LECTURE XXXIV. ON THE METHODS OF ESTIMATING THE SPECIFIC GRAVITY OF BODIES, ON AIR-BALLOONS, &c. FRO You ROM the principles explained to you in the preceding Lecture, it will be easy to fhew you in what manner you may eftimate the fpecific gravities of different bodies, whether folid or fluid. Now the fpecific gravity of a body is the weight of that body, under a known and determinate magnitude; as a cubic inch, a foot, &c. To acquire this knowledge, the body is to be weighed bydroftatically; that is, 1. in air; 2. in water. know that a body immerfed in water difplaces a volume of water exactly equal to it's own, and that it lofes a portion of it's weight exactly equal to the volume difplaced; we therefore obtain by this mode, 1. the weight of the body; 2. the weight of a volume of water perfectly equal in bulk to that of the body. Thefe two weights, compared together, give the relation between the fpecific gravity of water, which we fuppofe to be known, and that of the given body, by making the following proportion, in which 1000* represents the fpecific gravity of water. The weight of the volume of water difplaced by the body, is to the weight of this body, as 1000 is to a fourth term representing the specific gravity of this body: for In hydrostatic calculation, water, as the standard from which all the refpective gravities are taken, is reckoned as unity, or 1, 10, 100, 1000, &c. as the cafe requires. for the fpecific gravities are as the weights of equal bulks; therefore the fpecific gravity of the fluid is to that of the body, as the weight loft in the fluid is to the whole weight. Now let us fuppofe a piece of gold to weigh 38 grains in air, and only 36 grains when weighed in water; it has therefore loft two grains. Reafoning, therefore, from what has been already proved, we fay the gold has loft the weight of as much water as is equal in bulk to itself. But the gold itfelf weighs 38 grains; confequently, bulk for bulk, the weight of water is to that of gold, or the specific gravity of the fluid to that of the folid, as 2 to 38; that is, as the weight of the fluid is to the whole weight. Thus the whole art of comparing the fpecific gravity of bodies, confifts in finding out what the body weighs in air, and how much of that weight is loft in water; and then dividing the first weight by the difference between the first and fecond weight, and the quotient of this divifion fhews how many times the body is heavier than water. The definition of Specific gravity implies comparifon. Some kind of body must be fixed upon, whofe gravity must be made a ftandard for the gravity of other bodies of equal bulk to be compared with. This ftandard body fhould have two properties; firft, it must be easy to be had, or come at, upon all occafions; and, fecondly, it fhould be of as fixed and unalterable a nature as poffible, that there may be no variation in it's gravity in equal bulks, in different times or places. Now as the best way of difcovering the fpecific gravities of bodies is by immerfion, the body must be of the fluid kind; and, among fluids, water is that which poffcffes in the highest degree the requifites for a ftandard. Diftilled water is the leaft objectionable, objectionable, next to this pure rain-water; but common water, for many purposes, will anfwer exceeding well. The fpecific gravity, or weight, of a given bulk of diftilled water is nearly at all times the fame; and by comparing this with other fubftances, the ratio of their fpecific gravities may be difcovered; and denoting the fpecific gravity of water, by any number, taken at pleasure, the num→ bers expreffing the fpecific gravities of other bodies are hence given. As the weight of one cubical foot of pure diftilled water is equal to 1000 ounces avoirdupois, if it's fpecific gravity be denoted by 1, or 1000, the weight of one cubic foot, or other measure, of other substances, is hence found, and tables of the fpecific gravities of bodies are formed. One ounce avoirdupois is equal to 437.5 grains, and an ounce troy to 480 grains; confequently, one avoirdupois pound is to one troy pound, as 437X16 to 480 X 12, or as 1750 to 1440. A cubic foot of water is equal to 1000 ounces avoirdupois, or 62.5 lb. avoirdupois; whence we find it to be equal 75.95 lb. troy. A cubic inch of water is equal 253.18 grains, or .57869 parts of an avoirdupois ounce; and 253.18 grains, or 5274 parts of one troy ounce. THE USE OF THE HYDROSTATIC BALLANCE, IN DETERMINING THE QUALITY OF GOLD, &c. Being able to determine the fpecific gravities of bodies, you will thence be able, by weighing metals in water, to difcover their adulterations or mixtures, with greater exactnefs than by any other method whatfoever. By this means the counterfeit coin, which may be offered you as gold, will be eafily diftinguifhed, and known to be a bafer metal. The principal and diftinguishing qualities of pure gold, are the fimplicity, minutenefs, and close cohefion of it's parts; whereby a greater number of thofe parts is contained in lefs fpace than any other body with which we are acquainted. As all bodies weigh in proportion to their quantity of gravitating matter, under the fame bulk, the fpecific weight of gold must be fuperior to that of other metals. It follows from hence, that if gold be adulterated with any other metal, it's fpecific gravity, or comparative weight, must be lefs in proportion to the quantity of alloy. The weight, therefore, of gold, is a fure criterion of it's quality. In order to determine the precife quantity of alloy compounded with gold, gold must be weighed with fome other mafs as a standard, and their relative gravities be computed. I have already fhewn you, that water is the moft convenient ftandard. It will therefore, from what has been said, be eafy to you, by means of an accurate hydroftatic ballance, to determine it's quality and real value. Weigh a piece of gold firft in air, weigh it then in water, fubtract it's weight in water from the weight in air, and the difference fhews the lofs it has fuftained by being weighed in a denser medium. Divide the weight in air by the lofs in water; the quotient fhews the fpecific gravity, or how many times gold is heavier than water. On the contrary, the fpecific gravity of ferling gold being known, if the weight in air of any piece of gold coin be divided by the specific gravity of fterling gold, the quotient fhews what ought to be it's lofs in water; and if it be found to lose thore, the gold is bad, or has too great a quantity of alloy. Gold Gold is about eighteen times as heavy as common water; the specific gravity of fterling gold being to the weight of water as 17.793 to 1. If, therefore, a guinea weighs in air 129 grains, when weighed in water it must lose 7.25, or 7 grains of it's weight; because as 7.250 is to 129, fo is 1 to 17.793; fo that a quantity of water equal in bulk to a fterling guinea, weighs 74 grains. I fhall fhew you hereafter how to compute the proportion in which the quantity of alloy in counterfeit gold exceeds that which is allowed to a standard, and proceed to defcribe the hydrostatic ballance, and the method of applying it to use. * OF THE HYDROSTATIC BALLANCE. The beams of thefe ballances are in general made from eight to ten inches long; and with the perfections neceffary to a good ballance-beam, as pointed out in my Lecture on Mechanics, it either refts upon a stand or fulcrum, as at fig. 3, pl, 2, or is pendent, as at fig. 4, pl. 2. To this beam are adjufted a pair of fcalepans, which may be taken off at pleasure. There is alfo another fmaller pan, of equal weight with one of the others, furnished with fhorter ftrings, fo as to admit a veffel of water to be placed under it. When the ballance is ufed for hydroftatic purposes, this pan is to be fufpended at one end of the beam, and one of the common fcale-pans at the other. The glass bucket is to hold any folid body to be weighed in water, and is to be fufpended by the horfe-hair to the hook at the bottom of the fmall fcale. There is a weight to be placed in the oppofite * See an excellent little tract on the use of the hydrostatic ballance, by Becket, |