in medicine. By specifics is not meant such as infallibly and in all patients produce salutary 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 more infallible than any other 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. See **HYDROSTATICS**, Sect. III.

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 can... not 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 constancy 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 exits, 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 matras; 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 hydrostatics 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 Hydrostatics, p. 11.) 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 by, 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 hydrostatical 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 confirmed 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 Eratophyseus Batavus. He weighed a Rhineland 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 69,588 pounds poids de Paris. Duhamel obtained the very same result; but Mr Monge, in 1783, says that filtered rain-water of the temperature 12° (Reaumur) weighs 69,3792. Both these measures are considerably below Mr Everard's, which is 62.55, the former giving 62.53, 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 inconsistency 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 of the temperature 55° several times without varying 2 grains, and it lost 42805 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 1/10th of its bulk, and mercury only 1/135, 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. Those gentlemen observed the expansion of water to be very anomalous between $32^\circ$ and $45^\circ$. 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 hydrostatic 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 it with 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 first 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 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 platinum.

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 examiner 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 affec- tation 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 confidence 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 Gravelande'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 acometer, 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 Theo 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 hydrotactical balance. They consist of a ball (or rather a coccus) 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 sink 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, 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 730 gives 916 for the specific gravity, and shows it to be precisely exactly 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 178 to sink it to D thaton the item.

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 overleap, 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 1 and 1½; and the third, for the mineral acids, may reach from this to 2. 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 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 β of the mixture; and let D, d, and δ be the densities, or the weights, or the specific gravities (for they are in one ratio) Specific Gravity

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 \( s - d \). Therefore \( \beta : b = D - d : s - d \); 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 bulks, 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 item 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 item 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 item, 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 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 item 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 sort has been contrived, in which which the principle of both are combined. Suppose a hydrometer with a stem, whose bulk is \( \frac{1}{10} \)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 \( \frac{1}{10} \)th heavier, the whole stem will emerge; for the bulk of the displaced fluid is now \( \frac{1}{10} \)th of the whole, and the weight is the same as before, and therefore the specific gravity is \( \frac{1}{10} \)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 0.803 is \( \frac{1}{10} \)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 \( \frac{1}{10} \)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 (\( = 0.803 + 0.0803 \)), 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 1 = 0.0803, 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 exciseman 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 \( \frac{1}{10} \)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 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 \( \frac{1}{10} \)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 proportionals 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 proportionals 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 which God has of the human body as actually existing; that this idea of the body, and the body itself, are one and the same thing; and that thinking and extended substances are in reality but one and the same substance, which is sometimes comprehended under one attribute of the Deity, and sometimes under another.

If this impious jargon be not Atheism, or as it has been sometimes called Pantheism, we know not what it is (see Pantheism). According to Spinoza, there is but one substance, which is extended, infinite, and indivisible. That substance indeed he calls God; but he labours to prove that it is corporeal; that there is no difference between mind and matter; that both are attributes of the Deity variously considered; that the human soul is a part of the intellect of God; that the same soul is nothing but the idea of the human body; that this idea of the body, and the body itself, are one and the same thing; that God could not exist, or be conceived, were the visible universe annihilated; and therefore that the visible universe is either the one substance, or at least an essential attribute or modification of that substance. He sometimes indeed speaks of the power of this substance; but when he comes to explain himself, we find that by power he means nothing but blind necessity; and though he frequently talks of the wisdom of God, he seems to make use of the word without meaning. This we think evident from the long appendix to his 36th proposition; in which he labours to prove that the notion of final causes is an idle figment of the imagination, since, according to him, nothing but the prejudices of education could have led men to fancy that there is any real distinction between good and evil, merit and demerit, praise and reproach, order and confusion; that eyes were given them that they might be enabled to see; teeth for the purpose of chewing their food; herbs and animals for the matter of that food; that the sun was formed to give light, or the ocean to nourish fishes. If this be true, it is impossible to discover wisdom in the operations of his one substance; since, in common apprehension, it is the very characteristic of folly to act without any end in view.

Such are the reveries of that writer, whose works a German philosopher of some name has lately recommended to the public, as calculated to convey to the mind more just and sublime conceptions of God than are to be found in most other systems. The recommendation has had its effect. A literary journalist of our own, reviewing the volume in which it is given, feels a peculiar satisfaction from the discovery that Spinoza, instead of a formidable enemy to the cause of virtue and religion, was indeed their warmest friend; and piously hopes that we shall become more cautious not to suffer ourselves to be deceived by empty names, which those who cannot reason (Sir Isaac Newton and Dr Clarke perhaps) give to those who can (Hobbes, we suppose, and Spinoza). But though we have the honour to think on this question with our illustrious countrymen, we have no desire to depict Spinoza as a reprobate, which the critic says has often been done by ignorance and enthusiasm. We admit that his conduct in active life was irreproachable; and for his speculative opinions, he must stand or fall to his own Master. His Ethics appear to us indeed a system shockingly impious; and in the tract entitled Politica, power and right are confounded as in the former volume; but in the treatise De Intellectus Emendatione, are scattered many precepts of practical wisdom, as well as some judicious rules for conducting philosophical investigation; and we only regret, that the reader must wade through pages of fatalism, scepticism, and palpable contradictions. His Compendium Grammaticae Linguae Hebraeae, though left imperfect, appears to have so much merit, that it is to be wished he had fulfilled his intention of writing a philosophical grammar of that language, instead of wasting his time on abstruse speculations, which, though they seem not to have been injurious to his own virtue, are certainly not calculated to promote the virtue of others, or to increase the sum of human happiness.

SPIRAEA, in botany: A genus of plants belonging to the class of Icosandra, and to the order of pentagynia; and in the natural system arranged under the 26th order, Pomaceae. The calyx is quinquefied; there are five petals; and the capsule is polyperous. There are 18 species; of which two only are British, the filipendula and ulmaria. 1. The filipendula, dropwort, has pinnate leaves; the leaflets are serrated; the stalk is herbaceous, about a foot and a half high, terminated with a loose umbel of white flowers, often tinged with red. The petals are generally five, and the segments of the calyx are reflexed; the stamens are 30 or more; the germina 12 or upwards. It grows in mountainous pastures. 2. The ulmaria, meadow-sweet. The leaves have only two or three pair of pinnae, with a few smaller ones intermixed; the extreme one being larger than the rest, and divided into three lobes. The calyx is reddish; the petals white, and the number of capsules from six to ten twisted in a spiral. The tuberous pea-like roots of the filipendula dried and reduced to powder, have been used instead of bread in times of scarcity. Hogs are very fond of these roots. Cows, goats, sheep, and swine, eat the plant; but horses refuse it. The flowers of the ulmaria have a fragrant scent, which rises in distillation. The whole plant indeed is extremely fragrant, so that the common people of Sweden strew their floors with it on holidays. It has also an astringent quality, and has been found useful in dysenteries, ruptures, and in tanning of leather.

SPIRAL, in geometry, a curve line of the circular kind, which in its progress recedes from its centre.

SPIRE, in architecture, was used by the ancients for the base of a column, and sometimes for the atragal or tore; but among the moderns it denotes a fleche that continually diminishes as it ascends, whether conically or pyramidally.

SPIRIT, in metaphysics, an incorporeal being or intelligence;

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humanam hoc vel illud percipere, nihil aliud dicimus quam quod Deus, non quatenus infinitus est, sed quatenus per naturam humanae mentis explicatur, sive quatenus humanae mentis efficiat, hanc vel illam habet ideam: et cum dicimus Deum hanc vel illam ideam habere, non tantum, quatenus naturam humanae mentis constituit; sed quatenus simul cum mente humana alterius rei etiam habet ideam. Corol. prop. xi. part 2. SPIRIT, in chemistry and pharmacy, a name applied to every volatile liquid which is not infipid like phlegm or water; and hence the distinction into acid, alkaline, and vinous spirits. See PHARMACY INDEX.

SPIRIT OF WINE. See CHEMISTRY INDEX, DISTILLATION, and PHARMACY INDEX.

SPIRITS, or ANIMAL SPIRITS. See ANATOMY, Part V. no 136, and PHYSIOLOGY, no 185.