STATICS. Now the weight of a body of the first kind, may be gather'd from that of the water equal in magnitude to the immerfed part of the body, when it floats freely thereon. Thus, if a parallelopipid, or a cylinder of wood twelve inches long, placed upon water, fhould reft there when a twelfth part of it lies beneath the furface of the fluid; the weight of the water, equal in bulk to that immerfed twelfth part, would be equal in weight to the whole body of the wood. But because the bodies, whofe bulk phyficians and chymifts may have occafion to examine, will very feldom happen to have regular figures; 'tis proper to add another method, more fuitable to the prefent defign. To measure then the folid contents of bodies fpecifically lighter than water, but irregularly fhaped*; the body must, firft, be weigh'd in air. 2. A plate of lead, capable of finking this body in water, and of fome round fum in weight, fhould be provided. 3. This plate being weigh'd in water, and its weight therein fubftracted from its weight in air, will give the weight of as much water, as is equal in bulk to the immersed lead; or the specific weight of the lead in water. 4. The plate of lead, and the lighter body, muft be tied together with horse-hair, and the weight of the aggregate noted. 5. This aggregate must be weigh'd in water, and its weight therein fubftracted from that it had in air; and the difference will give the fpecific weight of the faid aggregate in water. 6. From this difference fubftract the fpecific weight of the plate in water, and the remainder will give the weight of the lighter body in the fame fluid. Then, lastly, that weight of the light body in water being divided by 256 grains, will give its folid content. To clear and confirm this method by an example; we took a conveniently shaped piece of oak, that weigh'd in air 193 grains; to this we tied, with an horfe-hair, a plate of lead, weighing juft 240 grains. But before we tied them together, the lead was weigh'd in water, where it loft of its former weight 20 grains; which, being deducted out of the 240 grains, left a difference of 20 grains, for the fpecific weight of the lead in the water. Then the aggregate of the wood and lead was weigh'd, first in the air, and found to be 433 grains, and next in water, where it amounted but to 162 grains; which being fubftracted from the aggregate of the fame bodies in air, the difference was 271+ grains; from which, the other difference of 20 grains of the leaden-plate in water being deducted, there remain'd 251 grains, for the weight of a bulk of water equal to that of the given piece of wood. Now, if this number of grains had amounted to 256, we might have concluded the folidity of the body There is a very eafy method of obtaining the content, or cubic measure, of any folid, tho' ever fo irregularly figured. For, fince fuch a body, immersed in a fluid wherin it will not diffolve, causes that fluid to rife in direct proportion to the bulk immerfed; if the fluid be contain'd in a cylindrical or prifmatic veffel, and the additional height given it by the body be marked on the veffel; this will enable us to measure a part of the whole cylinder or prifm, equal in bulk to the irregular body. And thus may the folid content of ftatues, carv'd or embois'd work, &c. be known. to be a cubic inch; fince 256 grains of water, which we formerly found STATICS. equal to a cubic inch of water, was alfo now found equal to the bulk of the given piece of wood. And having caufed the wood I employ'd to be formed into a cubic inch; the difference of its weight in water from 256 grains, may, probably, be imputed to fome little imperfection in the figure, or other like circumftance. First, then, the cube of oak in air, weigh'd 193grains. 2. The lead in air, 240 grains. 3. The lead in water, 220 grains; which, fubftracted from its weight in air, leaves for its specific weight in water, 20 grains. 4. The aggregate of the two in air, 433 grains. 5. The weight of both together in water, 162 grains; which, fubftracted from the fum of their weight in air, gives the difference of the two feveral aggregates, 271 grains. 6. The difference between the weight of the lead in air, and in water, 20 grains; which, fubftracted from the difference of the weights of the aggregates in air, and in water, gives for the weight of the propofed cube 251 grains. This way of measuring bodies is appropriated to fuch of them as will not readily diffolve in water. But, because there are many other solids, as falt, alum, vitriol, fugar, &c. whose magnitudes it may often be proper to know and compare; I fhall add, that the fame method is applicable, alfo, to folids diffoluble in water, if, instead of that fluid, be substituted oil of turpentine, whofe proportion of fpecific gravity to water is otherwife known. To discover this, I employ'd the hollow cubic inch of brass, made ufe of to find the weight of a cubic inch of water; and found, that, when carefully filled, it contained 221 grains of this oil: by which number, the difference of the weight of a folid in the air, and in that oil, being divided, the quotient will give the folid contents of the body to be examined. Let us now confider how fuch bodies as, by their porofity, are fubject' to imbibe too much of the liquor, while the experiment is in hand. Merfennus's expedient, in this cafe, is to cover the body to be weigh'd in water, with wax, pitch, or fome other glue, of a known fpecific weight in water. But I prefer bees wax for this purpofe; and proceed with it in the following manner. The folid which is lighter than water, having been first weigh'd in air, over-lay it carefully with thin bees-wax; then take, also, in the air, the weight of the wax employ'd; and fasten to the body thus coated, a plate of lead or tin, heavy enough to fink it; and obferve the weight of the aggregate in water. This done, fubftract the weight of as much water as is equal in bulk to the wax, and proceed as is before taught. But this method helps us only to the weight of the propofed body in water; to discover its folid content, we must divide the weight of the folid in water, by 256 grains. And, by the way, I have, fometimes, made ufe of another expedient to hinder small folids, whether lighter or heavier in fpecie than water, from imbibing the liquor wherein they were weigh'd: for having firft found the weight of a cubic inch of quick-filver; we placed the body to be mea fured, STATICS.. fured, in a veffel, whofe folid contents were known before-hand; when, the space that remain'd unpoffeffed by the firm body being fill'd with quickfilver, 'twas eafy to know, by the difference in weight of that quickfilver, from the weight of the quick-filver requifite to fill the whole veffel, how much thereof was equal to the furrounded body. And, by this means, and the knowledge before gain'd of the weight of a cubical inch of mercury, the folid content of the body propofed, was eafily obtain'd. What accuBefore I put an end to this difcourfe, 'tis proper to fhew what credit racy is to be may be given to the estimates of the weights and proportions of bodies expected in hydrostatical obtain'd by hydrostatical trials; because mathematicians, either not knowexperiments. ing, or not applying our observation about the fpecific gravity of rockcryftal, and the nature of oil of turpentine, have given us very different accounts of the proportions of metals, and a very few other familiar bodies, which are all they feem'd to have examin'd by this method. And, indeed, I fhould not be furprized to find, that the experiments of the fame perfon, made at diftant times, and under different circumftances, disagreed; for fome difference there may be betwixt the waters employ'd in this cafe; efpecially if the air be at one time intensely hot, and at another exceeding cold. The difference, alfo, of degrees in goodness of the balances ufed in nice experiments, is not altogether inconfiderable. But a greater hindrance to the accuracy of hydroftatical experiments, is the difficulty of finding an exact uniformity in weights of the fame denomination, which are vulgarly fuppofed to be exactly equal. I have myself found it fo difficult in practice to procure, and keep weights as exact as I desired, that I have left off the hopes of it; for the very air may, in time, caufe an alteration in them. And tho' the accurate Ghetaldus's tables of the weight of metals, and fome other bodies, in respect to one another, are look'd upon as the most authentic that have been publish'd; and are, accordingly, the most made ufe of; yet 'tis certain, the weights he employ'd are not divided as ours are. For tho', according to him, as well as with us, the ounce confifts of four and twenty fcruples; yet the fcruple, which with us is divided but into twenty grains, he divides into twenty-four. But tho' hydrostatical experiments are not, always, either fingly accurate, or exactly agreeable to one another; they prove accurate enough to be very ufetul in practice, and more exact than any other method, hitherto employ'd, of determining the proportions of bodies, in point of weight and bulk, and of measuring their folid contents; but, efpecially, fuch little ones as are neceffary to be examined in the Materia medica. And this is a corollary from the whole of what we have deliver❜d. And, indeed, as little as my skill is in hydrostatics, I would not be debarr'd from the ufe of it, for a very valuable confideration; for it has already done me acceptable fervice, and on a vast variety of occafions ; especially in the examination of metal and mineral bodies, and of feveral chymical productions. I have often been able, by its means, to undeceive artists in their perfuafion of poffeffing Luna fixa, and other valuable commodities; and to make a judgment, as to the genuineness or falfity, and as to the degrees of worth or ftrength of many rich and STATICS. poor metalline mixtures, and other bodies, both folid and fluid; whofe fair appearances might, otherwife, have greatly deceived me. And to fhew fome curious perfons how far hydrostatics might be ferviceable to as accurate menfurations as need be expected in phyfical experiments; I defired a virtuofo to mix tin and lead in a certain proportion, unknown to me; and melt them into one mafs; which I carefully weigh'd in water, and alfo examined it algebraically; and from hence affign'd the refpective quantities of each; which agreed, within little more than a grain, with thofe he had committed to paper, before he mixed them. And this fmall difference, probably, proceeded from fome fcarce avoidable inaccuracies in melting and managing the given bodies. To conclude; 'tis not to be expected, that the fpecific gravities of the bodies mention'd in the following table, fhall, all of them, be found, in future trials, precifely the fame as we there exhibit them. For, befides that experiments are made by perfons of different qualifications, with dif ferent degrees of care, and with different inftruments; the varieties may proceed from a difference in the texture and compactness that may be found in feveral bodies of the fame kind. For, neither nature, nor art, give to all the productions of the fame name, a mathematical preciseness,. either in gravity, or other qualities. Dr. Jurin recommends it, as a neceffary caution, to all those who fhall attempt to weigh dry, porous folids in water, for philofophical purposes, that, by fome proper means, they firft extricate the air out of all the fmall pores and cavities of them; whereby the water may have free liberty to enter thereat: otherwife the air contain'd therein, by keeping the water out, will render the folid lighter in water than it really is. The best way of avoiding this inconvenience, the Doctor tells us, is to fet the veffel of water, wherein the folid is immerfed, under the receiver of an air-pump, and extract the air out of the body; which 1 will fucceed the better, if the water be first. tor thinks, among other things, is owing Specific gravity of the Calculi bumani. And |