equal. This is not sufficiently attended to by the makers; and they commit an error here which is very considerable when the whole range of the instrument is great; for the value of one division of the scale, when the largest weight is on, is as much greater than its value when the instrument is not loaded at all, as the full loaded instrument is heavier than the instrument unloaded. No manner whatever of dividing the scale will correspond to equal differences of specific gravity through the whole range with different weights; but, if the divisions are made to indicate equal proportions of gravity when the instrument is used without a weight, they will indicate equal proportions throughout. This is evident from what we have been just now saying; for the proportion of the specific gravities corresponding to any two immediately succeeding weights is always the same. The best way, therefore, of constructing the instrument, so that the same divisions of the scale may be accurate in all its successive repetitions with the different weights, is to make these divisions in geometrical progression. The corresponding specific gravities will also be in geometric proportion. These being all inserted in a table, we obtain them with no more trouble than by inspecting the scale which usually accompanies the hydrometer. This table is of the most easy construction; for, the ratio of the successive bulks and specific gravities being all equal, the differences of the logarithms are equal. This will be illustrated by applying it to the example already given of a hydrometer extending from 0.73 to 1.068793 with three weights. This gives four repetitions of the scale on the stem. Suppose this scale divided into ten parts, we have forty specific gravities. Let these be indicated by the numbers 0, 1, 2, 3, &c., to 40. The mark 0 is affixed to the top of the stem, and the divisions downwards are marked 1, 2, 3, &c, the lowest being 10. These divisions are easily determined. The stem, which we may suppose five inches long, was supposed to be one-tenth of the capacity of the ball. It may therefore be considered as the extremity of a rod of eleven times its length, or fifty-five inches; and we must find nine mean proportionals between fifty and fiftyfive inches. Subtract each of these from fiftyfive inches, and the remainders are the distances of the points of division from 0, the top of the scale. The smallest weight is marked 10, the next 20, and the third 30. If the instrument loaded with the weight 20 sinks in some liquor to the mark 7, it indicates the specific gravity 27, that is, the twenty-seventh of forty mean proportionals between 0.73 and 1.068793, or 0.944242. To obtain all these intermediate specific gravities, we have only to subtract 98633229, the logarithm of 0.73, from that of 1.068793, viz. 0-0288937, and take 0.0041393, the fortieth part of the difference. Multiply this by 1, 2, 3, &c., and add the logarithm of 0.73 to each of the products. The sums are the logarithms of the specific gravities required. These will be found to proceed so equably that they may be interpolated ten times by a simple table of proportional parts without the smallest sensible error. Therefore the stem may be divided Nay, the trouble of inspecting a table may be avoided, by forming on a scale the logarithms of the numbers between 7.300 and 1078-793, and placing along side of it a scale of the same length divided into 400 equal parts, numbered from 0 to 400. Then, looking for the mark shown by the hydrometer on this scale of equal parts, we see opposite to it the specific gravity. We have been thus particular in the illustration of this mode of construction, because it is really a beautiful and commodious instrument, which may be of great use both to the naturalist and to the man of business. A table may be comprised in twenty pages octavo, which will contain the specific gravities of every fluid which can interest either, and answer every question relative to their admixture, with as much precision as the observations can be made. We therefore recommend it to our readers, and we recommend the very example which we have given as one of the most convenient. The instrument need not exceed eight inches in length, and may be contained in a pocket case of two inches broad and as many deep, which will also contain the scale, a thermometer, and even the table for applying it to all fluids which have been examined. There is another method of examining the specific gravities of fluids, first proposed by Dr. Wilson, late professor of astronomy in the university of Glasgow. This is by a series of small glass bubbles, differing equally, or according to some rule, from each other in specific gravity, and each marked with its proper number. When these are thrown into a fluid which is to be examined, all those which are heavier than the fluid will fall to the bottom. Then holding the vessel in the hand, or near a fire or candle, the fluid expands, and one of the floating bubbles begins to sink. Its specific gravity therefore was either equal to, or a little less than, that of the fluid; and the degree of the thermometer, when it began to sink, will inform us how much it was deficient, if we know the law of expansion of the liquor. Sets of these bubbles fitted for the examination of spirituous liquors, with a little treatise showing the manner of using them, and calculating by the thermometer, are made by Mr. Brown, an ingenious artist of Glasgow, and are often used by the dealers in spirits, being found both accurate and expeditious. Also, though a bubble or two should be broken, the strength of spirits may easily be had by means of the remainder, unless two or three in immediate succession be wanting; for a liquor which answers to No 4 will sink No. 2 by heating it few degrees, and therefore No. 3 may be spared. This is a great advantage in ordinary business. A nice hydrometer is not only an expensive instrument, but exceedingly delicate, being so very thin. If broken, or even bruised, it is useless, and can hardly be repaired except by the very maker. As the only question here is, to determine how many gallons of excise proof spirits are contained in a quantity of liquor, the artist has constructed this series of bubbles in the simplest manner possible, by previously making forty or fifty mixtures of spirits and water, and then adjusting the bubbles to these mixtures. In some sets the number on each bubble is the number of gallons of proof spirits contained in 100 gallons of the liquor. In other sets the number on each bubble expresses the gallons of water which will make a liquor of this strength, * if added to fourteen gallons of alcohol. Thus, if a liquor answers to No. 4, then four gallons of water added to fourteen gallons of alcohol will make a liquor of this strength. The first is the best method; for we should be mistaken in supposing that eighteen gallons, which answer to No. 4, contain exactly fourteen gallons of alcohol: it contains more than fourteen. By examining the specific gravity of bodies, the philosopher has made some very curious discoveries. The most remarkable of these is the change which the density of bodies suffers by mixture. It is a most reasonable expectation that, when a cubic foot of one substance is mixed any how with a cubic foot of another, the bulk of the mixture will be two cubic feet; and that eighteen gallons of water joined to eighteen gallons of oil will fill a vessel of thirty-six gallons. Accordingly this was never doubted; and even Archimedes, the most scrupulous of mathematicians, proceeded on this supposition in the solution of his famous problem, the discovery of the proportion of silver and gold in a mixture of both. He does not even mention it as a postulate that may be granted him, so much did he conceive it to be an axiom. Yet a little reflexion seems sufficient to make it doubtful, and to require examination. A box filled with musket balls will receive a considerable quantity of small shot, and after this a considerable quantity of fine sand, and after this a considerable quantity of water. Something like this might happen in the admixture of bodies of porous texture. But such substances as metals, glass, and fluids, where no discontinuity of parts can be perceived, or was suspected, seem free from every chance of this kind of introsusception. Lord Verulam, however, without being a naturalist or mathematician ex professo, inferred from the mobility of fluids that they consisted of discrete particles, which must have pores interposed, whatever be their figure. And, if we ascribe the different densities or other sensible qualities to difference in size or figure of those particles, it must frequently happen that the smaller particles will be lodged in the interstices between the larger, and thus contribute to the weight of the sensible mass without increasing its bulk. He therefore suspects that mixtures will be in general less bulky than the sum of their ingredients. Accordingly the examination of this question was one of the first employments of the Royal So ciety of London, and long before its institution had occupied the attention of the gentlemen who afterwards composed it. The register of the Society s early meetings contains many experiments on this subject, with mixtures of gold and silver, of other metals, and of various fluids, examined by the hydrostatical balance of Mr. Boyle. Dr. Hooke made a prodigious number, chiefly on articles of commerce, which were unfortunately lost in the fire of London. It was soon found, however, that lord Verulam's conjecture had been well founded, and that bodies changed their density very sensibly in many cases. In general it was found that bodies which had a strong chemical affinity increased in density, and that their admixture was accompanied with heat. By this discovery it is manifest that Archimedes had not solved the problem of detecting the quantity of silver mixed with the gold in king Hiero's crown, and that the physical solution of it requires experiments made on all the kinds of matter that are mixed together. We do not find that this has been done to this day, although we may affirm that there are few questions of more importance. It is a very curious fact in chemistry, and it would be most desirable to be able to reduce it to some general laws; for instance, to ascertain what is the proportion of two ingredients which produces the greatest change of density. This is important in the science of physics, because it gives us considerable information as to the mode of action of those natural powers or forces by which the particles of tangible matter are united. If this introsusception, concentration, compenetration, or by whatever name it be called, were a mere reception of the particles of one substance into the interstices of those of another, it is evident that the greatest concentration would be observed when a small quantity of the recipiend is mixed with, or disseminated through, a great quantity of the other. It is thus that a small quantity of fine sand will be received into the interstices of a quantity of small shot, and will increase the weight of the bagfull without increasing its bulk. The case is nowise different when a piece of freestone has grown heavier by imbibing or absorbing a quantity of water. If more than a certain quantity of sand has been added to the small shot, it is no longer concealed. In like manner, various quantities of water may combine with a mass of clay, and increase its size and weight alike. All this is very conceivable, occasioning no difficulty. But this is not the case in any of the mixtures we are now considering. In all these the first additions of either of the two substances produce but an inconsiderable change of general density; and it is in general most remarkable, whether it be condensation or rarefaction, when the two ingredients are nearly of equal bulks. We can illustrate even this difference by reflecting on the imbibition of water by vegetable solids, such as timber. Some kinds of wood have their weight much more increased than their bulks; other kinds of wood are more enlarged in bulk than in weight. The like happens in grains. This is curious, and shows in the most unquestionable manner that the particles of bodies are not in contact, but are kept together by forces which act at a distance; for this distance between the centres of the particles is most evidently susceptible of variation; and this variation is occasioned by the introduction of another substance, which, by acting on the particles by attraction or repulsion, diminishes or increases their mutual actions and makes new distances necessary for bringing all things again into equilibrium. We refer the curious reader to the ingenious theory of the abbé Boscovich for an excellent illustration of this subject.—Theor. Phil. Nat. § de Solutione Chemica. Specific gravity of Metals altered by mixture. -This question is no less important to the man of business. Till we know the condensation of those metals by mixture, we cannot tell the quantity of alloy in gold and silver by means of their specific gravity; nor can we tell the quantity of pure alcohol in any spirituous liquor, or that of the valuable salt in any solution of it. For want of this knowledge, the dealers in gold and silver are obliged to have recourse to the tedious and difficult test of the assay, which cannot be made in all places or by all men. It is therefore much to be wished that some persons would institute a series of experiments in the most interesting cases: for it must be observed that this change of density is not always a small matter; it is sometimes very considerable and paradoxical. A remarkable instance may be given of it in the mixture of brass and tin for bells, great guns, optical speculums, &c. The specific gravity of cast brass is nearly 8.006, and that of tin is nearly 7-363. If two parts of brass be mixed with one of tin, the specific gravity is 8-931; whereas, if each had retained its former bulk, the specific gravity would 2 x 8.006 +7-363have been only 7-793(= 3 A mixture of equal parts should have the specific gravity 7.684; but it is 8-441. A mixture of two parts tin with one part brass, instead of being 7577, is 8.027. In all these cases there is a great increase of specific gravity, and consequently a great condensation of parts or contraction of bulk. The first mixture of eight cubic inches of brass, for instance, with four cubic inches of tin, does not produce twelve cubic inches of bell-metal, but only ten and a half nearly, having shrunk one-fifth. It would appear that the distances of the brass particles are most affected, or perhaps it is the brass that receives the tin into its pores; for we find that the condensations in these mixtures are nearly proportional to the quantities of the brass in the mixtures. It is remarkable that this mixture with the lightest of all metals has made a composition more heavy and dense than brass can be made by any hammering. The most remark able instance occurs in mixing iron with platina If ten cubic inches of iron are mixed with one and a quarter of platina, the bulk of the compound is only nine inches and three-quarters. The iron therefore has not simply received the platina into its pores: its own particles are brought nearer together. There are similar results in the solution of turbith mineral, and of some other salts, in water. The water, instead of rising in the neck of the vessel, when a small quantity of the salt has been added to it, sinks considerably, and the two ingredients occupy less room than the water did alone. The same thing happens in the mixture of water with other fluids, and different fluids with each other:-But we are not able to trace any general rule that is observed with absolute precision. In most cases of fluids the greatest condensation happens when the bulks of the ingredients are nearly equal. Thus, in the mixture of alcohol and water, we have the greatest condensation when sixteen ounces and a half of alcohol are mixed with twenty ounces of water, and the condensation is about one-thirty-sixth of the whole bulk of the ingredients. It is extremely various in different substances, and no classification of them can be made in this respect. A dissertation has been published on this subject by Dr. Hahn of Vienna, entitled De Efficacia Mixtionis in Mutandis Corporum Voluminibus, in which all the remarkable instances of the variation of density have been collected. All we can do is to record such instances as are of chief importance, being articles of commerce. The most scrupulous examination of this, or perhaps of any mixture, has been lately made by Dr. Blagden (now Sir Charles Blagden) of the Royal Society, on the requisition of the Board of Excise. He has published an account of the examination in the Philosophical Transactions of 1791 and 1792. The alcohol was almost the strongest that can be produced; and its specific gravity, when of the temperature 60°, was 0/825. The whole mixtures were of the same temperature. Column 1 of the Table contains the lb. oz. or other measures by weight, of alcohol in the mixture. Col. 2 contains the pounds or ounces of water. Col. 3 is the sum of the bulks of the ingredients, the bulk of a pound or ounce of water being accounted 1. Col. 4 is the observed specific gravity of the mixture. Col. 5 is the specific gravity which would have been observed if the ingredients had each retained its own specific gravity; calcu lated by dividing the sum of the two numbers of the first and second columns by the corresponding number of the third. Col. 6 is the difference of col. 4 and col. 5, and exhibits the condensation. The condensation is greatest when sixteen ounces and a half of alcohol have been added to twenty of water, and the condensation is, or nearly one-thirty-sixth of the computed density. Since the specific gravity of alcohol is 0.825, it is evident that sixteen ounces and a half of alcohol and twenty ounces of water have equal bulks. So that the condensation is greatest when the substances are mixed in equal volumes; and eighteen gallons of alcohol mixed with eighteen gallons of water will produce not thirty-six gallons of spirits, but thirty-five only. This is the mixture to which our revenue laws refer, declaring it to be one to six or one in seven under proof, and to weigh seven pounds thirteen ounces per gallon. This proportion was probably selected as the most easily composed, viz. by mixing equal measures of water and of the strongest spirit which the known processes of distillation could produce. Its specific gravity is 0-939 very nearly. This elaborate examination of the mixture of water and alcohol is a standard se ries of experiments to which appeal may always be made, whether for the purposes of science or of trade. The regularity of the progression is so great that in the column we examined, viz. that for temperature 60°, the greatest anomaly does not amount to one part in 6000. The form of the series is also very judiciously chosen for the purposes of science. It would perhaps have been more directly stereometrical had the proportions of the ingredients been stated in bulks which are more immediately connected with density. But the author has assigned a very cogent reason for his choice, viz. that the temperature of bulks varies by a change of temperature, because the water and spirits follow different laws in their expansion by heat. Mr. Lambert, one of the first mathematicians and philosophers of Europe, in a dissertation in the Berlin Memoirs (1762), gives a narration of experiments on the brines of common salt, from which he deduces a very great condensation, which he attributes to an absorption in the weak brines of the salt, or a lodgment of its particles in the interstices of the particles of water. Mr. Achard of the same academy, in 1785, gives a very great list of experiments on the bulks of various brines, made in a different way, which show no such introsusception; and Dr. Watson, formerly regius professor of chemistry at Cambridge, thinks this confirmed by experiments which he narrates in his Chemical Essays. We cannot assent to either side, and do not think the experiments decisive. We incline to Mr. Lambert's opinion; for this reason, that in the successive dilutions of sulphuric acid and nitric acid there is a most evident and remarkable condensation. Now what are these but brines, of which we have not been able to get the saline ingredient in a separate form? The experiments of Mr. Achard and Dr. Watson were made in such a way that a single grain in the measurement bore too great a proportion to the whole change of specific gravity. At the same time, some of Dr. Watson's are so simple in their nature that it is very difficult to withhold the assent. Experiments have also been made which seem sufficient for deciding the question. 'Whether the salt can be received into the pores of the water, so as to increase its weight without increasing its bulk?' and we must grant that it may. We do not mean that it is simply lodged in the pores as sand is lodged in the interstices of small shot; but the two together occupy less room than when separate. The experiments of Mr. Achard were insufficient for a decision, because made on 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 the specific gravity of dissolved salts. Specific gravity, says Dr. Ure, is the density of the matter of which any body is composed, compared to the density of another body, assumed as the standard. This standard is water, at the temperature of 60° Fahrenheit. To determine the specific gravity of a solid we In the weigh it, first in air, and then in water. latter case it loses of its weight a quantity pre cisely equal to the weight of its own bulk of water; and hence, by comparing this weight with its total weight, we find its specific gravity. The rule therefore is, Divide the total weight by the loss of weight in water, the quotient is the specific gravity. If it be a liquid, or a gas, we weigh it in a glass or other vessel of known capacity; and, dividing that weight by the weight of the same bulk of water, the quotient is, as before, the specific gravity. To calculate the mean specific gravity of a compound from those of its components is a problem of perpetual recurrence in chemistry. It is only by a comparison of the result of that calculation, with the specific gravity of the compound experimentally ascertained, that we can discover whether the combination has been accompanied with expansion or condensation of volume. As several respectable experimental chemists (see ALLOY, and AMMONIA) seem deficient in this part of chemical computation, I shall here insert a short This value being constantly negative proves that the true value of the specific gravity of the W + w mixture, represented by is always V + v W abstract of a paper which I published on this smaller than the false value, (~~+~~~). subject in the seventh number of the Journal of Science. The specific gravity of one body is to that of another as the weight of the first, divided by its volume, is to the weight of the second, divided by its volume; and the mean specific gravity of the two is found by dividing the sum of the weights by the sum of the volumes. Let W, w, be the two weights; V, v, the two volumes; P, p, the two specific gravities; and M the calculated mean specific gravity. Then W+w M= ; the formula by which I computed Example of the last formula:- Gold and silver, 14.9 false (P-p or arithmetical mean specific gravity. 29.8 29.8 = 29.8 P+P =2·6 = 2A; and ▲ 1.3, which being subtracted from the Sulphuric acid TABLE, showing the erroneous re sults of the common method. W w Wp+wP And V+v= + P Pp V+v Wp+wP Pw+pW = (W+w) Pp Pp density. Experimental Apparent density. Volume. When the difference in density between the two substances is considerable, as it is with sulphuric acid and water, the errors produced by assuming the arithmetical mean for the true calIf we take copper culated mean are excessive. and tin, however, then the arithmetical mean, 8.897.29 8.09, differs very little fiom 8.01, the accurate mean density. 2 By a similar error, I suppose, in calculating the mean density of liquid muriatic acid in its different stages of dilution, the celebrated Kirwan has long misled the chemical world. He asserted that the mean specific gravity of the components being also the experimental mean, there is no condensation of volume as with other acid dilutions. And the illustrious Berthollet has even assigned a cause for this suppositious fact. I find, on the contrary, that 50 of acid, specific gravity 1.1920, with 50 of water, give out heat, and have their volume diminished in the ratio of 100 to 99-28. The experimental specific gravity is 1.0954; that by the exact rule is only 1.0875. The preceding formula may be presented under a still more convenient form. Pp being Mr. Robertson, in order to determine the specific gravity of men, prepared a cistern seventyeight inches long, thirty inches wide, and thirty inches deep; and, having procured ten men for his purpose, the height of each was taken, and his weight; and afterwards they plunged successively into the cistern. A ruler, graduated to inches and decimal parts of an inch, was fixed to one end of the cistern, and the height of the water noted before each man went in, and to what height it rose when he immersed himself under its surface. The following table contains the several results : |