equal. This is not sufficiently attended to by into 100 parts very sensible to the eye (each the makers; and they commit an error here being nearly the twentieth of an inch), and 400 which is very considerable when the whole range degrees of specific gravity obtained within the of the instrument is great; for the value of one range, which is as near as we can examine this division of the scale, when the largest weight is matter by any hydromoter. Thus the specific on, is as much greater than its value when the gravities corresponding to No. 26, 27, 28, 29, are instrument is not loaded at all, as the full loaded as follow:instrument is heavier than the instrument un Ist Diff. 2d Diff. loaded. No manner whatever of dividing the 26 0.93529 scale will correspond to equal differences of spe 895 27 0.94424 9 cific gravity through the whole range with diffe 904 28 0-95328 9 rent weights; but, if the divisions are made to 913 290-96241 indicate equal proportions of gravity when the instrument' is used without a weight, they will Nay, the trouble of inspecting a table may be indicate equal proportions throughout. This is avoided, by forming on a scale the logarithms of evident from what we have been just now say- the numbers between 7.300 and 1078-793, and ing; for the proportion of the specific gravities placing along side of it a scale of the same corresponding to any two immediately succeed- length divided into 400 equal parts, numbered ing weights is always the same. The best way, from 0 to 400. Then, looking for the mark therefore, of constructing the instrument, so that shown by the hydrometer on this scale of equal the same divisions of the scale may be accurate parts, we see opposite to it the specific gravity. in all its successive repetitions with the different We have been thus particular in the illustration weights, is to make these divisions in geometrical of this mode of construction, because it is really progression. The corresponding specific gravi- a beautiful and commodious instrument, which ties will also be in geometric proportion. These may be of great use both to the naturalist and being all inserted ju a table, we obtain them to the man of business. A table may be comwith no more trouble than by inspecting the prised in twenty pages octavo, which will conscale which usually accompanies the hydrometer. tain the specific gravities of every fluid which This table is of the most easy construction; for, can interest either, and answer every question the ratio of the successive bulks and specific relative to their admixture, with as much precigravities being all equal, the differences of the sion as the observations can be made.' We logarithms are equal. This will be illustrated therefore recommend it to our readers, and we by applying it to the example already given of recommend the very example which we have a hydrometer extending from 0.73 to 1.068793 given as one of the most convenient. The inwith three weights. This gives four repetitions strument need not exceed eight inches in length, of the scale on the stem. Suppose this scale di- and may be contained in a pocket case of two vided into ten parts, we have forty specific gra- inches broad and as many deep, which will also vities. Let these be indicated by the numbers contain the scale, a thermometer, and even the 0, 1, 2, 3, &c., to 40. The mark 0 is affixed table for applying it to all Auids which have to the top of the stem, and the divisions down- been examined. wards are marked 1, 2, 3, &c, the lowest be There is another method of examining the ing 10. These divisions are easily determined. specific gravities of Auids, first proposed by Dr. The stem, which we may suppose five inches Wilson, late professor of astronomy in the unilong, was supposed to be one-tenth of the capa- versity of Glasgow. This is by a series of small city of the ball. It may therefore be considered glass bubbles, differing equally, or according to as the extremity of a rod of eleven times its some rule, from each other in specific gravity, length, or fifty-five inches; and we must find and each marked with its proper number. When nine mean proportionals between fifty and fifty- these are thrown into a Auid which is to be five inches. Subtract each of these from fifty- examined, all those which are heavier than the five inches, and the remainders are the distances fluid will fall to the bottom. Then holding the of the points of division from 0, the top of the vessel in the hand, or near a fire or candle, the scale. "The smallest weight is marked 10, the fluid expands, and one of the floating bubbles next 20, and the third 30. If the instrument begins to sink. Its specific gravity therefore loaded with the weight 20 sinks in some liquor was either equal to, or a little less than, that of to ihe mark 7, it indicates the specific gravity the fluid; and the degree of the thermometer, 27, that is, the twenty-seventh of forty mean when it began to sink, will inform us how much proportionals between 0.73 and 1.068793, or it was deficient, if we know the law of expansion 0.944242. To obtain all these intermediate of the liquor. Sets of these bubbles fitted for specific gravities, we have only to subtract the examination of spirituous liquors, with a 9.8633229, the logarithm of 0.73, from that of little treatise showing the manner of using them, 1.068793, viz. 0·0288937, and take 0.0041393, and calculating by the thermometer, are made the fortieth part of the difference. Multiply this by Mr. Brown, an ingenious artist of Glasgow, by 1, 2, 3, &c., and add the logarithm of 0.73 to and are often used by the dealers in spirits, being each of the products. The sums are the logar- found both accurate and expeditious. Also, ithms of the specific gravities required. These though a bublile or two should be broken, the will be found to proceed so equably that they strength of spirits may easily be had by means may be interpolated ten times by a simple table of the remainder, unless two or three in imme. of proportional parts without the smallest sen- diate succession be wanting; for a liquor which sible error. Therefore the stem may be divided answers to No 4 will sink No. 2 by bearing it. few degrees, and therefore No. 3 may be spared. ciety of London, and long before its institution This is a great advantage in ordinary business. had' occupied the attention of the gentlemen A nice hydrometer is not only an expensive in- who afterwards composed it. The register of strument, but exceedingly delicate, being so very the Society s early meetings contains many exthin. If broken, or even bruised, it is useless, periments on this subject, with mixsures of gold and can hardly he repaired except by the very and silver, of other metals, and of various fluids, maker. As the only question here is, to deter- examined by the hydrostatical balance of Mr. mine how many gallons of excise proof spirits Boyle. Dr. Hooke made a prodigious number, are contained in a quantity of liquor, the artist chiefly on articles of commerce, which were unhas constructed this series of bubbles in the fortunately lost in the fire of London. It was simplest manner possible, by previously making soon found, however, that lord Verulam's conforty or fifty mixtures of spirits and water, and jecture had been well founded, and that bodies then adjusting the bubbles to these mixtures. changed their density very sensibly in many In some sets the number on each bubble is the cases. In general it was found that bodies number of gallons of proof spirits contained in which had a strong chemical affinity increased 100 gallons of the liquor. In other sets the in density, and that their admixture was accomnumber on each bubble expresses the gallons of panied with heat. By this discovery it is maniwater which will make a liquor of this strength, fest that Archimedes had not solved the problem • if added to fourteen gallons of alcohol. Thus, if of detecting the quantity of silver mixed with a liquor answers to No. 4, ther gallons of the gold in king Hiero's crown, and that the water added to fourteen gallons of alcohol will physical solution of it requires experiments make a liquos of this strength. The first is the best made on all the kinds of matter that are mixed method; for we should be mistaken in supposing together. We do not find that this has been that eighteen gallons, which answer to No. 4, done to this day, although we may affirm that contain exactly fourteen gallons of alcohol : it there are few questions of more importance. It contains more than fourteen. By examining the is a very curious fact in chemistry, and it would specific gravity of bodies, the philosopher has be most desirable to be able to reduce it to some made some very curious discoveries. The most general laws; for instance, to ascertain what is remarkable of these is the change which the den- the proportion of two ingredients which prosity of bodies suffers by mixture. It is a most duces the greatest change of density. This is reasonable expectation that, when a cubic foot important in the science of physics, because it of one substance is mixed any how with a cubic gives us considerable information as to the mode foot of another, the bulk of the mixture will be of action of those natural powers or forces by two cubic feet; and that eighteen gallons of which the particles of tangible matter are water joined to eighteen gallons of oil will fill a united. If this introsusception, concentration, vessel of thirty-six gallons. Accordingly this compenetration, or by whatever name it be was never doubted; and even Archimedes, the called, were a mere reception of the particles of most scrupulous of mathematicians, proceeded one substance into the interstices of those of on this supposition in the solution of his famous another, it is evident that the greatest concentraproblem, the discovery of the proportion of tion would be observed when a small quantity silver and gold in a mixture of both. He does of the recipiend is mixed with, or disseminated not even mention it as a postulate that may be through, a great quantity of the other. It is granted him, so much did he conceive it to thus that a small quantity of fine sand will be be an axiom. Yet a little reflexion seems suffi- received into the interstices of a quantity of small cient to make it doubtful, and to require exami- shot, and will increase the weight of the bagfull nation. A box filled with musket balls will without increasing its bulk. The case is nowise receive a considerable quantity of small shot, different when a piece of freestone has grown and after this a considerable quantity of fine heavier by imbibing or absorbing a quantity of sand, and after this a considerable quantity of water. If more than a certain quantity of sand water. Something like this might happen in the has been added to the small shot, it is no longer admixture of bodies of porous texture. But concealed. In like manner, various quantities such substances as metals, glass, and fluids, of water may combine with a mass of clay, and where no discontinuity of parts can be perceived, increase its size and weight alike. All this is or was suspected, seem free from every chance very conceivable, occasioning no difficulty. But of this kind of introsusception. Lord Verulam, this is not the case in any of the mixtures we are however, without being a naturalist or mathema- now considering. In all these the first additions tician ex professo, inferred from the mobility of of either of the two substances produce but an fluids that they consisted of discrete particles, inconsiderable change of general density; and it which must have pores interposed, whatever be is in general most remarkable, whether it be contheir figure. And, if we ascribe the different densation or rarefaction, when the two ingredensities or other sensiħle qualities to difference dients are nearly of equal bulks. We can inosize or figure of those particles, it must fre- illustrate even this difference by reflecting on the quently happen that the smaller particles will be imbibition of water by vegetable solids, such as lodged in the interstices between the larger, and timber. Some kinds of wood have their weight thus contribute 10 the weight of the sensible much more increased than their bulks; other mass without increasing its bulk. He therefore kinds of wood are more enlarged-in bulk than suspects that mixtures will be in general less in weight. The like happens in grains. This is hulky than the sum of their ingredients. Ac- curious, and shows in the most unquestionable cordingly the examination of this question was manner that the particles of bodies are not in one of the first employments of the Royal So. contact, but are kept together by forces which act ai a distance ; for this distance between the able instance occurs in mixing iron with platina centres of the particles is most evidently sus If ten cubic inches of iron are mixed with one ceptible of variation; and this variation is occa and a quarter of platina, the bulk of the comsioned by the introduction of another substance, pound is only nine inches and three-quarters. which, by acting on the particles by attraction or The iron therefore has not simply received the repulsion, diminishes or increases their mutual platina into its pores: its own particles are actions and makes new distances necessary for brought nearer together. There are similar rebringing all things again into equilibrium. We sults in the solution of turbith mineral, and of refer the curious reader to the ingenious theory some other salts, in water. The water, instead of the abbé Boscovich for an excellent illustra- of rising in the neck of the vessel, when a small tion of this subject.—Theor. Phil. Nat. § de So- quantity of the salt has been added to it, sinks lutione Chemica. considerably, and the two ingredients occupy Specific gravity of Metals altered by mirture. less room than the water did alone. - This question is no less important to the man The same thing happens in the mixture of of business. Till we know the condensation of water with other Guids, and different fluids with those metals by mixture, we cannot tell the each other :—But we are not able to trace any quantity of alloy in gold and silver by means of general rule that is observed with absolute pretheir specific gravity; nor can we tell the quan- cision. In most cases of fluids the greatest contity of pure alcohol in any spirituous liquor, or densation happens when the bulks of the ingre that of the valuable salt in any solution of it. dients are nearly equal. Thus, in the mixture For want of this knowledge, the dealers in gold of alcohol and water, we have the greatest conand silver are obliged to have recourse to the densation when sixteen ounces and a half of tedious and difficult test of the assay, which can- alcohol are mixed with twenty ounces of water, not be made in all places or by all men. It is and the condensation is about one-thirty-sixth therefore much to be wished that some persons of the whole bulk of the ingredients. It is exwould institute a series of experiments in the tremely various in different substances, and no most interesting cases : for it must be observed classification of them can be made in this rethat this change of density is not always a small spect. A dissertation has been published on this matter; it is sometimes very considerable and subject by Dr. Hahn of Vienna, entitled De paradoxical. A remarkable instance may be Efficacia Mixtionis in Mutandis Corporum Vogiven of it in the mixture of brass and tin for luminibus, in which all the remarkable instances bells, great guns, optical speculums, &c. The of the variation of density have been collected. specific gravity of cast brass is nearly 8.006, All we can do is to record such instances as are and that of tin is nearly 7:363. If two parts of chief importance, being articles of commerce. of brass be mixed with one of tin, the specific The most scrupulous examination of this, or gravity is 8-931; whereas, if each had retain- perhaps of any mixture, has been lately made ed its former bulk, the specific gravity would by Dr. Blagden (now Sir Charles Blagden) of 2 x 8:006 + 7.363 have been only 7-793( =? the Royal Society, on the requisition of the Board of Excise. He has published an account A mixture of equal parts should have the spe- of the examination in the Philosophical Transcific gravity 7.684; but it is 8:441. A mixture actions of 1791 and 1792. The alcohol was of two parts tin with one part brass, instead of almost the strongest that can be produced; and being 7-577, is 8·027. In all these cases there its specific gravity, when of the temperature 60°, is a great increase of specific gravity, and con was 04825. The whole mixtures were of the sequently a great condensation of parts or con same temperature. Column 1 of the Table traction of bulk. The first mixture of eight contains the lb. oz. or other measures by weight, cubic inches of brass, for instance, with four of alcohol in the mixture. Col. 2 contains the cubic inches of tin, does not produce twelve pounds or ounces of water. Col. 3 is the sum cubic inches of bell-metal, but only ten and a of the bulks of the ingredients, the bulk of a half nearly, having shrunk one-fifth. It would pound or ounce of water being accounted 1. appear that the distances of the brass particles Col. 4 is the observed specific gravity of the are most affected, or perhaps it is the brass that mixture. Col. 5 is the specific gravity which receives the tin into its pores; for we find that would have been observed if the ingredients had the condensations in these mixtures are nearly each retained its own specific gravity; calcuproportional to the quantities of the brass in the lated by dividing the sum of the two numbers mixtures. It is remarkable that this mixture of the first and second columns by the correwith the lightest of all metals has made a com- sponding number of the third. Col. 6 is the position more heavy and dense than brass can difference of col. 4 and col. 5, and exhibits the be made by any hammering. The most remark- condensation. 363). 3 1 4 17 ries of experiments to which appeal may always Specific Sp. Gr. Conden A. W. Volume. Gravity be made, whether for the purposes of science or calcu sation. of trade. The regularity of the progression is observed. lated. so great that in the column we exanıined, viz. 20 24.2424 0·8250 0.8250 that for temperature 60°, the greatest anomaly 00 20 25.2424 0.8360 0.8320 does not amount to one part in 6000. The form 20 of the series is also very judiciously chosen for 26.2424 0·8457 0.8383 74 20 27.2424 0.8543 0.8443 the purposes of science. It would perhaps have 100 20 28.2-24 0.8621 been more directly stereometrical had the pro 0-8498 123 20 29.2424 0.8692 0.8549 portions of the ingredients been stated in bulks 143 20 30.2424 0.8757 which are more immediately connected with 0.8597 160 density. But the author has assigned a very co20 31.2424 0.8817 0.8642 175 20 9 32.2424 0.8872 0.8684 gent reason for his choice, viz. that the tempe 188 20 rature of bulks varies by a change of temperature, 33.2424 0.8923 0.8725 199 because the water and spirits follow different 34.2424 0.8971 0.8762 216 20 laws in their expansion by heat. 12 35.2424 0.90 14 0.8796 218 20 13 36.2424 Mr. Lambert, one of the first mathematicians 0.9055 0.8829 226 and philosophers of Europe, in a dissertation in 20 14 37.2424 0.9093 0.8860 233 20 the Berlin Memoirs (1762), gives a narration of 15 38.2424 0.9129 0.8891 238 20 experiments on the brines of common salt, from 39.2434 0.9162 0.8919 243 which he deduces a very great condensation, 20 17 40.2424 0.9193 0.8946 247 which he attributes to an absorption in the weak 20 18 41.2424 0.9223 0.8971 252 brines of the salt, or a lodgment of its particles 20 19 42.2424 0.9250) 0.8996 25+ 20 in the interstices of the particles of water. Mr. 43.2424 0.9276 0.9019 257 20 Achard of the same academy, in 1785, gives a 44.2424 0.9300 0.9041 259 19 43.0303 0.9325 0.9063 262 very great list of experiments on the bulks of 18 20 48:1182 0.9349 0.9087 various brines, made in a different way, which 262 show no such introsusception; and Dr. Watson, 40.6061 0.9375 0.9112 263 16 20 39:3939 0.9402 0.9139 formerly regius professor of chemistry at Cam 263 15 bridge, thinks this confirmed by experiments 20 38:1818 0.9430 0.9167 263 which he narrates in his Chemical Essays. We 14 20 36.9697 0.9458 0.9197 261 13 20 35.7576 0 9488 0.9229 cannot assent to either side, and do not think 259 the experiments decisive. We incline to Mr. 12 20 34.5455 0.9518 0.9263 255 11 20 33.3333 0.9549 Lambert's opinion; for this reason, that in the 0.9300 249 10 32:1212 0.9580 0.9340 successive dilutions of sulphuric acid and nitric 240 acid there is a most evident and remarkable con9 20 30.9091 0-9612 0.9382 230 20 densation. Now what are these but brines, of 29.6970 | 0.9644 0.9429 215 7 20 which we have not been able to get the saline in28.4849 0.9675 0.9479 196 6 20 27.2727 0.9707 0.9533 174 gredient in a separate form? The experiments of Mr. Achard and Dr. Watson were made in 5 20 26-0606 0.9741 0 9593 148 20 24.8485 0.9777 0.9659 such a way that a single grain in the measure 118 23.6364 0.9818 0.9731 ment bore too great a proportion to the whole 87 22:4242 0.9864 0.9811 54 change of specific gravity. At the same time, 1 20 21.2121 some of Dr. Watson's are so simple in their na0.9924 0.9900 24 20 20.0000 ture that it is very difficult to withhold the as1.0000 1.0000 sent. Experiments have also been made which seem sufficient for deciding the question. “WheThe condensation is greatest when sixteen ounces ther the salt can be received into the pores of and a half of alcohol have been added to twenty the water, so as to increase its weight without of water, and the condensation is or nearly increasing its bulk?' and we must grant that it one-thirty-sixth of the computed density. Since may. We do not mean that it is simply lodged the specific gravity of alcohol is 0.825, it is in the pores as sand is lodged in the interstices evident that sixteen ounces and a half of alcohol of small shot ; but the two together occupy less and twenty ounces of water have equal bulks. room than when separate. The experiments of So that the condensation is greatest when the Mr. Achard were insufficient for a decision, besubstances are mixed in equal volumes ; nd cause made on so small quantity as 600 grains eighteen gallons of alcohol mixed with eighteen of water. Dr. Yvatson's experiments have, for gallons of water will produce not thirty-six gal- the most part, the same defect. Some of them, lons of spirits, but thirty-five only. This is the however, are of great value in this question, and mixture to which our revenue laws refer, de- are very fit for ascertaining the specific gravity claring it to be one to six or one in seven under of dissolved salts. proof, and to weigh seven pounds thirteen ounces Specific gravity, says Dr. Ure, is the density per gallon. This proportion was probably se of the matter of which any body is composed, lected as the most easily composed, 'viz. by 'mix- compared to the density of another body, assumed ing equal measures of water and of the strongest as the standard. This standard is pure distilled spirit which the known processes of distillation water, at the temperature of 60° Fahrenheit. To could produce. Its specific gravity is 0.939 determine the specific gravity of a solid we very nearly. This elaborate examination of the weigh it, first in air, and then in water. In the mixture of water and alcohol is a standard se- latter case it loses of its weight a quantity pre 3 2 20 V P = + W + w P+P cisely equal to the weight of its own bulk of the specific gravities of the two components, we water; and hence, by comparing this weight with W have P its total weight, we find its specific gravity. The and p =-; whence V = V rule therefore is, Divide the total weight by the loss of weight in water, the quotient is the spe р cific gravity. If it be a liquid, or a gas, we weigh In the condition when W=w=1, we have it in a glass or other vessel of known capacity; and, dividing that weight by the weight of the then V= P and consequently, theresame bulk of water, the quotient is, as before, р the specific gravity. fore, To calculate the mean specific gravity of a com 1 pound from those of its components is a problem P (P-p)(p-P). 2 A=(P-p) x = of perpetual recurrence in chemistry. It is only 1 P+P by a comparison of the result of that calculation, with the specific gravity of the compound expe (P-p) rimentally ascertained, that we can discover whether the combination has been accomparied with expansion or condensation of volume. As several that the true value of the specific gravity of the This value being constantly negative prores respectable experimental chemists (see Alloy, and AMMONIA) seem deficient in this part of mixture, represented by is always chemical computation, I shall here insert a short + V abstract of a paper which I published on this smaller than the false value, W + subject in the seventh number of the Journal of Science. Example of the last formula:The specific gravity of one body is to that of 19:3+10:5 another as the weight of the first, divided by its Gold and silver, = 14.9 = false 2 volume, is to the weight of the second, divided (P-P) by its volume; ånd the mean specific gravity of or arithmetical mean specific gravity. the two is found by dividing the sum of the (19-3—10:5)?_ (8.8)? 77.44 weights by the sum of the volumes. = 2:6=2A; Let W, w, be the two weights; V, v, the two 29.8 29.8 29.8 volumes ; P, p, the two specific gravities; and and a = 1:3, which being subtracted from the M the calculated mean specific gravity. Then arithmetical mean, 14:9, leaves 13.6 for the true mean specific gravity as directly obtained by the M= ; the formula by which I computed (W+w)P p formula the second colump of Table II. Pw+pW Sulphuric acid Table, showing the erroneous re- sults of the common method. Hence, (W+w) Pp Acid in Arithmetical Experimental Apparent 100. density. Pp density. When the difference in density between the 100 1.8480 100 two substances is considerable, as it is with sul 90 1.7632 1.8115 97.3 phuric acid and water, the errors produced by 80 1.6784 1.7120 98.0 assuming the arithmetical mean for the true cal 70 1.5936 culated mean are excessive. If we take copper 1:5975 99-7 60 1.5088 1.4860 101.5 and tin, however, then the arithmetical mean, 50 1.4240 8.89 + 7.29 1.3884 102.6 = 8:09, differs very little fiom 8.01, 40 1:3392 1.2999 103-02 2 30 1.2544 1.2184 102.95 the accurate mean density. 20 1.1696 1.1410 102.50 By a similar error, I suppose, in calculating 10 1.0848 1.0680 101.57 the mean density of liquid muriatic acid in its different stages of dilution, the celebrated Kirwan has long misled the chemical world. He asserted Mr. Robertson, in order to determine the spethat the mean specific gravity of the components cific gravity of men, prepared a cistern seventybeing also the experimental mean, there is no eight inches long, thirty inches wide, and thirty condensation of volume as with other acid dilu- inches deep; and, having procured ten men for tions. And the illustrious Berthollet has even his purpose, the height of each was taken, and assigned a cause for this suppositious fact. I his weight; and afterwards they plunged succesfind, on the contrary, that 50 of acid, specific sively into the cistern. A ruler, graduated to gravity 1.1920, with 50 of water, give out heat, inches and decimal parts of an inch, was fixed to and have their volume diminished in the ratio of one end of the cistern, and the height of the water 100 to 99.28. The experimental specific gravity noted before each man went in, and to what is 1.0954 ; that by the exact rule is only 1:0875. height it rose when he immersed himself under The preceding formula may be presented its surface. The following table contains the under a still more convenient form. Pp being several results : W +w V+v And V+v=7 W+w W+w = M. mean |