ent. Therefore two, or perhaps three, are necelary for general examination. One may reach from æther to water; another may ferve for all bquors of a specific gravity between 1 and 1; and the third, for the mineral acids, may reach from this to-2. If each of these be about two fohid inches in capacity, we may easily and expeditioully determine the fecific gravity within one ten thousandth part of the truth; and this is pre cilon enough for molt purposes of feience or bufinefs. The chiet queftions are, 1. To fcertain tae fpecic gravity of an unkown fluit. This needs no farther exp anation. 2. To ascertain the proportion of two fluids which are known to be in a mixture. This is done by difcovering the fɔecific gravity of the mixture by means of the hydrometer, and then deducing the proportion from a comparifon of this with the fpecific gravities of the ingredients. In this mode of exa mination the bulk is always the fame; for the hydrometer is immerged in the different fluids to the fame depth. Now if an inch, for example, of this buik is made up of the heaviest Buid, there is an inch wanting of the lightet; and the change made in the weight of the mix ture is the difference between the weight of an inch of the heaviest and of an inch of the lighteft ingredients. The number of inches therefore of the heaviest fluid is proportional to the addition made to the weight of the mixture. Therefore let B and b be the bulks of the heaviest and lightest fluids in the buik 3 of the mixture; and ki D, d, and be the dentities, or the weights, or the specific gravities (for they are in one ratio) of the heavy fluid, and the light fluid, and mixture (their bulk being that of the hydrometer. We have 3 B÷b. The addition which would have been made to the bulk 2, if the lighteft fluid were changed entirely for the heavieft, would be D 4; and the change which is really made is d-d. -Therefore 3:1 D-d:-d. For fimilar reafons we should have £: B=D~d: D−ò; or, in words, "the difference between the specific gravities of the two fluids, is to the difference between the fpecific gravities of the mixture and of the lighteft fluid, as the buk of the whole to the bulk of the heaviest contained in the mixture;" and "the difference of the fp cific gravities of the two fluids, is to the difference of the specific gravities of the mixture and of the bearret fluids, as the bulk of the whole to that of the lightest contained in the mixture." This is the form in which the ordinary bufinefs of life requires the answer to be expreffed, becaufe we generally reckon the quantity of liquors by bulk, in gallons, pints, quarts. But it would have been equally eafy to have obtained the anfwer in pounds and ounces; or it may be had from their bulks, fince we know their specific gravities. The hydrometer more commonly used is the an. cient one of HYPATIA, confifting of a ball, A. (Plate 312, fig. 2.) made fteady by an addition B, below it like the former, but having a long ftem CF above. It is fo loaded that it finks to the top F of the ftem in the lightest of all the fluids which we propofe to measure with it, and to fink only to C in the heavieft. In a fluid of intermediate fpecific gravity it will firk to fome point between C and F. In this form of the hydrome VOL. XXI. PART I.

ter the weight is always the fame, and the immediate information given by the inftrument is that of different bulke with equal weight. Because the initium at finks till the bulk of the difplaced fluid equals it in weight, and the addition to the dif placed flaid are all made by the ftem, it is evident that equal bulks of the stem indicate equal additions of volume. Thus the fem becomes a fcale of bulk to the fame weight. The only form in which the temn can be made with fulficient accuracy is cylindrical or prifinatical. Such a tem may be made in the most accurate manner by wiredrawing, that is paffing it through a hole made in a hardened Heel plate. If fuch a stem be divided into equal parts, it becomes a scale of bulks in arithmetical progreffion. This is the easiest and moft natural division of the scale; but it will not indicate denfities, fpecific gravities, or weights of the fame bulk in arithmetical progreffion. The specific gravity is as the weight divided by the bulk. Now a series of divifors (the bulks), in a rithmetical progreffion, applied to the fame dividend (the bulk and weight of the hydrometer as it floats in water,) will not give a feries of quotients (the specific gravities) in arithmetical progrefiion : they will be in what is called barmonic progreffion, their differences continually diminishing. This wil appear even when phyfically confidered. When the hydrometer finks a tenth of an inch near the the top of the stem, it displaces one roth of an inch of a light fluid, compared with that displaced by it when it is floating with all the stem above the furface. In order therefore that the divifions of the ftem may indicate equal changes of specific gravity, they must be in a feries of harmonic progreffionals increafing. The point at which the inftrument floats in pure water thould be marked 1000, and thofe above it 999, 998, 997, &c.; and thofe below the water mark must be numbered 1001, 1002, 1003, &c. Such a feale will be a very appofite picture of the denfities of fluids, for the denfity or vicinity of the divifions will be percifely fimilar to the density of the fluids. Each interval is a bulk of fluid of the fame weight. If the whole inftrument were drawn out into wire of the fame fize of the stem, the length from the water mark would be 1000. Such are the rules by which the fcale must be divided. But there must be fome points of it determined by experiment, and it will be proper to take the'n as remote from each other as poflible. For this purpose let the inftrument be accurately marked at the point where it ftands, in two fluids, differing as much in fpecific gravity as the inftrument will admit. Let it alfo be marked where it ftands in water. Then determine with the utmost precifion the specific gravities of thefe fluids, and put their values at the correfponding points of the fcale. Then the intermediate points of the fcale must be computed for the different intervening fpecific gravities, or it must be divided from a pattern fcale of harmonic progreffionals in a way well known to the mathematical inftrument-makers. If the specific gravities have been accurarely determined, the value 1000 will be found to fall precifely in the water mark. If we attempt the divifion entirely by experiment, by making a number of fluids of different fpecific gravities, and mark

Kk

ing

ing the fem as it flands in them, we fhall find the divifions turn out very anomalous. This is however the way ufually practifed; and there are few hydrometers, even from the beft maker, that hold true to a tingle divifion or two. Yet the method by computation is not more troublefome; and one fcale of harmonic progreffionals will ferve to divide every ftem that offers. We may make ufe of a fcale of equal parts for the ftem, with the affiftance of two little tables. One of thefe contains the fpecific gravities in harmonic progreffion, conefponding to the arithmetical feale of bulks on the filem of the hydrometer; the other contains the divifions and fractions of a divifion of the feale of bulk, which correspond to an arithiretical feale of fpecific gravities. We believe this to be the beft method of all. The scale of equal parts on the fem is fo early made, and the little table is fo eafily infpected, that it has every advantage of accuracy and difpatch, and it gives, by the way, an amufing view of the relation of the bulks and denfities. We have hitherto fuppofed a feale extending from the lighteft to the t.cavieft Buid. But unk is it be of a very inconvenient length, the divifion, muft be very miunte. And when the bulk of the ftem bears a great proportion to that of the body, the intrument does not fwim steady; it is therefore proper to limit the range of the inftrument in the fame manner as thole of the firft ki d. A range from the denfity of æther to that of water may be very well executed in an ioftrument of very moderate fize, and two others will do for all the heavier licuors; or an equal range in any other densities as may fuit the vial occupations of the experimenter. To avoid the inconveniences of a hydrometer with a very long and lender item, or the neceffity of having a series of them, a third fort has been contrived, in which the principle of both are combined. Suppoíc a hydrometer with a item, whofe bulk is one foth of that of the ball, and that it faks in ether to the top of the fiem; it is evident that in a fluid which is one roth heavier, the whole fem will emerge; for the bulk of the difplaced fluid is now one icth of the whole lefs, and the weight is the fame as before, and therefore the fpecific gravity is one roth greater. Thus we have obtained a hydrometer which will indicate, by means of divifions marked on the ftem, all ipeeine gravities from c*73 to 0803; for 0803 is one Yoth greater than e 73. Thefe divifions must be ride in harmonic progreflions, as before directed for an entire feale, placing o'73 at the top of the ftem and o83 at the bottom. When floats at the lowett divifion, a weight may be put on the top of the flem, which will again fink it to the top. This weight must evidently be 0073, or one roth of the weight of the fluid difplaced by the unloaded inflrument. The hydrometer, thus joaded, indicates the fime ipecific gravity, by the top of the ftein, that the unloaded inftrument incates by the lowel divifion. Therefore, when Jded, it wil indicate another series of specific gravities, from 0803 to p8.3 (=0803+0 ́0803), ad will float in a liquor of the fpecific gravity 08833 with the whole ftem above the furface. I like manner, if we take off this weight and put c085,3, it will fink the hydrometer to the

1

top of the ftem; and with this new weight it will indicate another series of specific gravities from o8833 to 097163 (=c8833 +008633). And, in the fame manner, a third weight=08833 will a gain link it to the top of the ftem, and fit it for another feries of specific gravities up to ro68793. And thus, with three weights, we have procured a hydrometer fitted for all liquors from æther to a wort for a malt liquor of two barrels per quarter. Another weight, in the fame progretion, will extend the inftrument to the ftrongest wort that is brewed. This is a very commodious form of the inftru rent, and is now in very general ufe for examining fpirituous liquors, worts, ales, brines, and many tuch articles of commerce. But the divifions of the fcale are generally adapted to the queftion's which naturally occur in the business. Thus, in the commerce of ftrong liquors, it is ufual to estimate the article by the quantity of fpirit of a certain ftrength whit, the liquor contains.

This we have been accustomed to call PROOF SPIRIT, and it is fuch that a wine gallon weighs 7 lb 12 oz.; and it is by this ftrength that the excife duties are levied. Therefore the divifions on the feale, and the weights which connect the suc cellive repetitions of the fcale, are made to exprefs at once the number of gallons or parts of a gallon of proof fuirits contained in a gallon of the liquor. Such inftruments fave all trouble of calculation to the exisèman or dealer; but they limit the use of a very delicate and expenfive inftrument to a very narrow employment. It would be much better to adhere to the expreffion either of specific gravity or of bulk; and then a very finall table, which could be comprifed in the finallest cafe for the inftrument, might render it applicable to every kind of fluid. The reader cannot but have obferved that the fuccellive weights, by which the fhort fca'e of the inftrument is extended to a great range of specific gravities, do not increase by equal quantities. Each difference is the weight of the liquor difplaced by the graduated stem of the inftrument when it is funk to the top of the feale. It is a determined aliquot part of the whole weight of the inftrument fo loaded, (in our exam. ple it is always one 11th of it.) It increases therefore in the fame proportion with the preceding weight of the loaded inftrument. In fhort, both the fucceffive additions, and the whole weights of the loaded instrument, are quantities in geometri cal progreffion; and in like manner, the divifions on the feale, if they correspond to equal differences of specific gravity, must also be unequal.-This is not fufficiently attended to by the makers; and they commit an error here, which is very confiderable when the whole range of the inftrument is great. For the value of one divifion of the scale, when the largest weight is on, is as much greater than its value, when the inftrument is not loaded at all, as the full loaded inftrument is heavier than the inftrument unloaded. No manner whatever of dis viding the feale will correfpond to equal differences of foecific gravity through the wrote range with different weights; but if the divifions are made to indicate equal proportions of gravity when the inftrument is ufed without a weight, they will indicate qual proportions throughout. This is e vident from what we have been just now fayings

for

for the proportion of the specific gravities correfponding to any two immediately fucceeding weights is always the fame. The best way, there. fore, of conftructing the inftrument, fo that the fame divifions of the fcale may be accurate in all its fucceffive repetitions with the different weights, i- to make thefe divifions in geometrical progreffion. The correfponding specific gravities will alfo be in geometric proportion, Thefe being all inferted in a table, we obtain them with no more trouble than by infpecting the fcate which ufually accompanies the hydrometer. This table is of the most eafy conftruction; for the ratio of the fucceffive bulks and fpecific gravities being all equal, the differences of the logarithms are equal. This will be illuftrated by applying it to the example already given of a hydrometer extending from 073 to 068793 with three weights. This gives four repetitions of the feale on the ftem. Suppofe this fcale divided into 1o parts, we have 40 fpecific gravities.-Let these be indicated by the numbers o, 1, 2, 3, &c. to 40. The mark o, is affixed to the top of the ftem, and the divifions downwards are marked 1, 2, 3, &c. the lowest being 10. Thefe divifions are easily determined. The ftem, which we may fuppofe 5 inches long, was fuppofed to be one roth of the capacity of the ball. It may therefore be confidered as the extremity of a rod of 11 times its length, or 55 inches; and we must find nine mean proportionals between 50 and 55 inches. Subtract each of these from 55 inches, and the remainders are the diftances of the points of divifion from o, the top of the feale. The fmalleft weight is marked 10, the next 20, and the third 30. If the inftrument loaded with the weight 20 finks in fome liquor to the mark 7, it indicates the specific gravity 27, that is, the 27th of 40 mean proportionals between 073 and 1068793, or 0914242. To obtain all thefe intermediate fpecific gravities, we have only to fubtract 9.8533229, the logarithm of 073, from that of 1068793, viz. co288937, and take 0'0041393, the 40th part of the difference. Multiply this by 1, 2, 3, &c. and add the logarithm of 073 to each of the products. The fums are the logarithms of the fpecific gravities required. Thefe will be found to proceed fo equably, that they may be interpolated ten times by a fimple table of proportional parts without the smallest fenfible error. Therefore the flem may be divided into a hundred parts very fenfible to the eye (each being nearly the 20th of an inch), and 400 degrees of specific gravity obtained within the range, which is as near as we can examine this matter by any hydrometer. Thus the fpecific gravities correfponding to no 26, 27, 28, 29, are as follow:

hydrometer on this feale of equal parts, we fee opposite to it the fpecific gravity. We have been thus particular in the illuftration of this mode of conftruction, because it is really a beautiful and commodious inftrument, which may be of great ufe both to the naturalift and to the man of bufinefs.-A table may be comprifed in 20 pages 8vo. which will contain the fpecific gravities of every fluid which can intereft either, and answer every queftion relative to their admixture with as much precifion as the obfervations can be made. We therefore recommend it to our readers, and we recommend the very example which we have given as one of the moft convenient. The inftrument need not exceed 8 inches in length, and may be contained in a pocket cafe of 2 inches broad and as many deep, which will alfo contain the feale, a thermometer, and even the table for applying it to all fluids which have been examined." (9.) SPECIFIC GRAVITY, METHODS OF EXAMINING. There is another method of examining the foecific gravities of fluids, first propofed b7 Dr Wilfon, late profeffor of aftronomy in the university of Glasgow. This is by a series of fmail glfs bubbles, differing equally, or according to fome rule, from each other in fpecific gravity, and each marked with its proper number. When thefe are thrown into a fluid which is to be examined, all thofe which are heavier than the fluid will fall to the bottom. Then holding the vellel in the hand, or near a fire or candle, the fluid expands, and one of the floating bubbles begins to fink. 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 fink, will inform us how much it was deficient, if we know the law of expansion of the liquor. Sets of thefe bubbles fitted for the examination of foirituous liquors, with a little treatife showing the manner of ufing them, and calculating by the thermometer, are made by Mr Brown, an ingenious artist of Glasgow, and are often ufed by the dealers in fpirits, being found both accurate and expeditious. Alfo, though a bubble or two thou) t be broken, the ftrength of fpirits may easily be had by means of the remainder, unlefs two or three in immediate fucceffion be wanting for a liquor which anfwers to N° 4 will fink N° 2 by heating it a few degrees, and therefore N° 3 may be fpared. This is a great advantage in ordinary bufinefs. A nice hydrometer is not only an expenfive inftrument, but exceedingly delicate, being fo very thin. If broken or even bruifed, it is ufelefs, and can hardly be repaired except by the very maker. As the only queftion here is, to determine how many gallons of excite proof fpirits are contained in a quantity of liquor, the artist has conftructed this feries of bubbles in the fimpleft manner poffible, by previoutly making 40 or 50 mixtures of fpirits and water, and then adjusting the bubbles to thefe mixtures. In fome fets the number on each bubble is the number of gallors of proof fpirits cotained in 100 gallons of the liquor. In other fets the number on each bubb'e expreffes the gallons of water which will make a liquor of this ftrength, if added to 14 gailons of alcohol. Thus, if a liquor anfwers to N° 4, then 4 gallons of water added to 14 gallons of alcolel Kk 2

will

will make a liquor of this ftrength. The firft is the best method; for we thould be mistaken in fuppofing that 18 gallons, which anfwer to N° 4. contains exactly 14 gallons of alcohol: it contains more than 14. By examining the specific gravity of bodies, the philofopher has made fome very curious difcoveries. The moft remarka' le of thefe is the change which the denfity of bodies fuffers by mixture. It is a molt reafonable expectation, that when a cubic foot of one substance is mixed any how with a cubic foot of another, the bulk of the mixture wil be two cubic feet; and that 18 gallons of water joined to 18 galions of oil will fil a veffel of 36 gallons. Accordingly this was never doubted; and even Archimedes, the most fcrupulous of mathematicians, proceeded on this fuppofition in the fylation of his famous problem, the difcovery of the proportion of tiver and gold in a mixture of bath. He does not even mention it as a poftulate that may be granted him, fo much did he conceive it to be an axiom. Yet a little reflection feems fufficient to make it doubtful, and to require examination. A box filled with musket-balls will receive a confiderable quantity of imali thot, and after this a confiderabi- quantity of fine fand, and after this a confiderable quity of water. Something like this might happen the admixture of bodies of porous texture. But fush fubftances as metals, gafs, and fluids, where no ifcontinuity of parts can be perceived, or was fufpected, feem free from every chance of this kind of introfufception. Lord Ve. rulam, however, without being a naturalift or mathematician ex profeffo, inferred from the mobility of Huids that they confifted of difcrete particles, which must have pores interpofed, whate ver be their figure. And if we afcribe the different densities, or other fenfible qualities, to difference in fize or figure of thofe particies, it must frequently happen that the smaller particles will be lodged in the interftices between the larger, and thus contribute to the weight of the fenfible mifs without increafing its bulk. He therefore fufpects that mixtures will be in general lefs buiky than the fum of their ingredients. Accordingly, the examination of this queftion was one of the first employments of the Royal Society of London, and long before its inftitution had occupied the attention of the gentlemen who afterwards compofed it. The regifter of the Society's early meetings contains many experiments on this fubject, with mixtures of gold and filver, of other metals, and of various fluids, examined by the hydroftatical balance of Mr Boyie, Dr Hooke made a prodigious number, chiefly on articles of commerce, which were unfortunately loft in the tire of London. It was foon found, however, that Lord Verulam's conjecture had been well found. ed, and that bodies changed their density very fenfibly in many cafes. In general, it was found that bodies which had a ftrong chemical affinity increafed in denfity, and that their admixture was accompanied with heat. By this difcovery it is manifeft that ARCHIMEDES had not folved the problem of detecting the quantity of filver mixed with the gold in King HIERO'S CROWN, and that the phyfical folution 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 moft defirable to be able to reduce it to fome general laws: For inftance, to ascertain what is the proportion of two ingredients which produces the greiteft change of denfity. This is important in the fcience of phyfies, because it gives us confi derable information as to the mode of action of thofe natural powers or forces by which the particles of tangible matter are united. If this introfaception, concentration, compenetration, or by whatever name it be called, were a mere recep tion of the particls of one substance into the interitices of thofe of another, it is evident that the greatest concentration would be obferved when a fmall quantity of the recipiend is mixed with, or diffeminated through, a great quantity of the other. It is thus that a mail quantity of fine fand will be received into the interfices of a quantity of fmall that, and will increase the weight of the bagful without increafing its buik. The cafe is nowife different when a piece of freeftone has grown heavier by imbibing or abforbing a quan tity of water. If more than a certain quanti ty of fard 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 fize and weight alike. All this is very conceivable, occafioning no difficulty. But this is not the cafe in any of the mixtures we are now confidering. In all these, the first additions of either of the two fubftances produce but an inconfiderable change of general dentity; and it is in general moit remarkable, whether it be condenfation or rarefaction, when the two ingre dients are nearly of equal bulks. We can illuf trate even this difference, by reflecting on the im bibition of water by vegetable folids, fuch as timber. Some kinds of wood have their weight much more increated than their bulks; other ki: ds of wood are more enlarged in bulk than in weight. The like happens in grains. This is cu rious, and fhows in the most unquestionable manner that the particles of bodies are not in contact, but are kept together by forces which act at a diflance. For this diftance between the centres of the particles is moft evidently fufceptible of variation; and this variation is occafioned by the introduction of another fubftance, which, by acting on the particles by attraction or repulfion, dimi nithes or increafts their mutual actions, and makes new distances neceffary for bringing all things a gain into equilibrium. We refer the curious reader to the ingenious the ry of the Abbé Bogcovich for an excellent illuftration of this fubject. Theor. Phil. Nat. § de Solutione Chemica.

(10.) SPECIFIC GRAVITY OF METALS ALTERED BY MIXTURE. This question is no leis import ant to the man of butines. Till we know the condenfation of thofe metals by mixture, we cannot tell the quantity of alloy in gold and fiver by means of their specific gravity; nor can we tell the quantity of pure alcohol in any fpirituous liquor, or that of the vantable falt in any folution of it. For want of this knowledge, the dealers in gold and liver are obliged to have recourfe to the te