SPIRITUOUS LIQUORS have in all nations been considered as a proper subject of heavy taxation for the support of the state. This has naturally occasioned a nice examination of their strength. It having been at last found that this was intimately connected with the specific gravity, this has been examined with the most scrupulous attention to every circumstance which could affect it, so that the duties might be exactly proportioned to the quantity of spirit in any strong liquor, independent on every other circumstance of flavour or taste, or other valued quality. The chemist at last found that the basis of all strong liquors is the same, produced by the vinous fermentation of pure saccharine matter dissolved in water. He also found, that whether this vegetable salt be taken as it is spontaneously formed in the juices of plants and fruits, or as it may be formed or extracted from farinaceous fruits and roots by a certain part of the process of vegetation, it produces the same ardent spirit, which has always the same density in every mixture with water. The minute portions of aromatic oils, which are in some degree inseparable from it, and give it a different flavour according to the substance from which it was obtained, are not found to have any sensible effect on its density or specific gravity. This seems very completely established in consequence of the unwearyed attempts of the manufacturers to lessen the duties payable on their goods by mixtures of other substances, which would increase their density without making them less palatable. The vigilance of the revenue officers was no less employed to detect every such contrivance. In short, it is now an acknowledged point, that the specific gravity is an accurate test of the strength.
But though this is true in general, we cannot derive much benefit from it, unless we know the precise relation between the strength and the density of a spirituous liquor. Do they increase pari passu, or by what law Spirituous law are they connected? It was natural to expect that equal additions of ardent spirits or alcohol to a given quantity of water would produce equal diminutions of density. Areometers were accordingly made on this principle above 200 years ago, as may be seen in the works of Gaspar Schottus, Sturmius, Agricola, and other old authors. But when mathematical physics became more generally known, this was easily discovered to be erroneous; and it was shown (we think first by Mr Boyle) that equal additions to the specific gravity would be produced by successively taking out of any vessel a certain measure of alcohol and replacing it with an equal measure of water. This was the most convenient discovery for all parties, because then the duties payable on a cask of spirits would be in the exact proportion of the diminution of its density. But it was soon found by those who were appointed guardians of the revenue that this conclusion was erroneous, and that a mixture which appeared by this rule to contain 35 gallons of alcohol did really contain 35½. They found by actually making such a mixture: 18 gallons of alcohol mixed with 18 of water produced only 35 gallons of spirits. The revenue officers, finding that this condensation was most remarkable in mixtures of equal parts of water and the strongest spirits which could then be procured, determined to levy the duties by this mixture; because, whether the spirituous liquor was stronger or weaker than this, it would appear, by its specific gravity, rather stronger than it really was. This sagacious observation, and the simplicity of the composition, which could at all times be made for comparison, seem to be the reasons for our excise offices selecting this mode of estimating the strength and levying the duties. A mixture of nearly equal measures of water and alcohol is called proof spirit, and pays a certain duty per gallon; and the strength of a spirituous liquor is estimated by the gallons, not of alcohol, but of proof spirit which the cask contains. But because it might be difficult to procure at all times this proof spirit for comparison, such a mixture was made by order of the board of excise: and it was found, that when five gallons of it was mixed with one gallon of water, a wine gallon of the mixture weighed 7 pounds 13 ounces avoirdupois. The board therefore declared, that the spirituous liquor of which the gallon weighed 7 pounds 13 ounces should be reckoned 1 to 6 or 1 in 7 under proof. This is but an awkward and complex formula; it was in order to suit matters to a mode of examination which had by time obtained the sanction of the board. Mr Clarke, an ingenious artist of that time, had made a hydrometer incomparably more exact than any other, and constructed on mathematical principles fit for computation. This had a set of weights corresponding to the additions of water or proof spirit, and the mixture 1 to 6 or 1 in 7 was the only one which weighed an exact number of ounces per gallon without a fraction.
Thus stands the excise law; and Clarke's hydrometer is still the instrument of authority, although others have been since constructed by Dicas, Quin, and others, which are much more ingenious and convenient. The mathematician who examines Dicas's hydrometer, with its sliding scale, by which it is adjusted to the different temperatures, and points out the condensations, will perceive a beautiful and sagacious combination of quantities, which he will find it difficult to bring under any analytical formula. Perhaps Quin's may have some preference in respect of convenience; but facile inventis addere. Mr Dicas's was originally (A).
As naturalists became more accustomed to exact observations in every topic of inquiry, the condensation which obtains in the mixture of different substances became more familiarly known. This evidently affects the present question; and both the excise and the distillers are interested in its accurate decision. This occasioned an application to the Royal Society; and a most scrupulous examination of the strength of spirituous liquors was made by Sir Charles Blagden and Mr Gilpin, of which they have given a very particular account in the Philosophical Transactions for 1792 and 1793.
We have taken notice of this in the article Specific Gravity, mentioning such circumstances of the results as fitted our purposes of physical discussion. At present,
(A) Among the various contrivances which have been thought of, among manufacturers and dealers, as well as for the purposes of revenue, for ascertaining the specific gravity, and consequently the real strength and value of high-priced and high-taxed liquids, we are persuaded there is none equal, in point of accuracy, simplicity, and facility of application, to the areometrical beads lately announced to the public by Mrs Lovi of Edinburgh, under the privilege of a patent; and with this persuasion we have no hesitation in recommending them to those to whom the use of a simple and accurate instrument is of great importance in determining the value of high-priced spirituous liquors. Our recommendation rests not solely on our own opinion, but is supported by that of others who are well acquainted with such subjects. We know, too, that the beads have been examined and compared by several intelligent manufacturers and dealers with some of the most accurate hydrometrical instruments, and after a fair trial, a decided preference has been given to the beads. The whole apparatus consists of 30 beads, a sliding rule, a thermometer, a glass jar and brass hook, which are packed in a neat small box; and it is accompanied with directions, which point out, 1. In what manner the real strength of spirits may be ascertained at any given temperature between 40° and 80°; 2. How much per cent. the spirit to be tried is over or under proof according to the practice of spirit-dealers; and, 3. The proportion of water and the strongest spirits or alcohol, according to the views and language of excisemen. The advantages of these beads are, that being made of a substance which is little acted on by chemical agents, they are less liable to be injured by use, than instruments composed of metal; and when a bead happens to be broken, it can be easily replaced. They possess this farther advantage, that with the application of the thermometer, and the calculation of the sliding rule, the real strength of the spirits may be taken at all temperatures. It has been suggested, that these beads, from their being less liable to change than other instruments, might be usefully employed in checking the errors and variations of other hydrometers. Beads are prepared by Mrs Lovi on the same principle for ascertaining the strength of worts, acids, &c., Spiritous sent we give the general result in the table of specific gravity, as peculiarly belonging to spiritous 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 different 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 examiner to operate at ease. The first and last compartments 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 spiritous 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 so kept, it expands instead of contracting; while cooling down from 35° or thereabouts, and as it approaches to 30°, 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 | Bulk of 1000 ounces | |------|-------------------| | | Of Water | Diff. | Of Alcohol | Diff. | | 30° | | | | | | 35 | 99910 | 4 | 119195 | 319 | | 40 | 99976 | 8 | 119514 | 325 | | 45 | 99914 | 18 | 119839 | 332 | | 50 | 99932 | 30 | 120172 | 342 | | 55 | 99902 | 38 | 120514 | 348 | | 60 | 100000 | 50 | 120868 | 350 | | 65 | 100050 | 56 | 121212 | 355 | | 70 | 100106 | 64 | 121565 | 353 | | 75 | 100170 | 71 | 121919 | 354 | | 80 | 100241 | 79 | 122279 | 360 | | 85 | 100320 | 84 | 122645 | 366 | | 90 | 100404 | 96 | 123017 | 372 | | 95 | 100500 | 108 | 123393 | 376 | | 100 | 100608 | 128 | 123773 | 380 |
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 let by, for at least a month, that the mixture and the whole process of condensation might be completed. The same method SPI
Spirits 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 sensitive, 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 1/50th 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 95804, 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 | The pure Spirit. | 100 grains of spirit to 5 grains of water. | 100 grains of spirit to 15 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 55 grains of water. | 100 grains of spirit to 65 grains of water. | |------|-----------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------|------------------------------------------| | deg. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | | 30 | 2487.35 | 2519.92 | 2548.42 | 2566.66 | 2617.30 | 2636.23 | 2655.73 | | 35 | 2480.87 | 2513.43 | 2541.84 | 2560.74 | 2610.87 | 2629.92 | 2647.47 | | 40 | 2474.30 | 2506.75 | 2535.41 | 2550.16 | 2604.18 | 2623.56 | 2641.08 | | 45 | 2467.62 | 2500.14 | 2528.75 | 2544.00 | 2597.98 | 2617.03 | 2634.64 | | 50 | 2460.75 | 2493.33 | 2521.96 | 2547.47 | 2570.42 | 2591.38 | 2610.54 | | 55 | 2453.80 | 2480.37 | 2515.23 | 2540.60 | 2533.64 | 2583.05 | 2561.80 | | 60 | 2447.00 | 2479.56 | 2508.27 | 2533.83 | 2556.90 | 2577.95 | 2597.22 | | 65 | 2440.12 | 2472.75 | 2501.53 | 2526.99 | 2551.24 | 2571.24 | 2590.55 | | 70 | 2433.23 | 2465.88 | 2494.56 | 2520.03 | 2543.32 | 2564.47 | 2583.88 | | 75 | 2426.23 | 2458.78 | 2487.62 | 2513.68 | 2536.39 | 2557.61 | 2576.93 | | 80 | 2419.02 | 2451.67 | 2480.45 | 2506.08 | 2529.24 | 2550.50 | 2569.86 | | 85 | 2411.92 | 2444.03 | 2473.33 | 2499.01 | 2522.29 | 2543.34 | 2536.11 | | 90 | 2404.90 | 2437.62 | 2466.32 | 2491.99 | 2515.28 | 2530.63 | 2524.02 | | 95 | 2397.68 | 2430.33 | 2459.13 | 2484.74 | 2508.10 | 2529.46 | 2519.43 | | 100 | 2390.60 | 2423.22 | 2452.13 | 2477.64 | 2500.91 | 2522.30 | 2541.92 |
| Heat | 100 grains of spirit to 75 grains of water. | 100 grains of spirit to 85 grains of water. | 100 grains of spirit to 95 grains of water. | 100 grains of spirit to 100 grains of water. | |------|--------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------| | deg. | Grains. | Grains. | Grains. | Grains. | | 30 | 2744.20 | 2753.75 | 2762.72 | 2771.08 | | 35 | 2738.13 | 2747.74 | 2756.94 | 2765.32 | | 40 | 2732.24 | 2741.86 | 2750.06 | 2759.50 | | 45 | 2726.09 | 2735.77 | 2744.82 | 2753.36 | | 50 | 2719.93 | 2729.61 | 2738.74 | 2747.47 | | 55 | 2713.60 | 2723.51 | 2732.64 | 2741.24 | | 60 | 2707.40 | 2717.30 | 2726.52 | 2735.17 | | 65 | 2701.05 | 2710.20 | 2719.26 | 2727.98 | | 70 | 2694.76 | 2701.64 | 2713.87 | 2722.75 | | 75 | 2688.14 | 2697.49 | 2707.49 | 2716.35 | | 80 | 2681.50 | 2696.94 | 2706.94 | 2715.76 | | 85 | 2674.95 | 2684.08 | 2694.53 | 2703.33 | | 90 | 2668.29 | 2678.49 | 2687.99 | 2696.91 | | 95 | 2661.51 | 2671.82 | 2681.34 | 2690.23 | | 100 | 2654.76 | 2664.99 | 2674.62 | 2683.63 |
| Heat | 60 grains of spirit to 100 grains of water. | 55 grains of spirit to 100 grains of water. | 50 grains of spirit to 100 grains of water. | 45 grains of spirit to 100 grains of water. | 40 grains of spirit to 100 grains of water. | 35 grains of spirit to 100 grains of water. | 30 grains of spirit to 100 grains of water. | 25 grains of spirit to 100 grains of water. | 20 grains of spirit to 100 grains of water. | 15 grains of spirit to 100 grains of water. | 10 grains of spirit to 100 grains of water. | 5 grains of spirit to 100 grains of water. | Water. | |------|--------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------| | deg. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | Grains. | | 30 | 2852.03 | 2859.71 | 2867.12 | 2874.43 | 2881.34 | 2887.77 | 2894.22 | 2900.85 | 2906.82 | 2917.10 | 2928.80 | 2944.53 | | 35 | 2847.45 | 2855.32 | 2863.16 | 2870.78 | 2878.21 | 2885.27 | 2892.07 | 2899.31 | 2905.47 | 2916.05 | 2928.09 | 2945.02 | | 40 | 2842.62 | 2850.88 | 2859.06 | 2867.08 | 2874.81 | 2882.30 | 2889.78 | 2897.61 | 2904.69 | 2916.41 | 2928.03 | 2945.25 | | 45 | 2837.64 | 2846.16 | 2854.67 | 2863.24 | 2871.22 | 2879.22 | 2887.33 | 2895.67 | 2904.99 | 2915.53 | 2923.39 | 2945.20 | | 50 | 2832.76 | 2841.52 | 2850.29 | 2858.06 | 2865.52 | 2873.58 | 2881.57 | 2889.58 | 2903.39 | 2914.42 | 2927.81 | 2944.73 | | 55 | 2827.68 | 2836.69 | 2845.72 | 2854.75 | 2863.75 | 2872.67 | 2881.60 | 2891.11 | 2901.42 | 2913.02 | 2926.73 | 2943.08 | | 60 | 2822.65 | 2831.90 | 2841.10 | 2850.50 | 2859.87 | 2869.15 | 2878.72 | 2888.62 | 2899.35 | 2911.32 | 2927.20 | 2942.08 | | 65 | 2817.49 | 2826.93 | 2836.30 | 2845.97 | 2855.65 | 2865.45 | 2875.49 | 2884.83 | 2897.20 | 2909.43 | 2927.33 | 2942.24 | | 70 | 2812.16 | 2821.78 | 2831.61 | 2841.42 | 2851.33 | 2861.63 | 2871.26 | 2882.60 | 2894.56 | 2907.33 | 2924.24 | 2940.13 | | 75 | 2806.75 | 2816.63 | 2826.36 | 2836.88 | 2847.14 | 2857.70 | 2868.49 | 2879.67 | 2891.79 | 2905.04 | 2920.17 | 2938.33 | | 80 | 2801.25 | 2811.23 | 2821.38 | 2831.92 | 2842.56 | 2853.18 | 2864.54 | 2876.22 | 2887.88 | 2892.35 | 2907.35 | 2931.77 | | 85 | 2795.69 | 2805.85 | 2816.32 | 2827.12 | 2838.07 | 2848.41 | 2858.60 | 2869.16 | 2882.25 | 2896.58 | 2912.84 | 2934.14 | | 90 | 2790.13 | 2800.40 | 2811.05 | 2821.25 | 2833.38 | 2844.81 | 2855.80 | 2866.58 | 2882.25 | 2898.44 | 2910.02 | 2932.19 | | 95 | 2784.36 | 2794.91 | 2805.79 | 2811.80 | 2823.53 | 2835.30 | 2848.18 | 2861.12 | 2875.07 | 2890.04 | 2906.97 | 2926.28 | | 100 | 2778.64 | 2789.32 | 2800.25 | 2811.80 | 2823.53 | 2835.30 | 2848.18 | 2861.12 | 2875.07 | 2890.04 | 2906.97 | 2926.28 | ### 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 15 grains of water | 100 grains of spirit to 20 grains of water | 100 grains of spirit to 25 grains of water | 100 grains of spirit to 30 grains of water | 100 grains of spirit to 35 grains of water | 100 grains of spirit to 40 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 60 grains of water | 100 grains of spirit to 65 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 | .89345 | .90027 | .90596 | .91026 | .91428 | .91799 | .92099 | | 40 | .83445 | .84539 | .85507 | .86361 | .87134 | .87838 | .88481 | .89127 | .89790 | .90380 | .90812 | .91211 | .91584 | .91979 | | 45 | .83214 | .84310 | .85277 | .86131 | .86907 | .87617 | .88255 | .88899 | .89569 | .90160 | .90596 | .91016 | .91370 | .91759 | | 50 | .82977 | .84076 | .85042 | .85902 | .86676 | .87384 | .88030 | .88666 | .89314 | .89984 | .90416 | .90837 | .91211 | .91584 | | 55 | .82736 | .83844 | .84802 | .85664 | .86414 | .87150 | .87796 | .88443 | .89083 | .89733 | .90160 | .90596 | .90997 | .91370 | | 60 | .82500 | .83599 | .84568 | .85430 | .86186 | .86936 | .87586 | .88236 | .88876 | .89526 | .90054 | .90484 | .90893 | .91279 | | 65 | .82262 | .83362 | .84334 | .85193 | .85956 | .86706 | .87357 | .88006 | .88656 | .89306 | .89840 | .90332 | .90738 | .91138 | | 70 | .82023 | .83124 | .83992 | .84851 | .85612 | .86362 | .87013 | .87663 | .88313 | .88963 | .89504 | .89946 | .90347 | .90747 | | 75 | .81780 | .82878 | .83741 | .84610 | .85371 | .86132 | .86792 | .87442 | .88092 | .88742 | .89384 | .89925 | .90336 | .90736 | | 80 | .81530 | .82631 | .83592 | .84467 | .85228 | .86000 | .86661 | .87322 | .87982 | .88642 | .89284 | .89925 | .90336 | .90736 | | 85 | .81282 | .82486 | .83443 | .84311 | .85072 | .85843 | .86604 | .87365 | .88025 | .88685 | .89327 | .89925 | .90336 | .90736 | | 90 | .81039 | .82242 | .83294 | .84171 | .84932 | .85703 | .86464 | .87225 | .87885 | .88546 | .89187 | .89827 | .90336 | .90736 | | 95 | .80788 | .82008 | .83145 | .84051 | .84812 | .85583 | .86344 | .87105 | .87766 | .88427 | .89068 | .89708 | .90336 | .90736 | | 100 | .80543 | .81774 | .82963 | .83843 | .84604 | .85375 | .86136 | .86897 | .87658 | .88419 | .89059 | .89708 | .90336 | .90736 |
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**Note:** The table provides specific gravities for various temperatures and volumes of spirit relative to water. Each row corresponds to a different temperature in degrees (deg.), and each column represents the ratio of spirit to water for different grain volumes. 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 \(w + m s\) is its bulk.
We have the following proportions:
1. \(w + s = a : x\) 2. \(w + m s = a : y\), and \(y = \frac{m s}{w + m s}\)
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, Plate CCCCXIX or stiff card-paper, draw a line EF (fig. 1), 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 distance from the principal line AB. Let GPL be a thin slip of whalebone, Liquors 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 AB.
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 AB 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 flatwise till the points K and H fall somewheres 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
\[ \frac{a s}{w + s} = x, \quad \text{and} \quad \frac{m s}{w + m s} = y. \]
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 \(\frac{w + s}{w + m s}\), 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 \((= \frac{w + s}{w + m s})\), 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 bulk of the compound must be to 100 gallons as \(g\) to SPI
Spiritous Liquors.
And since we want to make it fill 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 \( a \times \frac{m s}{w + m s} \), and instead of \( \frac{I}{G} \) 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 spiritous 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 s 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 \( m = \frac{I}{0.825} = 1.21212 \), and \( m = 94.54545 \). Therefore
\[ z = 0.94128 \times 100 \times \frac{94.54545}{194.54545} = 49.997, \text{ or very nearly } 50. \]
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 3rd equation \( y = a \times \frac{m s}{w + m s} \), which is equivalent to \( G \times \frac{m s}{w + s} \). For the present example \( y \) will be found 48.599, and \( a - y \), or the water per cent. 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 spiritous 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 accurately ascertain the strength within one part in 500, as will presently appear.
Sir Charles Blagden, or Mr Gilpin, has published * Philof. 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- Spiritous Lished at Edinburgh tables somewhat similar, founded on the same experiments. Both of these tables show the quantities by measure corresponding to every unit by weight of Sir Charles Blagden's experiments, and for every degree of temperature. They also show the percentage of alcohol, and the condensation or the quantity lost by mixture. But as they both retain the original series of parts by weight, which is very unusual, the spirit traders will find considerable difficulty in making use of them. Retaining this series also causes all the percentage numbers (which are the only interesting ones to the trader) to be fractional, and no answer can be had without a double interpolation.
We have therefore calculated a table in the form in which it must be most useful and acceptable to those who are engaged in the spirit trade, showing at once the specific gravity which results from any proportion of admixture in hundredth parts of the whole. This answers immediately the chief questions in the terms in which they are usually conceived and proposed. The two first or leading columns show the proportion in gallons, pints, or other cubic measures, of the mixture, the whole quantity being always 100. The second column shows the corresponding specific gravity; so that we can either find the proportion of the ingredients by the observed specific gravity, or find the gravity resulting from any proportion of the ingredients. A third column shows how much the hundred measures of the two ingredients fall short of making an hundred measures of the compound. A simple proportion, which can be done without the pen, will determine what part of this deficiency must be made up by spirit. The use of this table must now be so familiar to the reader's mind, that we need not give further instructions about it.
This is followed by another similar table, giving an immediate answer to the most usual question, "How many measures of alcohol are there really contained in 100 measures?" This is also accompanied by a column of condensation. It would have been somewhat more elegant, had the specific gravities in this table made the equable series and leading column. But we did not advert to this till we had computed the table, and the labour was too great to be repeated for slight reasons. The tables are only for the temperature 60°. To this the spiritous liquors can always be brought in these climates; and in cases where we cannot, a moment's inspection of Sir Charles Blagden's table will point out very nearly (or exactly, by a short computation) the necessary corrections.
| Compound | Specific Gravity | Cond. per cent. | |----------|------------------|-----------------| | S. | W. | | | 100 | 0 | 0.8250 | | 99 | 1 | 0.8278 | | 98 | 2 | 0.8306 | | 97 | 3 | 0.8333 | | 96 | 4 | 0.8360 | | 95 | 5 | 0.8387 | | 94 | 6 | 0.8413 | | 93 | 7 | 0.8439 | | 92 | 8 | 0.8465 | | 91 | 9 | 0.8491 | | 90 | 10 | 0.8516 | | 89 | 11 | 0.8542 | | 88 | 12 | 0.8567 | | 87 | 13 | 0.8592 | | 86 | 14 | 0.8617 | | 85 | 15 | 0.8641 | | 84 | 16 | 0.8666 | | 83 | 17 | 0.8690 | | 82 | 18 | 0.8713 | | 81 | 19 | 0.8737 | | 80 | 20 | 0.8760 | | 79 | 21 | 0.8784 | | 78 | 22 | 0.8807 | | 77 | 23 | 0.8830 | | 76 | 24 | 0.8853 | | 75 | 25 | 0.8876 | | 74 | 26 | 0.8899 | | 73 | 27 | 0.8921 | | 72 | 28 | 0.8944 | | 71 | 29 | 0.8966 | | 70 | 30 | 0.8988 | | 69 | 31 | 0.9010 | | 68 | 32 | 0.9031 | | 67 | 33 | 0.9053 | | 66 | 34 | 0.9073 |
| Compound | Specific Gravity | Cond. per cent. | |----------|------------------|-----------------| | S. | W. | | | 66 | 34 | 0.9073 | | 65 | 35 | 0.9095 | | 64 | 36 | 0.9116 | | 63 | 37 | 0.9137 | | 62 | 38 | 0.9157 | | 61 | 39 | 0.9177 | | 60 | 40 | 0.9198 | | 59 | 41 | 0.9218 | | 58 | 42 | 0.9238 | | 57 | 43 | 0.9257 | | 56 | 44 | 0.9277 | | 55 | 45 | 0.9296 | | 54 | 46 | 0.9316 | | 53 | 47 | 0.9335 | | 52 | 48 | 0.9353 | | 51 | 49 | 0.9371 | | 50 | 50 | 0.9388 | | 49 | 51 | 0.9406 | | 48 | 52 | 0.9423 | | 47 | 53 | 0.9440 | | 46 | 54 | 0.9456 | | 45 | 55 | 0.9473 | | 44 | 56 | 0.9489 | | 43 | 57 | 0.9505 | | 42 | 58 | 0.9520 | | 41 | 59 | 0.9535 | | 40 | 60 | 0.9549 | | 39 | 61 | 0.9563 | | 38 | 62 | 0.9577 | | 37 | 63 | 0.9592 | | 36 | 64 | 0.9603 | | 35 | 65 | 0.9616 | | 34 | 66 | 0.9628 | | 33 | 67 | 0.9640 |
| Compound | Specific Gravity | Cond. per cent. | |----------|------------------|-----------------| | S. | W. | | | 33 | 67 | 0.9640 | | 32 | 68 | 0.9651 | | 31 | 69 | 0.9662 | | 30 | 70 | 0.9673 | | 29 | 71 | 0.9683 | | 28 | 72 | 0.9693 | | 27 | 73 | 0.9704 | | 26 | 74 | 0.9713 | | 25 | 75 | 0.9724 | | 24 | 76 | 0.9734 | | 23 | 77 | 0.9744 | | 22 | 78 | 0.9754 | | 21 | 79 | 0.9763 | | 20 | 80 | 0.9773 | | 19 | 81 | 0.9783 | | 18 | 82 | 0.9793 | | 17 | 83 | 0.9802 | | 16 | 84 | 0.9812 | | 15 | 85 | 0.9822 | | 14 | 86 | 0.9832 | | 13 | 87 | 0.9842 | | 12 | 88 | 0.9853 | | 11 | 89 | 0.9863 | | 10 | 90 | 0.9874 | | 9 | 91 | 0.9886 | | 8 | 92 | 0.9897 | | 7 | 93 | 0.9909 | | 6 | 94 | 0.9921 | | 5 | 95 | 0.9933 | | 4 | 96 | 0.9946 | | 3 | 97 | 0.9959 | | 2 | 98 | 0.9972 | | 1 | 99 | 0.9985 | | 0 | 100 | 1.0000 | In the first table, of which the sole intention is to point out the proportion of ingredients, the specific gravities are computed only to four places, which will always give the answer true to \( \frac{1}{1000} \)th part. In the last, which is more immediately interesting to the merchant in his transactions with the excise office, the computation is carried one place further.
The consideration of the first of these two tables will furnish some useful information to the reader who is interested in the philosophy of chemical mixture, and who endeavours to investigate the nature of those forces which connect the particles of tangible matter. These vary with the distance of the particle; and therefore the law of their action, like that of universal gravitation, is to be discovered by measuring their sensible effects at their various distances. Their change of distance is seen in the change of density or specific gravity.
Did the individual densities of the water and spirit remain unchanged by mixture, the specific gravity would change by equal differences in the series of mixtures on which this table is constructed; for the bulk being always the same, the change of specific gravity must be the difference between the weight of the gallon of water which is added and that of the gallon of spirit which is taken out. The whole difference of the specific gravities of spirits and water being 1.750 parts in 10,000, the augmentation by each successive change of a measure of spirit for a measure of water would be the 100th part of this, or 17.5. But, by taking the successive differences of density as they occur in the table, we see that they are vastly greater in the first additions of water, being then about 10; after which they gradually diminish to the medium quantity 17\(\frac{1}{2}\), when water and spirits are mixed in nearly equal bulks. The differences of specific gravity still diminish, and are reduced to 9, when about 75 parts of water are mixed with 25 of spirit. The differences now increase again; and the last, when 99 parts of water are mixed with one part of spirit, the difference from the specific gravity of pure water is above 14.
The mechanical effect, therefore, of the addition of a measure of water to a great quantity of spirit is greater than the similar effect of the addition of a measure of spirits to a great quantity of water. What we call mechanical effect is the local motion, the change of distance of the particles, that the corporeal forces may again be in equilibrio. Observe, too, that this change is greater than in the proportion of the distance of the particles; SPIRITOUS particles; for the density of water is to that of spirits nearly as 6 to 5, and the changes of specific gravity are nearly as 6 to 3.
We also see that the changing cause, which produces the absolute condensation of each ingredient, ceases to operate when 75 parts of water have been mixed with 25 of alcohol: for the variation of specific gravity, from diminishing comes now to increase; and therefore, in this particular state of composition, is equable. Things are now in the same state as if we were mixing two fluids which did not act on each other, but were mutually disseminated, and whose specific gravities are nearly as 9 to 10; for the variation of specific gravity may be considered as the 100th part of the whole difference, in the same manner as 17.7 would have been had water and alcohol sustained no contraction.
The imagination is greatly assisted in the contemplation of geometrical quantity by exhibiting it in its own form. Specific gravity, being an expression of density (a notion purely geometrical), admits of this illustration.
Therefore let AB (fig. 2) represent the bulk of any mixture of water and alcohol. The specific gravity of water may be represented by a line of such a length, that AB shall be the difference between the gravities of alcohol and water. Suppose it extended upwards, towards a, till B a is to A a as 10,000 to 8250. It will suit our purpose better to represent it by a parallelogram a BF e, of any breadth BF. In this case the difference of the specific gravities of alcohol and water will be expressed by the parallelogram ABFE. If there were no change produced in the density of one or both ingredients, the specific gravity of the compound would increase as this parallelogram does, and AGHE would be the augmentation corresponding to the mixture of the quantity AG of alcohol with the quantity GB of water, and so of other mixtures. But, to express the augmentation of density as it really obtains, we must do it by some curvilinear area DABCHD, which varies at the rate determined by Sir Charles Blagden's experiments. This area must be precisely equal to the rectangle ABFE. It must therefore fall without it in some places, and be deficient in others. Let DMHKC be the curve which corresponds with these experiments. It is evident to the mathematical reader, that the ordinates LM, GH, IK, &c. of this curve are in the ultimate ratio of the differences of the observed specific gravities. If A a, b b, &c. are each = s, the little spaces a a b b, &c. will be precisely equal to the differences of the specific gravities 0.8250; 0.8387; 0.8516; &c. corresponding to the different mixtures of water and alcohol. The curve cuts the side of the parallelogram in K, where the ordinate GK expresses the mean variation of density 0.0017.5. IK is the smallest variation. The condensation may be expressed by drawing a curve dmGfk parallel to DMGKF, making Dd = AE. The condensation is now represented by the spaces comprehended between this last curve and the abscissa AGB, reckoning those negative which lie on the other side of it. This shows, not only that the condensation is greatest in the mixture AG × GB, but also that in mixing such a compound with another AI × IB, there is a rarefaction. Another curve ANOPB may be drawn, of which the ordinates LN, GP, IO, &c. are proportional to the areas ALmd, AGmD, AIkGmd (=AGmd—GIk), &c. This curve shows the whole condensation.
This manner of representing the specific gravities of mixtures will suggest many curious inferences to such as will consider them in the manner of Bozovich, with a view to ascertain the nature of the forces of cohesion and chemical affinities: And this manner of viewing the subject becomes every day more promising, in consequence of our improvements in chemical knowledge; for we now see, that mechanism, or motive forces, are the causes of chemical action. We see in almost every case, that chemical affinities are comparable with mechanical prejudices; because the conversion of a liquid into a vapour or gas is prevented by atmospheric pressure, and produced by the great chemical agent heat. The action of heat, therefore, or of the cause of heat, is a mechanical action, and the forces are common mechanical forces, with which we are familiarly acquainted.
"It may be also remarked in the column of contractions, that in the beginning the contractions augment nearly in the proportion of the quantity of spirits (but more slowly); whereas, in the end, the contractions are nearly in the duplicate proportion of the quantity of water. This circumstance deserves the consideration of the philosopher. We have represented it to the eye by the curve n g h d."
We should here take some notice of the attempt made to elude some part of the duties, by adding some ingredient to the spirits. But our information on this subject is not very exact; and besides it would be doing no service to the trader to put fraud more in his power. There are some facts which make a very great augmentation of density, but they render the liquor unpalatable. Sugar is frequently used with this view; 16 grains of refined sugar dissolved in 1000 grains of proof spirits gave it no fuliginous taste, and increased its specific gravity from 0.920 to 0.925, which is a very great change, equivalent to the addition of 9 grains of water to a mixture of 100 grains of alcohol and 80 of water.