mentioning such circumstances of the results as suited our purposes of physical discussion. At present we give the general result in the table of specific gravity, as peculiarly belonging to spirituous liquors, affording the most exact account of their density in every state of dilution of alcohol with water. And as the relation between the proportion of ingredients and the density is peculiar to every substance, so that scarcely any inference can be made from one to another, the reader will consider the tables here given as characteristic with respect to alcohol. In all solutions of salts we found that the condensation increases continually with the dilution, whereas it is greatest when equal bulks of water and alcohol are mixed; yet we do not consider this as an exception; for it is certain, that in the strongest brine the saline ingredient bears but a small proportion to the water—and when we mix two solutions, the condensation is greatest when they are nearly equal in bulk. But we think ourselves entitled to infer, that alcohol is not a dilution of a substance in a quantity of water; but that water, in a certain proportion, not very distant from what we can produce by slow distillation, is an ingredient of alcohol, or is one of its component parts, and not merely a vehicle or menstruum. We therefore imagine that proof spirit contains nearly equal bulks of water and ardent spirits.
The great difficulty in this examination arose from the very dissimilar expansions of water and alcohol by heat. This determined Sir Charles Blagden to estimate the proportions of ingredients by weight, and make it absolutely necessary to give a scale of specific gravity and strength for every temperature. For it must be remarked, that the question (whether in commerce or philosophy) always is, "How many gallons of alcohol and of water, taken just now and mixed together, will produce a hundred gallons of the spirit we are examining?" The proportion of these two will be different according to the temperature of both. As many mixtures therefore must have been made in each proportion as there were temperatures considered; but by taking the ingredients by weight, and examining the density of the compound in one temperature, it is then heated and cooled, and its change of density observed. Calculation then can tell us the change in the proportion of the bulks or numbers of gallons in the mixture, by means of a previous table showing the expansions of water and of alcohol.
The alcohol selected for this examination had the specific gravity 0.825. This is not the purest that can be procured; some was produced of 0.816, of 0.814, and 0.813, both obtained from rum, from brandy, and from malt spirit. We are informed that Dr Black has obtained it of the specific gravity 0.8 by digesting alcohol with fixed ammonia (muriatic acid united with lime) made very dry. It dephlegmates alcohol very powerfully without decomposing it, which always happens when we use caustic alkali. Alcohol of 0.825 was chosen because expressed by a number of easy management in computation.
The examination commenced by ascertaining the expansions of water and alcohol. The temperature 60° of Fahrenheit's scale was selected for the general temperature of comparison, being easily attainable even in cold weather, and allowing the examinator to operate at ease. The first and last copartments of the tables contain the weights and specific gravities of alcohol and water for every fifth degree of heat from 30° to 100°.
From these we have constructed the two following little tables of expansion. The bulk of 1000 ounces, pounds, or other weight of water and of alcohol of the temperature 60°, occupies the bulks expressed in the tables for every other temperature. Water could not be easily or usefully examined when of the temperature 30°, because it is with great difficulty kept fluid in that temperature. It is very remarkable, that when it can be kept, it expands instead of contracting; while cooling down from 35° or thereabouts, and as it approaches to 32°, it expands rapidly. We observe the same thing in the crystallization of Glauber salt, martial vitriol, and some others, which contain much water in their crystals. We observe, on the other hand, a remarkable contraction in the zeolite just before its beginning to swell into bubbles by a red heat.
| Heat | Of Water | Diff. | Of Alcohol | Diff. | |------|----------|------|------------|------| | 30° | 99910 | 119195 | 319 | | 35° | 99956 | 119574 | 325 | | 40° | 99914 | 119939 | 332 | | 45° | 99932 | 120172 | 339 | | 50° | 99962 | 120514 | 346 | | 55° | 100000 | 120868 | 353 | | 60° | 100050 | 121212 | 360 | | 65° | 100100 | 121565 | 367 | | 70° | 100150 | 121919 | 374 | | 75° | 100200 | 122279 | 381 | | 80° | 100250 | 122645 | 388 | | 85° | 100300 | 123017 | 395 | | 90° | 100350 | 123393 | 402 | | 95° | 100400 | 123773 | 409 | | 100° | 100450 | 124157 | 416 |
This being premised, the examination was conducted in the following manner. It was determined to mix 100 parts by weight of pure alcohol with five, ten, fifteen, twenty, parts of distilled water, till they were compounded in equal quantities, and then to mix 100 parts of distilled water with 95, 90, 85, 80, &c. parts of alcohol, till they were mixed in the proportion of 100 to 5. Thus a series of mixtures would be obtained, extending from pure alcohol to pure water. This series would be such, that the examinations would be most frequent in the cases most usual in the commerce of strong liquors. A set of phials, fitted with ground stoppers, were provided, of sizes fit to hold the intended mixtures. These mixtures were made by suspending the phial to the arm of a very nice balance, in the opposite scale of which (besides the counterpoise of the phial) there was placed the weight 100. Spirit was then poured into the phial till it exactly balanced the weight 100. The weight for the water to be added was then put into the opposite scale, and water was poured into the phial by means of a slender glass funnel, by small quantities at a time, and the phial frequently agitated to promote the mixture. When the additional weight was exactly balanced, the phial was taken off, its stopper put in, and leather tied over it, and it was set by, for at least a month, that the mixture and the whole Spiritous process of condensation might be completed. The same method was followed in the mixtures where the water was predominant.
When the ingredients of these mixtures were judged to have completely incorporated, their specific gravity was examined by weighing with the most scrupulous precision the contents of a vessel which held 2925 troy grains of water, of the temperature 60°. The balance was so exceedingly sensible, that the 50th part of a grain greatly deranged its position when loaded with the scales and their contents. It was constructed by Mr Ramsden, and some account of its exquisite sensibility may be seen in the Journal de Physique, vol. xxxiii. This quantity of materials was therefore thought abundantly sufficient for ascertaining the density of the liquor. It is needless to detail the precautions which were taken for having the contents of the weighing bottle brought to the precise temperature proper for the experiment. They were such as every person conversant with such things is accustomed to take—The bottle had a slender neck, and being put on a lathe, a mark was made round it with a diamond. The bottle was filled till the bottom of the hollow surface of the fluid was in the plane of this mark; and to judge of the accuracy attainable in filling the bottle, the operation was several times repeated and the contents weighed, without the difference of $\frac{1}{3}$th of a grain in 2925. The only source of error which was to be guarded against was air-bubbles adhering to the inside of the bottle, or moisture condensing (in the experiments with low temperatures) on the outside. Both of these were attended to as much as possible.
This method of determining the specific gravity was preferred to the usual method, observing the weight lost by a lump of glass when suspended in water; for Mr Gilpin had been enabled, by means of this nice balance, to discover, even in pure water and in alcohol, a want of perfect fluidity. Something like viscosity rendered the motion of a lump of glass through the liquor sensibly sluggish, so that when the balance was brought to a level, there was not a perfect equilibrium of weights: (See what we have said of this matter in Specific Gravity). Mr Gilpin also tried the ingenious instrument proposed for such experiments by Mr Ramsden, and described by him in a pamphlet on this very subject; and he found the anomalies of experiment much greater than in this method by weighing.—Indeed the regular progression of weights to be seen in the annexed tables is an unquestionable proof of the sufficiency of the method; and it has the evident advantage of all other methods in point of simplicity and practicability without any uncommon apparatus. Any person possessed of a good ordinary balance and a set of exact weights may examine all questions of this kind, by weighing pure water and the liquor which he may have occasion to examine in a common 6 or 8 ounce phial. For this reason, it is recommended (in preference to all hydrometers) to the board of excise to provide this simple apparatus in every principal office.
Every experiment was made at least three times; and the mean result (which never differed one grain from the extreme) was taken.
From these experiments the annexed tables were constructed. The first is the simple abstract of the experiments, containing the weights of the contents of the bottle of every mixture. The second contains the specific gravities deduced from them.
We have said that the experiments appear surprisingly accurate. This we say on the authority of the regular progression of the specific gravity in any of the horizontal rows. In the series, for instance, for the temperature 60°, the greatest anomaly is in the mixture of 50 parts of spirit with 100 of water. The specific gravity is 9.5804, wanting 3 or 4 of the regular progression. This does not amount to 1 in 18000. ### TABLE I.—Weights at the different Degrees of Temperature.
| Heat | Grains | Grains | Grains | Grains | Grains | Grains | Grains | Grains | Grains | Grains | Grains | Grains | |------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------| | 30 | 2487.35 | 2519.92 | 2548.42 | 2573.80 | 2596.64 | 2617.30 | 2636.23 | 2653.73 | 2669.83 | 2684.74 | 2698.51 | 2711.42 | | 35 | 2480.87 | 2513.43 | 2541.84 | 2567.02 | 2590.16 | 2610.87 | 2629.92 | 2647.47 | 2663.64 | 2678.09 | 2692.43 | 2705.14 | | 40 | 2474.30 | 2506.75 | 2535.41 | 2560.74 | 2583.66 | 2606.45 | 2625.30 | 2641.08 | 2657.23 | 2672.30 | 2686.32 | 2698.94 | | 45 | 2467.62 | 2500.14 | 2528.75 | 2554.09 | 2577.10 | 2597.98 | 2617.03 | 2634.64 | 2650.87 | 2666.04 | 2679.99 | 2692.77 | | 50 | 2460.75 | 2493.63 | 2521.90 | 2547.47 | 2570.42 | 2591.38 | 2610.45 | 2628.21 | 2644.43 | 2659.15 | 2673.64 | 2686.54 | | 55 | 2453.80 | 2486.37 | 2515.03 | 2540.60 | 2563.64 | 2584.56 | 2603.60 | 2621.62 | 2638.76 | 2653.90 | 2667.14 | 2679.98 | | 60 | 2447.00 | 2479.55 | 2508.27 | 2533.83 | 2556.90 | 2577.95 | 2597.97 | 2615.73 | 2633.17 | 2648.53 | 2662.60 | 2675.35 | | 65 | 2440.12 | 2472.75 | 2501.53 | 2526.99 | 2552.50 | 2572.71 | 2592.59 | 2610.95 | 2628.42 | 2643.75 | 2658.55 | 2671.55 | | 70 | 2433.23 | 2465.85 | 2494.50 | 2520.03 | 2543.32 | 2564.47 | 2583.88 | 2601.67 | 2617.96 | 2633.32 | 2647.52 | 2660.63 | | 75 | 2426.23 | 2458.87 | 2487.62 | 2513.08 | 2536.39 | 2557.01 | 2576.93 | 2594.82 | 2611.10 | 2626.55 | 2640.81 | 2653.99 | | 80 | 2419.02 | 2451.67 | 2480.45 | 2506.08 | 2529.24 | 2550.50 | 2569.86 | 2587.93 | 2604.29 | 2619.72 | 2633.99 | 2647.17 | | 85 | 2411.92 | 2444.63 | 2473.33 | 2499.01 | 2522.29 | 2543.54 | 2563.01 | 2580.93 | 2597.45 | 2613.02 | 2627.39 | 2640.60 | | 90 | 2404.90 | 2437.62 | 2466.32 | 2487.42 | 2510.80 | 2532.40 | 2552.49 | 2570.43 | 2587.95 | 2604.32 | 2618.70 | 2633.37 | | 95 | 2397.68 | 2430.33 | 2459.13 | 2478.47 | 2501.85 | 2523.60 | 2543.69 | 2561.63 | 2579.07 | 2595.59 | 2610.37 | 2624.94 | | 100 | 2390.60 | 2423.22 | 2452.13 | 2477.16 | 2500.91 | 2522.30 | 2541.92 | 2559.96 | 2576.50 | 2592.14 | 2606.50 | 2621.97 |
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**Note:** The table provides weights in grains for various degrees of temperature, with columns for pure spirit, water, and combinations of both. Each row corresponds to a specific degree of heat, and each column represents different quantities of spirit and water. ### TABLE II.—Real specific Gravities at the different Temperatures.
| Heat | The pure spirit. | 100 grains of spirit to 5 grains of water. | 100 grains of spirit to 10 grains of water. | 100 grains of spirit to 25 grains of water. | 100 grains of spirit to 35 grains of water. | 100 grains of spirit to 45 grains of water. | 100 grains of spirit to 50 grains of water. | 100 grains of spirit to 55 grains of water. | 100 grains of spirit to 64 grains of water. | |------|-----------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------| | deg. | | | | | | | | | | | 30 | 83896 | 84995 | 85957 | 86825 | 87585 | 88282 | 88921 | 89511 | 90054 | 90558 | 91023 | 91449 | 91847 | 92217 | | 35 | 83672 | 84769 | 85729 | 86587 | 87357 | 88059 | 88701 | 89294 | 89839 | 90345 | 90811 | 91241 | 91640 | 92009 | | 40 | 83445 | 84539 | 85457 | 86361 | 87134 | 87838 | 88481 | 89073 | 89617 | 90127 | 90596 | 91026 | 91428 | 91799 | | 45 | 83214 | 84310 | 85277 | 86131 | 86907 | 87613 | 88255 | 88849 | 89396 | 89929 | 90380 | 90812 | 91211 | 91584 | | 50 | 82977 | 84076 | 85042 | 85902 | 86676 | 87384 | 88030 | 88626 | 89174 | 89684 | 89958 | 90367 | 90768 | 91144 | | 55 | 82736 | 83834 | 84802 | 85664 | 86441 | 87150 | 87796 | 88393 | 88945 | 89458 | 89933 | 90307 | 90768 | 91144 | | 60 | 82500 | 83599 | 84568 | 85430 | 86198 | 86861 | 87508 | 88106 | 88654 | 89160 | 89596 | 89997 | 90370 | 90768 | | 65 | 82262 | 83362 | 84334 | 85193 | 85967 | 86638 | 87287 | 87837 | 88390 | 88896 | 89349 | 89707 | 90144 | 90527 | 90927 | | 70 | 82023 | 83124 | 84092 | 84851 | 85619 | 86286 | 86937 | 87486 | 88038 | 88545 | 88996 | 89392 | 89790 | 90194 | 90507 | | 75 | 81780 | 82878 | 83651 | 84416 | 85184 | 85852 | 86501 | 87050 | 87599 | 88148 | 88598 | 88998 | 89398 | 89793 | 90193 | 90502 | | 80 | 81530 | 82631 | 83406 | 84172 | 84940 | 85608 | 86267 | 86816 | 87365 | 87914 | 88364 | 88798 | 89203 | 89603 | 90002 | 90401 | | 85 | 81283 | 82386 | 83155 | 83922 | 84690 | 85358 | 86017 | 86566 | 87115 | 87664 | 88114 | 88564 | 88994 | 89394 | 89794 | 90194 | 90502 | | 90 | 81030 | 82142 | 82811 | 83579 | 84347 | 85015 | 85674 | 86233 | 86782 | 87331 | 87880 | 88330 | 88760 | 89160 | 89559 | 90000 | 90400 | | 95 | 80788 | 81888 | 82556 | 83324 | 84092 | 84760 | 85429 | 86088 | 86637 | 87186 | 87735 | 88284 | 88734 | 89134 | 89534 | 90000 | 90400 | | 100 | 80543 | 81643 | 82312 | 83080 | 83848 | 84516 | 85185 | 85844 | 86493 | 87042 | 87591 | 88140 | 88689 | 89139 | 89539 | 90000 | 90400 |
---
**Note:** The table provides specific gravities for various temperatures and quantities of spirit and water. Each row corresponds to a different temperature in degrees, and each column represents a different quantity of spirit relative to water. The values are given as decimals. We formerly observed, that the series of mixtures chosen by Sir Charles Blagden, for the advantages attending it in making the experiment, was not suited for solving the questions which commonly occur in the spirit business. He accordingly suggests the propriety of forming tables in a convenient series from the data furnished by these experiments, indicating the proportion of ingredients contained in some constant weight or bulk.
To facilitate the construction of such tables, it is necessary to consider the subject in the most general manner. Therefore let \(a\) represent the constant number 100. Let \(w\) and \(s\) represent the quantities of water and spirit by weight in any mixture; that is, the pounds, ounces, or grains of each. Let \(x\) represent the quantity per cent. of spirits also by weight; that is, the number of pounds of spirits contained in 100 pounds of the mixture; and let \(y\) be its quantity per cent. in gallons, or the number of gallons contained in 100 gallons of the unmixed ingredients. Let \(m\) be the bulk of a pound of spirit of any given temperature, the bulk of a pound of water of the same temperature being accounted 1.
Then \(w + s\) is the weight of any mixture, and \(w + ms\) is its bulk.
We have the following proportions:
\[ \frac{w}{w + s} = \frac{a}{x}, \quad \text{and} \quad x = \frac{as}{w + s} \quad \text{(Equation 1st);} \]
and hence \(s\) may be found when \(x\) the percentage in weight is given, for
\[ s = \frac{w}{a - x} \quad \text{(Equation 2nd.)} \]
\[ \frac{w + ms}{ms} = \frac{a}{y}, \quad \text{and} \quad y = \frac{ms}{w + ms} \quad \text{(Equation 3rd.)} \]
\(y\) may be found when \(y\) the percentage in gallons, is given; for
\[ s = \frac{my}{a - y} \quad \text{(Equation 4th.)} \]
The usual questions which can be solved from these experiments are,
1. To ascertain the quantity of spirits per cent. in bulk from observation of the specific gravity, or to tell how many gallons of spirit are in 100 gallons of mixture.
Look for the specific gravity in the table, and at the head of the column will be found the \(w\) and \(s\) corresponding. If the precise specific gravity observed is not in the tables, the \(s\) must be found by interpolation. And here it is proper to remark, that taking the simple proportional parts of specific gravity will not be sufficiently exact, especially near the beginning or the end of the table, because the densities corresponding to the series of mixtures do not change uniformly. We must have recourse to the general rules of interpolation, by means of first and second differences, or be provided with a subsidiary table of differences. A good deal of practice in computations of this kind suggested the following method of making such interpolations with great dispatch and abundant accuracy. On a plate of wood, or metal, or stiff card-paper, draw a line EF (fig. 3.), as a scale of equal parts, representing the leading or equable arithmetical series of any table. (In the present case EF is the scale on which \(s\) is computed.) Through every point of division draw the perpendiculars BA, EC, FD, &c. Make one of them AB more conspicuous than the rest, and distinguish the others also in such sort, that the eye shall readily catch their Spirituous distance from the principal line A B. Let GPL be a thin slip of whalebone, of uniform breadth and thickness, also divided into equal parts properly distinguishable. Lastly, let there be a pin P fixed near the middle of the principal line A B.
Now suppose that a value of \(s\) is to be interpolated by means of an observed specific gravity not in the table. Look for the nearest to it, and note its distance from the preceding and the following. Let these be PH and PK on the flexible scale. Also take notice of the lines K 10 and H 10, whose distances from A B are equal to the constant difference between the successive values of \(S\), or to any easily estimated multiple of it (as in the present case we have taken 10 and 10, instead of 5 and 5, the running difference of Sir Charles Blagden's table). Then, leaning the middle point P of the whalebone on the pin P in the board, bend it, and place it slantwise till the points K and H fall somewhere on the two parallels K 10 and H 10. No matter how oblique the position of the whalebone is. It will bend in such a manner that its different points of division (representing different specific gravities) will fall on the parallels which represent the corresponding values of \(s\). We can say that all this may be done in less than half a minute, and less time than is necessary for inspecting a table of proportional parts, and not the tenth part of that necessary for interpolating by second differences. Yet it is exact enough (if of the size of a duodecimo page) for interpolating three decimal places. This is ten times more exact than the present case requires. To return from this digression.
Having thus found \(s\) in the table, we get \(x\) or \(y\) by the equations
\[ \frac{as}{w + s} = x, \quad \text{and} \quad \frac{ms}{w + ms} = y. \]
But here a material circumstance occurs. The weight of alcohol \(s\), and its percentage \(x\), was rightly determined by the specific gravity, because it was interpolated between two values, which were experimentally connected with this specific gravity. But in making the transition from \(x\) to \(y\), we only give the percentage in gallons before mixture, but not the number of gallons of alcohol contained in an hundred gallons of mixed liquor. For when we have taken \(a - y\) and \(y\) instead of \(w\) and \(s\), they will indeed make a similar compound when mixed, because the proportion of their ingredients is the same. But they will not make 100 gallons of this compound, because there is a shrinking or condensation by mixture, and the specific gravity by which we interpolated \(s\) is the physical or real specific gravity corresponding to \(w\) and \(s\); while \(\frac{w + s}{w + ms}\), the specific gravity implied in the value of \(y\), is the mathematical density independent on this condensation. Since therefore \(y\), together with \(a - y\), make less than 100 gallons of the compound, there must in 100 gallons of it be more alcohol than is expressed by \(y\).
Let \(G\) be the mathematical specific gravity \((= \frac{w + s}{w + ms})\), and \(g\) the physical or real observed specific gravity (which we cannot express algebraically); and let \(z\) be the gallons of alcohol really contained in 100 gallons of the compound. The bulk being inversely as the density or specific gravity, it is evident that the SPI
Spirituous bulk of the compound must be to 100 gallons as \( g \) to Liquors. \( G \). And since we want to make it still up to 100 gallons, we must increase it in the proportion of \( G \) to \( g \). And because this augmentation must be of the same strength with this contracted liquor, both ingredients must be increased in the proportion of \( G \) to \( g \), and we must have \( G : g = y : z \), and \( z = g \times \frac{y}{G} \). Now, instead of \( y \), write \( a \frac{m s}{w + m s} \), and instead of \( \frac{1}{G} \) write \( \frac{w + m s}{w + s} \), which are respectively equal to them. This gives us \( z = g \times \frac{w + m s}{w + s} \times \frac{m s}{w + s} = g \times \frac{m s}{w + s} \).
All this will be illustrated by an example.
Suppose that we have observed the specific gravity of a spirituous liquor of the temperature 60° to be 0.94128. Looking into Sir Charles Blagden's table, we find the gravities 0.94018 and 0.94296, and the corresponding to them is 80 and 75, the water in each mixture being 100. By interpolation we obtain the \( s \) corresponding to 0.94128, viz., 78. At this temperature \( m = \frac{1}{0.825} = 1,212.12 \), and \( ms = 9454545 \). Therefore \( z = 0.94128 \times 100 \times \frac{9454545}{19454545} = 49,997 \), or very nearly 50.
We have seen even persons not unacquainted with subjects of this kind puzzled by this sort of paradox. \( z \) is said to be the percentage of spirit in the compound. The compound has the same proportion of ingredients when made up to 100 gallons as before, when \( y \) was said to be its percentage, and yet \( y \) and \( z \) are not the same. The fact is, that although \( z \) is the number of gallons of alcohol really contained in 100 gallons of the compound, and this alcohol is in the same proportion as before to the water, this proportion is not that of 50 to 50; for if the ingredients were separated again, there would be 50 gallons of alcohol and 52,876 of water.
The proportion of the ingredients in their separate state is had by the 3d Equation \( y = a \frac{m s}{w + m s} \), which is equivalent to \( G a \frac{m s}{w + s} \). For the present example \( y \) will be found 48,599, and \( a - y \), or the water percent. 51,401, making 100 gallons of unmixed ingredients. We see then that there has been added 1,398 gallons of alcohol; and since both ingredients are augmented in the proportion of \( G \) to \( g \), there have also been added 1,478 of water, and the whole addition for making up the 100 gallons of compound is 2,876 gallons; and if the ingredients of the compound were separate, they would amount to 102,876 gallons. This might have been found at the first, by the proportion, \( G : g - G = 100 \): (The addition.)
The next question which usually occurs in business, is to find what density will result from any proposed mixture per gallon. This question is solved by means of the equation \( \frac{w y}{m(a-y)} = s \). In this examination it will be most convenient to make \( w = a \). If the value of \( s \) found in this manner falls on a value in the tables, we have the specific gravity by inspection. If not, we must interpolate.
N.B. The value of \( m \), which is employed in these reductions, varies with the temperature. It is always obtained by dividing the specific gravity of alcohol of that temperature by the specific gravity of water of the same temperature. The quotient is the real specific gravity of alcohol for that temperature. Both of these are to be had in the first and last compartments of Sir Charles Blagden's table.
These operations for particular cases give the answers to particular occasional questions. By applying them to all the numbers in the table, tables may be constructed for solving every question by inspection.
There is another question which occurs most frequently in the excise transactions, and also in all compositions of spirituous liquors, viz. What strength will result from a mixture of two compounds of known strength, or mixing any compound with water? To solve questions of this kind by the table so often quoted, we must add into one sum the water per gallon of the different liquors. In like manner, take the sum of the spirits, and say, as the sum of the waters is to that of the alcohols, so is \( a \) to \( s \); and operate with \( a \) and \( s \) as before.
Analogous to this is the question of the duties. These are levied on proof spirit; that is, a certain duty is charged on a gallon of proof spirit; and the gauger's business is to discover how many gallons of proof spirit there is in any compound. The specification of proof spirit in our excise laws is exceedingly obscure and complex. A gallon weighing 7 pounds 13 ounces (at 55°) is accounted 1 to 6 under proof. The gallon of water contains 58476 grains, and this spirit is 54688. Its density therefore is 0.93523 at 55°, or (as may be inferred from the table) 0.9335 at 60°. This density corresponds to a mixture of 100 grains of water with 93,457 of alcohol. If this be supposed to result from the mixture of 6 gallons of alcohol with 1 of water (as is supposed by the designation of 1 to 6 under proof), the gallon of proof spirits consists of 100 parts of spirits by weight, mixed with 75 parts of water. Such a spirit will have the density 0.9162 nearly.
This being premised, in order to find the gallons of proof spirits in any mixture, find the quantity of alcohol by weight, and then say, as 100 to 175, so is the alcohol in the compound to the proof spirit that may be made of it, and for which the duties must be paid.
We have considered this subject at some length, because it is of great importance in the spirit-trade to have these circumstances ascertained with precision; and because the specific gravity is the only sure criterion that can be had of the strength. Firing of gunpowder, or producing a certain bubble by shaking, are very vague tests; whereas, by the specific gravity, we can very securely ascertain the strength within one part in 500, as will presently appear.
Sir Charles Blagden, or Mr Gilpin, have published a most copious set of tables, calculated from these valuable experiments. In these, computations are made for every unit of the hundred, and for every degree of the thermometer. But these tables are still not in the most commodious form for business. Mr John Wilson, an ingenious gentleman residing at Dundee, has just pub- ### The Alphabet with the Double and Triple Consonants
| Let. Char. | Arb. Abbrev. | D.C.& Char. | Arb. Abbrev. | |------------|--------------|-------------|--------------| | a | a, an, above | ab | each, such | | b | be, by, because | sb | shall, she' | | c | | lb | that, they | | d | de, did | thr | therefore | | e | ever, every, mid | str | strive, strong | | f | from, if | mb | who, which | | g | God, give, gives | | | | h | he, had, his | | | | i | I, eye, below | | | | j | king, know | | | | k | Lord, will, all | | | | l | me, my, most | | | | m | and, in, nature | | | | n | O, oh, ove, above | | | | o | people, peace | | | | p | by, quest, quantity | | | | q | or, are | | | | r | us, us, soon | | | | s | the, to, it | | | | t | have, save | | | | u | you, view, middle | | | | v | we, with | | | | w | except, example | | | | x | ye, your, yes, bel | | | | y | | | | | z | | | |
### Vowels Places
| a | e | i | o | u | y | |---|---|---|---|---|---|
### Prepositions and Terminations
| Prepos. | Char.Ex. | Signifi. | Term.Char.Ex. | Signifi. | |---------|----------|----------|---------------|----------| | abs obs | c | abstain | able, ble | stable | | anti ante | | antidote | flit | flext | | anta | | | | conflict | | contr i-a | | | | conflict | | contro | | | | conflict | | counter | | | | conflict | | dis-incom | | | | conflict | | hyp-o-er | | | | conflict | | magn-i-a | | | | conflict | | multi | | | | conflict | | omni | | | | conflict | | inter-ro | | | | conflict | | enter | | | | conflict | | post | | | | conflict | | preter | | | | conflict | | recon | | | | conflict | | recom | | | | conflict | | satis | | | | conflict | | super | | | | conflict | | trans | | | | conflict | | ext-er-in | | | | conflict | | extra | | | | conflict |
### Arbitrariess
- on one - as - for - only - of oft often - nothing - at am - wherefore
### Figures
1 2 3 4 5 6 7 8 9 0
### Points
- A Comma - A Semicolon ; - A Colon - A Period / - A Point of Interrogation ? - A Point of Admiration !
### Abbreviating Marks
- A Substantive - An Adjective - A Verb - A Participle
### Division
- Divisible - Divide - Dividing
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The LORDS Prayer:
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A.Bell Print.Walshapton fecit. 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 4th 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 composition, 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 5277 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.
| Brine | Water (grains) | Salt (grains) | |-------|---------------|--------------| | 8th | 3770 | 1257 | | 9th | 4156 | 157 | | 10th | 4218 | 198 |
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 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 brine the space left for the portion of salt is continually diminishing. In the first dilution 5277 grains of water were added to fill up the vessel; but $\frac{1}{8}$th of its contents of pure water is only 525; so that here is a diminution of 2$\frac{1}{4}$ grains in the space occupied by the remaining salt. The subsequent additions are 6047; 7065; 847; 10545; 1405; 2102; 21055; 2102; 2102; instead of 600; 700; 840; 1050; 1400; 2100; 2100; 2100; 2100. Nothing can more plainly show 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 six 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 scrupulous 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 Watson'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 flour; but the two together occupy less room than when separate. The experiments of Mr Achard were insufficient for a decision, because made on so small a quantity as 600 grains of water. Dr Watson'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... taining 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 greater 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 lye for the purposes of bleaching or soap-making, whose specific gravity is 1.234, or exceeds that of water by 23.4%, 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 7 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.
| Weight Cub. Ft. Brine | Salt in Cub. Ft. | Weight Cub. Ft. Brine | Salt in Cub. Ft. | |-----------------------|-----------------|----------------------|-----------------| | 1,000 | 0 | 1,115 | 170 | | 1,008 | 10 | 1,122 | 180 | | 1,015 | 20 | 1,129 | 190 | | 1,022 | 30 | 1,134 | 200 | | 1,029 | 40 | 1,140 | 210 | | 1,036 | 50 | 1,147 | 220 | | 1,043 | 60 | 1,153 | 230 | | 1,050 | 70 | 1,159 | 240 | | 1,057 | 80 | 1,165 | 250 | | 1,064 | 90 | 1,172 | 260 | | 1,070 | 100 | 1,178 | 270 | | 1,077 | 110 | 1,184 | 280 | | 1,083 | 120 | 1,190 | 290 | | 1,090 | 130 | 1,197 | 300 | | 1,096 | 140 | 1,203 | 310 | | 1,103 | 150 | 1,209 | 316 | | 1,109 | 160 | 1,215 | 320 |
The table differs considerably from Mr Lambert's. The quantities of salt corresponding to any specific gravity are about 1/8th 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 1/8ths of all the bitter salts. Our aim being to ascertain the quantities of pure sea-salt, and to learn by the by 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 65°, 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 deposits 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 1/8th 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 1.240, we must increase it by 20 (half of 40); and having found the strength 240 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-salt in comparison with other salts. We presume that our readers are apprised of this peculiarity of sea-salt, 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 dryest sea salt, 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 \( \frac{340}{1000} = x : \frac{1000}{340} x \). This is the bulk to which every cubic foot (valued at 1000) must be boiled down. Thus suppose the brine has the specific gravity 1199. 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 assures 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 magnesia salts) though moistened with 1 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 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 \( 290 \times \frac{1197}{1190} \), or 291\(\frac{1}{2}\) ounces, and there is 8\(\frac{1}{2}\) 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 lixivias. We shall not therefore refuse them, but simply give another table or two of such as are most interesting. Of those alkaline leys are the chief, being of extensive use in bleaching, soap-making, glats-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 3549 grams 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 4200 grams of water held 6165 of this ley when of the temperature 55°. Its specific gravity was therefore 1.4678, and the 6165 grams of ley contained 3264 grain of salt. We examined its specific gravity in different flutes of dilution, till we came to a brine containing 51 grams of salt, and 4180 grams of water, and the contents of the flask weighed 4240 grams: 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.
| Weight of Cub.Foot | Salt cont. oz. | Weight of Cub.Foot | Salt cont. oz. | Weight of Cub.Foot | Salt cont. oz. | |-------------------|---------------|-------------------|---------------|-------------------|---------------| | 1000 | 0 | 1224 | 340 | 1417 | 680 | | 1016 | 20 | 1236 | 360 | 1428 | 700 | | 1031 | 40 | 1248 | 380 | 1438 | 720 | | 1045 | 60 | 1259 | 400 | 1449 | 740 | | 1058 | 80 | 1270 | 420 | 1460 | 760 | | 1071 | 100 | 1281 | 440 | 1471 | 780 | | 1084 | 120 | 1293 | 460 | 1482 | 800 | | 1098 | 140 | 1305 | 480 | 1493 | 820 | | 1112 | 160 | 1317 | 500 | 1504 | 840 | | 1125 | 180 | 1329 | 520 | 1515 | 860 | | 1138 | 200 | 1340 | 540 | 1526 | 880 | | 1150 | 220 | 1351 | 560 | 1537 | 900 | | 1162 | 240 | 1362 | 580 | 1547 | 920 | | 1174 | 260 | 1372 | 600 | 1557 | 940 | | 1187 | 280 | 1384 | 620 | 1567 | 960 | | 1200 | 300 | 1395 | 640 | 1577 | 980 | | 1212 | 320 | 1406 | 660 | 1586 | 1000 | 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 800 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 845 ounces of salt; its density is therefore
\[ \frac{318}{845} = 0.379 \]
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 sal 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 lay 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 interstices of the other, "ou ils se nichent, en augmentant le poids sans affecter le volume de la soumure," as Eller and Lambert express themselves, is impossible here, when both are fluids. Indeed it is but a slovenly way of 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 \( \frac{1}{4} \) th 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 314 oz. 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 absorption 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 refer too 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
\[ \frac{1698 \times 960}{4466} = 365 \text{ grains of salt.} \]
The specific gravity was
\[ \frac{1698}{1600} = 1.061, \]
and the cubic foot weighed 1061 ounces. It also contained
\[ \frac{1061 \times 365}{1698} = 228 \text{ ounces of salt.} \]
By repeated abstraction of brine, and replacing with water, we had the following series:
| Series | Brine | Sp. Gr. | Oz. Salt | |--------|-------|---------|----------| | Weight of brine, | 1/8, 1698 | 1.061 | 228 | | After taking out | 2/8, 1676 | 1.048 | 174 | | After taking out | 3/8, 1653 | 1.033 | 114 | | After taking out | 4/8, 1630 | 1.019 | 57 | | After taking out | 5/8, 1616 | 1.010 | 28 | | 1/2, 1610 | 1.0063 | 14 | | 1/2, 1605 | 1.0038 | 7 |
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.
| Substance | Specific Gravity | |-----------|-----------------| | Borax | 1.010 | | Cor. Sublim. | 1.037 | | Alum | 1.033 | | Glaub. Salt | 1.054 | | Common Salt | 1.098 | | Sal. cath. amar. | 1.232 | | Sal. ammon. | 1.072 | | Vol. alk. mite | 1.087 | | Nitre | 1.095 | | Rochelle salt | 1.114 | | Blue vitriol | 1.150 | | Green vitriol | 1.157 | | White vitriol | 1.286 | | Pearl ash | 1.534 |