>3472.5<br>1054.5</td> <td>Remains.<br>Water added</td> <td></td> </tr> <tr> <td>471.2<br>157.1</td> <td>3)4527<br>1509</td> <td></td> <td>6th Brine.<br>Taken out.</td> <td>1077.9<br>112.23</td> </tr> <tr> <td></td> <td></td> <td>3018<br>1405</td> <td>Remains.<br>Water added</td> <td></td> </tr> <tr> <td>314.1<br>157.1</td> <td>2)4423<br>2212</td> <td></td> <td>7th Brine.<br>Taken out.</td> <td>1053.3<br>74.82</td> </tr> <tr> <td></td> <td></td> <td>2211<br>2102</td> <td>Remains.<br>Water added</td> <td></td> </tr> <tr> <td>157.0</td> <td>4313</td> <td></td> <td>8th Brine.</td> <td>1027.9<br>37.41</td> </tr> </table>

Thus, by repeated abstraction of brine, so as always to take out 1/8th of the salt contained in one constant bulk, we have obtained a brine consisting of 157 grains of salt united with 4313 - 157, or 4156 grains of water.

Its specific gravity is \( \frac{4313}{4200} = 1.0279 \), and a cubic foot of it weighs 1028 ounces, and contains 37 1/2 ounces of dry salt. In like manner may the specific gravity, the weight of a cubic foot, and the salt it contains, be estimated for the intermediate brines.

When these eight quantities of salt contained in a cubic foot are made the abscisse, and the weights of the cubic foot of brine are the corresponding ordinates, the curve will be found to be extremely regular, resembling a hyperbolic arch whose asymptote makes an angle of 30° with the axis. Ordinates were then interpolated analytically for every 10 ounces of contained salt, and thus the table was constructed. We did not, however, rest it on one series alone; but made others, in which one-fourth of the salt was repeatedly abstracted. They agreed, in the case of common salt, with great exactness, and in some others there were some very inconsiderable irregularities.

To show the authority of the tables of strength was, by no means our only motive for giving an example of the process. It may be of use as a pattern for similar experiments. But, besides, it is very instructive. We see, in the first place, that there is a very sensible change of density in one or both of the ingredients. For the series is of that nature (as we have formerly explained), that if the ingredients retained their densities in every proportion of commixture, the specific gravities would have been in arithmetical progression; whereas we see, that their differences continually diminish as the brines grow more dense. We can form some notion of this by comparing the different brines. Thus in the first brine, weighing 5027 grains, there are 3770 grains of water in a vessel holding 4200. If the density of the water remains the same, there is left for the salt only as much space as would hold 430 grains of water. In this space are lodged 1257 grains of salt, and its specific gravity, in its liquid form, is \( \frac{1257}{430} = 2.8907 \) very nearly. But in the 8th brine the quantity of water is 4156, the space left for 157 grains of salt is only the bulk of 44 grains of water, and the density of the salt is \( \frac{157}{44} = 3.568 \), considerably greater than before. This induced us to continue the dilution of the brine as follows, beginning with the 8th brine.

\[ \begin{array}{l} 157 \\ 78.5 \\ \hline 2156.5 \\ 2105.5 \\ \hline 78.5 \\ 39.7 \\ \hline 2131 \\ 2102 \\ \hline 39.7 \\ \hline 2)4262.0 \\ 2131 \\ \hline 2102 \\ \hline 2)4233 \\ 2116.5 \\ 2102 \\ \hline 19.8 \\ 4218 \\ \end{array} \]

This last brine contains 4198.2 grains of water, leaving only the bulk of 1.8 grains of water to contain 19.8 of salt, so that the salt is ten times denser than water. This will make the strength 243 instead of 210 indicated by the specific gravity. But we do not pretend to measure the densities with accuracy in these diluted brines. It is evident from the process that a single single grain of excess or defect in taking out the brine and replacing it with water has a sensible proportion to the whole variation. But we see with sufficient evidence, that from the strong to the weak brines the space left for the portion of salt is continually diminishing. In the first dilution 527\( \frac{1}{2} \) grains of water were added to fill up the vessel; but one-eighth of its contents of pure water is only \( \frac{525}{8} \); so that here is a diminution of two grains and a half in the space occupied by the remaining salt. The subsequent additions are 604.7; 706.5; 847; 1054.5; 1405; 2102; 2105.5; 2102; 2102; instead of 600; 700; 840; 1050; 1400; 2100; 2100; 2100; 2100. Nothing can more plainly shew the condensation in general, though we do not learn whether it happens in one or both of the ingredients; nor do the experiments show with sufficient accuracy the progression of this diminution. The excesses of the added water being only fix or seven grains, we cannot expect a nice repartition. When the brine is taken out, the upper part of the vessel remains lined with a briny film containing a portion of salt and water, perhaps equal or superior to the differences. Had our time permitted, we should have examined this matter with ferulous attention, using a vessel with a still narrower neck, and in each dilution abstracting one half of the brine. The curve, whose abscissae and ordinates represent the weight of the contained salt and the weight of a constant bulk of the brine, exhibits the best and most synoptical view of the law of condensation, because the position of the tangent in any point, or the value of the symbol \( \frac{x}{y} \), always shows the rate at which the specific gravity increases or diminishes. We are inclined to think that the curve in all cases is of the hyperbolic kind, and complete; that is, having the tangent perpendicular to the axis at the beginning of the curve. The mathematical reader will easily guess the physical notions which incline us to this opinion; and will also see that it is hardly possible to discover this experimentally, because the mistake of a single grain in the very small ordinates will change the position of the tangent many degrees. It was for this reason that we thought it useless to prosecute the dilution any farther. But we think that it may be prosecuted much farther in Dr Watfon's or Mr Achard's method, viz. by dissolving equal weights of salt in two vessels, of very different capacities, having tubular necks, in which the change of bulk may be very accurately observed. We can only conclude, that the condensation is greatest in the strongest brines, and probably attains its maximum when the quantities of true saline matter and water are nearly equal, as in the case of vitriolic acid, &c.

We consider these experiments as abundantly sufficient for deciding the question, "Whether the salt can be received into the pores of the water, or the water into the pores of the salt, so as to increase its weight without increasing its bulk?" and we must grant that it may. We do not mean that it is simply lodged in the pores as sand is lodged in the interstices of small shot; but the two together occupy less room than when separate. The experiments of Mr Achard were insufficient for a decision, because made on too small a quantity as 600 grains of water. Dr Watfon's experiments have, for the most part, the same defect. Some of them, however, are of great value in this question, and are very fit for ascertaining the specific gravity of dissolved salts. In one of them (not particularly narrated) he found that a quantity of dissolved salt occupied the same bulk in two very different states of dilution. We cannot pretend to reconcile this with our experiments. We have given these as they stood; and we think them conclusive, because they were so numerous and so perfectly consistent with each other; and their result is so general, that we have not found an exception. Common salt is by no means the most remarkable instance of condensation. Vegetable alkali, sal ammoniac, and some others, exhibit much condensation.

We thought this a proper opportunity of considering this question, which is intimately connected with the principles of chemical solution, and was not perhaps considered in sufficient detail under the article CHEMISTRY. We learn from it in general, that the quantities of salt in brines increase at somewhat a greater rate than their specific gravities. This difference is in many cases of sensible importance in a commercial view. Thus an alkaline lixivium for the purposes of bleaching or soap-making, whose specific gravity is 1.234, or exceeds that of water by 234, contains 361 ounces of salt in a cubic foot; a ley which exceeds the weight of water twice as much, or 468 ounces per cubic foot, contains 777 ounces of salt, which exceeds the double of 361 by 55 ounces more than seven per cent. Hence we learn, that hydrometers for discovering the strength of brines, having equal divisions on a cylindrical stem, are very erroneous; for even if the increments of specific gravity were proportional to the quantities of salt in a gallon of brine, the divisions at the bottom of the stem ought to be smaller than those above.

The construction of the following table of strengths from the above narrated series of brines is sufficiently obvious. Column 1st is the specific gravity as discovered by the balance or hydrometer, and also is the number of ounces in a cubic foot of the brine. Col. 2d is the ounces of the dry salt contained in it.

<table> <tr> <th>Weight<br>Cub. Ft.<br>Brine.</th> <th>Salt<br>in Cub.Ft.</th> <th>Weight<br>Cub. Ft.<br>Brine.</th> <th>Salt<br>in Cub.Ft.</th> </tr> <tr> <td>1.000</td> <td>0</td> <td>1.115</td> <td>170</td> </tr> <tr> <td>1.008</td> <td>10</td> <td>1.122</td> <td>180</td> </tr> <tr> <td>1.015</td> <td>20</td> <td>1.128</td> <td>190</td> </tr> <tr> <td>1.022</td> <td>30</td> <td>1.134</td> <td>200</td> </tr> <tr> <td>1.029</td> <td>40</td> <td>1.140</td> <td>210</td> </tr> <tr> <td>1.036</td> <td>50</td> <td>1.147</td> <td>220</td> </tr> <tr> <td>1.043</td> <td>60</td> <td>1.153</td> <td>230</td> </tr> <tr> <td>1.050</td> <td>70</td> <td>1.159</td> <td>240</td> </tr> <tr> <td>1.057</td> <td>80</td> <td>1.165</td> <td>250</td> </tr> <tr> <td>1.064</td> <td>90</td> <td>1.172</td> <td>260</td> </tr> <tr> <td>1.070</td> <td>100</td> <td>1.178</td> <td>270</td> </tr> <tr> <td>1.077</td> <td>110</td> <td>1.184</td> <td>280</td> </tr> <tr> <td>1.083</td> <td>120</td> <td>1.190</td> <td>290</td> </tr> <tr> <td>1.090</td> <td>130</td> <td>1.197</td> <td>300</td> </tr> <tr> <td>1.096</td> <td>140</td> <td>1.203</td> <td>310</td> </tr> <tr> <td>1.103</td> <td>150</td> <td>1.206</td> <td>316</td> </tr> <tr> <td>1.109</td> <td>160</td> <td>1.208</td> <td>320</td> </tr> </table>

TABLE of Brines of Common Salt. The table differs considerably from Mr Lambert's. The quantities of salt corresponding to any specific gravity are about \( \frac{1}{7} \)th less than in his table. But the reader will see that they correspond with the series of experiments above narrated; and these were but a few of many which all corresponded within an hundredth part. The cause of the difference seems to be, that most kinds of common salt contain magnesian salts, which contain a very great proportion of water necessary for their crystallization. The salt which we used was of the purest kind, but such as may be had from every salt work, by Lord Dundonald's very easy process, viz. by passing through it a saturated solution boiling hot, which carries off with it about four-fifths of all the bitter salts. Our aim being to ascertain the quantities of pure sea-salt, and to learn by the bye its relation to water in respect of density, we thought it necessary to use the purest salt. We also dried it for several days in a stove, so that it contained no water not absolutely necessary for its crystallization. An ounce of such salt will communicate a greater specific gravity to water than an ounce of a salt that is less pure, or that contains extraneous water.

The specific gravity 1.090 is that of ordinary pickles, which are estimated as to strength by floating an egg.

We cannot raise the specific gravity higher than 1.206 by simply dissolving salt in cold water. But it will become much denser, and will even attain the specific gravity 1.240 by boiling, then holding about 366 ounces in the cubic foot of hot brine. But it will deposit by cooling, and when of the temperature 55° or 60°, hardly exceeds 1.206. We obtained a brine by boiling till the salt gained very rapidly. When it cooled to 60°, its specific gravity was 1.2063; for a vessel which held 3506 grains of distilled water held 4229 of this brine. This was evaporated to dryness, and there were obtained 1344 grains of salt. By this was computed the number interposed between 310 and 320 in the table. We have, however, raised the specific gravity to 1.217, by putting in no more salt than was necessary for this density, and using heat. It then cooled down to 60° without quitting any salt; but if a few grains of salt be thrown into this brine, it will quickly deposit a great deal more, and its density will decrease to 1.206. We find this to hold in all salts; and it is a very instructive fact in the theory of crystallization; it resembles the effect which a magnet produces upon iron filings in its neighbourhood. It makes them temporary magnets, and causes them to arrange themselves as if they had been really made permanent magnets. Just so a crystal already formed disposes the rest to crystallize. We imagine that this analogy is complete, and that the forces are similar in both cases.

The above table is computed for the temperature 55°; but in other temperatures the strength will be different on two accounts, viz. the expansion of the brine and the dissolving power of the water. Water expands about 40 parts in 1000 when heated from 60° to 212°. Saturated brine expands about 48 parts, or one-fifth more than water; and this excess of expansion is nearly proportional to the quantity of salt in the brine. If therefore any circumstance should oblige us to examine a brine in a temperature much above 60°, allowance should be made for this. Thus, should the specific gravity of brine of the temperature 130 (which is nearly half way between 60 and 212) be 1.140, we must increase it by 20 (half of 40); and having found the strength 2.40 corresponding to this corrected specific gravity, we must correct it again by adding 1 to the specific gravity for every 45 ounces of salt.

But a much greater and more uncertain correction is necessary on account of the variation of the dissolving power of water by heat. This indeed is very small in the case of sea-fall in comparison with other salts. We presume that our readers are apprised of this peculiarity of sea-fall, that it dissolves nearly in equal quantities in hot or in cold water. But although water of the temperature 60° will not dissolve more than 320 or 325 ounces of the purest and driest sea-fall, it will take up above 20 ounces more by boiling on it. When thus saturated to the utmost, and allowed to cool, it does not quit any of it till it is far cooled, viz. near to 60°. It then deposits this redundant salt, and holds the rest till it is just going to freeze, when it lets it go in the instant of freezing. If evaporated in the state in which it continues to hold the salt, it will yield above 400 ounces per cubic foot of brine, in good crystals, but rather overcharged with water. And since in this state the cubic foot of brine weighs about 1220 ounces, it follows, that 820 ounces of water will, by boiling, dissolve 400 of crystallized salt.

The table shows how much any brine must be boiled down in order to grain. Having observed its specific gravity, find in the table the quantity of salt corresponding. Call this x. Then, since a boiling hot graining or saturated solution contains 340 ounces in the cubic foot of brine, say \( 340 : 1000 = x : \frac{1000}{340} x \). This is the bulk to which every cubic foot (valued at 1000) must be boiled down. Thus suppose the brine has the specific gravity 1109. It holds 160 ounces per foot, and we must boil it down to \( \frac{1000 \times 160}{340} \) or 471; that is, we must boil off \( \frac{529}{1000} \) of every cubic foot or gallon.

These remarks are of importance in the manufacture of common salt; they enable us to appreciate the value of salt springs, and to know how far it may be prudent to engage in the manufacture. For the doctrine of latent heat affords us, that in order to boil off a certain quantity of water, a certain quantity of heat is indispensably necessary. After the most judicious application of this heat, the consumption of fuel may be too expensive.

The specific gravity of sea-water in these climates does not exceed 1.03, or the cubic foot weighs 1030 ounces, and it contains about 41 ounces of salt. The brine-pits in England are vastly richer; but in many parts of the world brines are boiled for salt which do not contain above 10 or 20 ounces in the cubic foot.

In buying salt by weight, it is of importance to know the degree of humidity. A salt will appear pretty dry (if free from magnesian salts) though moistened with one per cent. of water; and it is found that incipient humidity exposes it much to farther deliquescence. A much smaller degree of humidity may be discovered by the specific gravity of a brine made with a few ounces of the salt. And the inspection of the table informs us, that the brine should be weak; for the differences of specific gravity go on diminishing in the stronger brines: 300 ounces of dry salt dissolved in 897 ounces of water should give the specific gravity 1197. Suppose it be but 1190, the quantity of salt corresponding is only 290; but when mixed with 897 ounces of water, the weight is 1197, although the weight of the cubic foot is only 1190. There is therefore more than a cubic foot of the brine, and there is as much salt as will make more than a cubic foot of the weight 1190. There is \( 290 \times \frac{1197}{1195} \), or 291\( \frac{1}{3} \) ounces, and there is 8\( \frac{1}{3} \) ounces of water attached to the salt.

The various informations which we have pointed out as deducible from a knowledge of the specific gravity of the brines of common salt, will serve to suggest several advantages of the knowledge of this circumstance in other lixivia. We shall not therefore resume them, but simply give another table or two of such as are most interesting. Of those, alkaline lyes are the chief, being of extensive use in bleaching, soap-making, glass-making, &c.

We therefore made a very strong ley of the purest vegetable alkali that is ever used in the manufactories, not thinking it necessary, or even proper, to take it in its state of utmost purity, as obtained from cubic nitre and the like. We took salt of tartar from the apothecary, perfectly dry, of which 3983 grains were dissolved in 3540 grains of distilled water; and after agitation for several days, and then standing to deposit sediment, the clear ley was decanted. It was again agitated; because, when of this strength, it becomes, in a very short time, rarer above and denser at the bottom. A flask containing 4220 grains of water held 6165 of this ley when of the temperature 55°. Its specific gravity was therefore 1.4678, and the 6165 grains of ley contained 3264 grains of salt. We examined its specific gravity in different states of dilution, till we came to a brine containing 51 grains of salt, and 4189 grains of water, and the contents of the flask weighed 4240 grains: its specific gravity was therefore 1.0095. In this train of experiments the progression was most regular and satisfactory; so that when we constructed the curve of specific gravities geometrically, none of the points deviated from a most regular curve. It was considerably more incurvated near its commencement than the curve for sea-salt, indicating a much greater condensation in the diluted brines. We think that the following table, constructed in the same manner as that for common salt, may be depended on as very exact.

<table> <tr> <th>Weight of Cub. Foot oz.</th> <th>Salt cont. oz.</th> <th>Weight of Cub. Foot oz.</th> <th>Salt cont. oz.</th> <th>Weight of Cub. Foot oz.</th> <th>Salt cont. oz.</th> <th>Weight of Cub. Foot oz.</th> <th>Salt cont. oz.</th> </tr> <tr> <td>1000</td><td>0</td><td>1174</td><td>260</td><td>1329</td><td>520</td><td>1471</td><td>780</td> </tr> <tr> <td>1016</td><td>20</td><td>1187</td><td>280</td><td>1340</td><td>540</td><td>1482</td><td>800</td> </tr> <tr> <td>1031</td><td>40</td><td>1200</td><td>300</td><td>1351</td><td>560</td><td>1493</td><td>820</td> </tr> <tr> <td>1045</td><td>60</td><td>1212</td><td>320</td><td>1362</td><td>580</td><td>1504</td><td>840</td> </tr> <tr> <td>1058</td><td>80</td><td>1224</td><td>340</td><td>1372</td><td>600</td><td>1515</td><td>860</td> </tr> <tr> <td>1071</td><td>100</td><td>1236</td><td>360</td><td>1384</td><td>620</td><td>1526</td><td>880</td> </tr> <tr> <td>1084</td><td>120</td><td>1248</td><td>380</td><td>1395</td><td>640</td><td>1537</td><td>900</td> </tr> <tr> <td>1098</td><td>140</td><td>1259</td><td>400</td><td>1406</td><td>660</td><td>1547</td><td>920</td> </tr> <tr> <td>1112</td><td>160</td><td>1270</td><td>420</td><td>1417</td><td>680</td><td>1557</td><td>940</td> </tr> <tr> <td>1125</td><td>180</td><td>1281</td><td>440</td><td>1428</td><td>700</td><td>1567</td><td>960</td> </tr> <tr> <td>1138</td><td>200</td><td>1293</td><td>460</td><td>1438</td><td>720</td><td>1577</td><td>980</td> </tr> <tr> <td>1150</td><td>220</td><td>1305</td><td>480</td><td>1449</td><td>740</td><td>1586</td><td>1000</td> </tr> <tr> <td>1162</td><td>240</td><td>1317</td><td>500</td><td>1460</td><td>760</td><td></td><td></td> </tr> </table>

We see the same augmentation of the density of the salt in the diluted brines here as in the case of common salt. Thus a brine, of which the cubic foot weighs 1482 ounces, or which has the specific gravity 1.482, contains 820 ounces of dry alkali and 682 of water. Therefore, if we suppose the density of the water unchanged, there remains the bulk of 318 ounces of water to receive 840 ounces of salt: its density is therefore \( \frac{800}{318} = 2.512 \) nearly. But in the brine whose weight per foot is only 1016 there are 20 ounces of salt, and therefore 996 of water; and there is only four ounce-measures of water, that is, the bulk of four ounces of water, to receive 20 ounces of salt. Its specific gravity therefore is \( \frac{20}{4} = 5 \), almost twice as great as in the strong brine. Accordingly Mr Achard is disposed to admit the absorption (as it is carelessly termed) in the case of salt tart. But it is a general (we think an universal) fact in the solution of salts. It must be carefully distinguished from the first contraction of bulk which salts undergo in passing from a solid to a fluid form. The contraction now under consideration is analogous to the contraction of oil of vitriol when diluted with water; for oil of vitriol must be considered as a very strong brine which we cannot dephlegmate by distillation, and therefore cannot obtain the dry saline ingredient in a separate form, so as to observe its solid density, and say how much it contracts in first becoming fluid. The way of conceiving the first contraction in the act of solution as a lodging of the particles of the one ingredient on the intertices of the other, "qu'ils ne nichent, en augmentant le poids sans affecter le volume de la saumure," as Euler and Lambert express themselves, is impossible here, where both are fluids. Indeed it is but a slovenly way of thinking. thinking in either case, and should be avoided, because inadvertent persons are apt to use as a physical principle what is merely a mode of speech.

We learn from the table, that a hydrometer with equidistant divisions on a cylindrical or prismatical stem is still more erroneous than in the brines of common salt.

We learn from the experiments of Kirwan, Lavoisier, and others, that dry salt of tartar contains about one-fourth of its weight of fixed air. In many applications of this salt to the purposes of manufacture, this ingredient is of no use. In some it is hurtful, and must be abstracted by lime. Soap-maker's ley consists of the pure alkaline salt dissolved in water. It is therefore of importance to ascertain its quantity by means of the specific gravity of the brine. For this purpose we took a ley of sal tart, whose specific gravity was 1.20417, containing 3 1/4 ounces of mild alkali in a cubic foot of ley, and we rendered it nearly caustic by lime. The specific gravity was then 1.1897. This is a very unexpected result. Nothing is employed with more success than quicklime for dephlegmating any watery fluid. We should rather have expected an increase of specific gravity by the abstraction of some of the water of the menstruum, and perhaps the water of the crystallization, and the aerial part of the salt. But we must ascribe this to the great density in which the fixed air exists in the mild alkali.

It is unnecessary to give similar tables for all the salts, unless we were writing a dissertation on the theory of their solution. We shall only observe, that we examined with particular attention sal ammoniac, because Mr Achard, who denies what is called the abstraction of salts, finds himself obliged to allow something like it in this salt. It does not, however, differ from those of which we have given an account in detail in any other respect than this, that the changes of fluid density are much less than in others (instead of being greater, as Achard's experiments seem to indicate) in all brines of moderate strength. But in the very weak brines there is indeed a remarkable difference; and if we have not committed an error in our examination, the addition of one part of sal ammoniac to 64 of water occupies less room than the water alone. We think that we have met with this as an accidental remark by some author, whose work we do not recollect. But we do not choose to rest so much on our form of the experiment in such weak brines. The following mixtures will abundantly serve for constructing the table of its strength: Sal ammoniac = 960 grains was dissolved in 3506 grains of water, making a brine of 4466 grains. A phial which held 1600 grains water held 1698 of this brine. It contained

\[ \frac{1698 \times 960}{4466}, \text{or } 365 \text{ grains of salt.} \]

The specific gravity was

\[ \frac{1698}{1600^3} = 1.061, \]

and the cubic foot weighed

\[ 1061 \text{ ounces. It also contained } \frac{1061 \times 365}{1698}, \text{or } 288 \]

ounces of salt. By repeated abstraction of brine, and replacing with water, we had the following series:

<table> <tr> <th>Series.</th> <th>Brine.</th> <th>Sp. Gr.</th> <th>Oz. Salt.</th> <th>Specific Gravity</th> <th>Cub. Ft. Spectacle</th> </tr> <tr> <td>Weight of brine,</td> <td>1/4, 1698</td> <td>1.061</td> <td>228</td> <td></td> <td></td> </tr> <tr> <td>After taking out 1/4, 2d, 1676</td> <td></td> <td>1.048</td> <td>171</td> <td></td> <td></td> </tr> <tr> <td>After taking out 1/4, 3d, 1653</td> <td></td> <td>1.033</td> <td>114</td> <td></td> <td></td> </tr> <tr> <td>After taking out 1/4, 4th, 1630</td> <td></td> <td>1.019</td> <td>57</td> <td></td> <td></td> </tr> <tr> <td>After taking out 1/4, 5th, 1616</td> <td></td> <td>1.010</td> <td>28</td> <td></td> <td></td> </tr> <tr> <td>After taking out 1/4, 6th, 1610</td> <td></td> <td>1.0063</td> <td>14</td> <td></td> <td></td> </tr> <tr> <td>After taking out 1/4, 7th, 1605</td> <td></td> <td>1.0038</td> <td>7 1/2</td> <td></td> <td></td> </tr> </table>

This series is extremely regular, and the progress of density may be confidently deduced from it.

From the whole of this disquisition on the relation between the specific gravities of brines and the quantities of salt contained, we see in general that it may be guessed at, with a useful degree of precision, from the density or specific gravity of saturated solutions. We therefore conclude with a list of the specific gravities of several saturated solutions, made with great care by the bishop of Landaff.—The temperature was 42°. The first numerical column is the density of saturated brine, and the next is the density of a brine consisting of 12 parts (by weight) of water and one of salt. From this may be inferred the quantity in the saturated solution, and from this again may be inferred the quantity corresponding to inferior densities.

<table> <tr> <th>Borax,</th> <th>1.910</th> <th></th> <th></th> <th></th> <th></th> </tr> <tr> <td>Cor. Sublim.</td> <td>1.037</td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>Alum,</td> <td>1.033</td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>Glaub. salt,</td> <td>1.054</td> <td>1.029</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Common salt,</td> <td>1.198</td> <td>1.059</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Sal. cath. amar.</td> <td>1.232</td> <td>1.039</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Sal ammon.</td> <td>1.072</td> <td>1.026</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Vol. alk. mite,</td> <td>1.087</td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>Nitre,</td> <td>1.095</td> <td>1.050</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Rochelle salt,</td> <td>1.114</td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>Blue vitriol,</td> <td>1.150</td> <td>1.052</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Green vitriol,</td> <td>1.157</td> <td>1.043</td> <td></td> <td></td> <td></td> </tr> <tr> <td>White vitriol,</td> <td>1.386</td> <td>1.045</td> <td></td> <td></td> <td></td> </tr> <tr> <td>Pearl ash,</td> <td>1.534</td> <td></td> <td></td> <td></td> <td></td> </tr> </table>