Example to Case I. A piece or lead ore was weighed, which was 124 grains; and in water it 124 weighed 104 grains, the difference is 20; then = 6.2, the specific 20 gravity of ore. Cor. 1. As the weight lost in a fluid, is to the absolute weight of the body; so is the specific gravity of the fluid to the specific gravity of the body. Cor. 2. Having the specific gravity of a body, and the weight of it, the solidity may be found thus: multiply the weight in pounds by 62} ; then say, as that product is to one, so is the weight of the body in pounds to the content in feet. And, having the content given, one may find the weight by working backwards. For a cubic foot of water weighs 624 lb. avoirdupois ; and therefore a cubic foot of the body weighs 624 X by the specific gravity of the boily. Whence the weight of the body, divided by that product, gives the number of feet in it. Or, as I to that product, so is the content to the weight. SCHOLIUM.—The specific gravities of bodies may be found with a pair of scales, suspending the body in water by a horse-hair. But there is an jystrument for this purpose, called the Hydrostatical Balance, (fig. 13,) the construction of which is thus. AB is the stand and pedestal, having at the top two cheeks of steel, on which the beam CD is suspended, which is like the beam of a pair of scales, and must play freely, and be itself exactly in equilibrio. "To this belongs the glass bubble G, and the glass bucket H, and four other parts E, F, I, L. To these are loops fastened to hang them by. And the weights of all these are so adjusted that E=F + the bubble in the water, or= I + the bucket out of water, or =I+L + the bucket in water. Whence L = differenc of the weights of the bucket in and out of water. And, if you please, you may have a weight K, so that K + bubble in water = bubble out water; or else find it in grains. The piece L has a slit in it to slip it upon tbe sbank of I. Fig. 13. It is plain the weight K = weight of water as big as the bubblo, or a water bubble. Then to find the specific gravily of a solid. -Hang E at one end of the balance, and I and the bucket with the solid in it, at the other end; and und hat weight is a balance to it. Then slip L upon I, and immerge the bucket and solid in the water and find again what weight balances it. Then the first weight dividea by the difference of the weights, is the specific gravity of the body; tha of water being 1. For fluids. Hang E at one end, and F with the bubble at the other plunge the bubble into the fluid in the vessel MN. Then find the weight P, which makes a balance. Then the specific gravity of the fluid is K+P K-P when P is laid on E. K For E being equal to 1 + the bucket; the first weight found for a ba. Jance, is the weight of the solid. Again E being equal to 1 + L + the bucket in water; the weight to balance that, is the weight of the solid in water; and the difference is = to the weight of as much water. Therefore (Cor 1.) the first weight divided by that difference, is the specific gravity of the body. Again, since E is = to F + the bubble in water, therefore P is the difference of the weights of the Buid and so much water; that is, P=ditference of K and a fluid bubble; or P=fluid - K, when the fluid is heavier than water, or when P is laid on F. And therefore P=Kthe fluid bubble, when contrary. Whence the fluid bubble = K = P, for a heavier or a lighter Ouid. And the specific gravities being as the weights of these egual bubbles; specific gravity of water: specific gra K + P vity of the fluid ::K: KP :: 1: the specific gravity of K , the fluid. Where if P be 0, it is the same as that of water. Obs. The method of ascertaining the specific gravities of bodies was discovered accidentally by Archimedes. · He had been employed by the king of Syracuse to investigate the metals of a golden crown, wbich, he suspected, had been adulterated by the workman. The philosopher Jaboured at the problem in vain, till, going one day into the bath, he perceived that the water rose in the bath in proportion to the bulk of his hody; be instantly saw that any other substance of equal size would have raised the water just as much, though one of equal weight and of less bulk could not have produced the same effect. He immediately felt that the solution of the king's question was within bis reach, and he was so transported with joy, that he leaped from the bath, and, running naked through the streets, cried out, “ Eupnra, Eupruce," —“ I have found it out, -I have found it out!” He then got two masses, one of gold and one of silver, each equal in weight to the crown, and, having filled a vessel very accurately with water, he first plunged the silver mass into it, and observed the quantity of water that flowed over; he then did the same with the gold, and found that a less quantity had passed over than before. Hence he inferred that, though of equal weight, the bulk of the silver was grcater than that of the gold, and that the quantity of water displaced was, in each experiment, equal to the bulk of the metal. He next made a like trial with the crown, and found it displaced more water than the gold, and less than the silver, which led him to conclude that it was neither pire gold nor purr silver. TABLES OF SPECIFIC GRAVITIES. Solids. Platina .. .20,722 Marble, green, Campanian 2,742 Gold, pure, hammered .19,362 Parian 2837 Guinea of George III. ...17,629 Norwegian 2,728 Tungsten ...17,600 2,668 Mercury, at 320 Fahrenheit 13,598 Emerald 2,775 Lead. 11,352 Pearl.... 2,752 Palladium .11,300 Chalk, British 2,784 Rhodium 11,000 Jasper 2,710 Virgin Silver 10,744 Coral 2,680 Shilling of George III. ...10,534 Rock Crystal 2,653 Bismith, molten.. 9,822 | English Pebble 2,619 Copper, wire-drawn 8,878 Limpid Feldspar 2,564 Red Copper, molten 8,788 Glass, green.. 2,642 Molybdena 8,611 2,892 Arsenic... 8,308 2,733 Nickel, molten 8,279 Porcelaine, China 2,385 Uranium 8,109 Limoges 2,341 Steel.. from 7,769 to 7,816 Native Sulphur 2,033 Cobalt, molten 7.812 Ivory 1,917 Bar Iron 7,788 Alabaster. 1,874 Pure Cornish Tin 7,291 1,720 Dıhardened 7,299 Copal, opaque 1,140 Cast Iron, 7,207 Sodium.... 973 Ziuc 6,862 Oak, heart of 950 Antimony. 6,712 Ice 930 Tellurium 6,115 Potassium 866 Chromium 5,900 Beech 852 Spar, heavy 4,430 845 Jargon of Ceylon 4.416 Apple-Tree 793 Oriental Ruby.. 4,283 Orange-Wood 705 Sapphire, Oriental 3,994 Pear. Tree 661 Do. Brazilian 3,131 604 Oriental Topaz 4,019 Cypress 598 Oriental Beryl 3,549 Cedar 561 Diamond from 3,501 to 3,531 Fir 550 English Flint Glass 3,329 Poplar 383 Tourmalin 3,155 Cork... 240 Asbestus 2,996 LIQUIDS. Sulphuric Acid 1,841 | Burgundy Wine 991 Nitrous Acid 1,550 Olive Oil 915 Water from the Dead Sea .. 1,240 | Muriatic Ether. 874 Nitric Acid 1,218 Oil of Turpentine 870 Sea-Water 1,026 Liquid Bitumen 848 Milk... 1,030 | Alcohol, absolute 792 Distilled Water 1,000 Sulphuric Ether 716 Wine of Bourdeaux 944 | Air at the Earth's surface, about 13 Since a cubic foot of water, at the temperature of 40° Fahrenheit, weiglis 1000 ounces, avoirdapois, or 62{ pounds, the numbers in the precedling tables exliinit very ncarly the respective weights of a cubic foot of the several substances tabulated. . Obs.-1. The above table shews the specific weights of the various substances contained in it, and the absolute weight of a cubic foot of cach body is ascertained in avoirdupois ounces, by multiplying the nupiber opposite to it by 1000, the weight of a cubic foot of water; thus the weight of a cubic foot of mercury is 14,019 ounces avoirdupois, or 876 lb. 2. If the weight of a body be known in avoirdupois ounces, its weight in Troy ounces will be found in multiplying it into .91145. And, if the weight be given in 'Troy ounces, it will be found in avoirdupois by multiplying it into 1.0971. MISCELLANEOUS COMPUTATIONS AND EXPERIMENTS. The pendulum vibrating seconds of mean solar tiine at London in a vacuum, and reduced to the level of the sea, is 39 1393 inches; consequently the descent of a heavy body from rest in one second of time in a vacuum, will be 193 145 inches. The logaritbm 2.2858828. A platina metre at the temperature of 3:20, supposed to be the ten mil. Jionth part of the quadrant of the meridian, 39-3708 inches. The ratio to the imperial measure of three feet as 1:09363 to 1, the logarithm 0·0388717. The five following standards, accurately measured, give these results :Gen. Lambton's scale, used in the 'Trig. Surv. of India, 35 99934 inches. Sir G. Shuckburgh's scale (which for all purposes may ? be considered as identical with the imperial standard) S 35 99998 Gen. Roy's scalc .... 36-00088 Royal Society's standard 36.00135 Ramsdep's bar 36 00249 Weight of a cubic inch of distilled water in a vacuum ai the temp. 620, as opposed to brass weights in a log. 2.4026430 vacuum also, 252 722 grains .... Consequently a cubic foot 62:3862 pounds avoirdupois. . log. 1:7950837 Weight of a cubic inch of distilled waier in air at 620 2 of temperature with a mean height of the barometerlog. 2.4021857 252:456 grains Consequently a cubic foot 62 3206 pounds avoirdupois. .log. 1•7946314 And an ounce of water 1.73298 cubic inches.. .log. 0:2387924 Cnbic inches in the imperial gallon, 277.276.. log. 2 4429124 Diameterof the cylinder containing a gallon at one inch log. 1-2739112 high, 1878933 .. Specific gravity of water at different temperatures, that at 62° being taken as uniiy. 700 0 99913 620 1 520 1 00076 440 1.00107 68 099936 58 1 00035 50 1.00087 42 1.00111 66 009958 56 1.00050 48 1:000955 40 Twi13 099980 1.00061 46 1:00102 38 1:00113 The difference of temperatures between 62° and 390, where water attains its greatest density, will vary the bulk of a gallon of water rather less than the third of a cubic inch. And, assuming from the mean of numerous estimates the expansion of brass 0.00001044 for caci degree of Fahrenheit's thermometer, the dis. ference of temperatures from 620 to 39° will vary the content of a brass gallou-measure just one filio of a cubic inch. It appears that the specific gravity of clear water from the Thames riceeds that of distilled water, at the mean temperature, in the proportion of 1.0006 to 1, making a diff. of about one-sixth of a cubic in, on a gallon. Rain water does not differ from distilled water, so as to require any allowance for common purposes. 54 HYDRAULICS, Definitions.-1. The science of Hydraulics teaches how to estimate the velocity and force of fluids in motion. Upon the principles of this science all machines worked by water are constructed, as engines, mills, pumps, fountains, &c. 9. Water can be set in motion only by its own gravity; as when it is allowed to descend from a higher to a lower level: by an increased pressure of the air, or by removing the pressure of the at. mosphere, it will rise abuve its natural level. Obs.- In the former case it will seek the lowest situation, in the latter it may be forced to almost any height. Prop. 1.-If a fluid runs through a pipe, 80 as to leave no vacuities; the velocity of the fluid in different parts of it, will be reciprocally as the transverse sections, in these parts. Let AC, LB, fig. 5, be the sections at A and L. And let the part of the Quid ACBL come to the place acbl. Then will the solid ACBL= solid acbl ; take away the part acBL common to both; and we have ACca=Lßbl. But in equal solids the bases and heights are recipro. cally proportional. But, if Df be the axis of the pipe, the heights Dd, Ff, passed through in equal times, are as the velocities. Therefore, section, AC : section LB :: velocity along Ff : velocity along Dd. PROP. 2.-If AD, fig. 6, be a vessel of water or any other fluid; B a hole in the bottom or side. Then, if the vessel be always kept full ; in the time a heavy body falls through half the height of The water above the hole AB, a cylinder of water will flow out of the hole, whose height is AB, and base the area of the hole. The pressure of the water against the hole B, by which the motion is generated, is equal to the weight of a column of water whose beight is AB, and base the area B (See Hydrostatics, Prop. 4). But equal forces generate cqual motions; and, since a cylinder of water falling through JAB hy its gravity, acquires such a motion, as to pass through the whole beight AB in that time ; therefore in that time the water running out must acquire the same motion. And, that the effluent water may have the same motion, a cylinder must run out whose length is AB; and then the space described by the water in that time will also be AB, for that space is the length of the cylinder run out. Therefore this is the quantity run ont in that tiine. Cor. 1. The quantity run out in any time is equal to a cylinder or prism, whose length is the space described in that time by the velocity acquired by falling through half the height, and whose base is the hole. For the length of the cylinder is as the time of running out. Cor. 2. The velocity, a little without the hole, is greater than in the hole; and is nearly equal to the velocity of a body falling through the whole height AB. For without the hole the stream is contracted by the water's converging from all sides to the centre of the hole, and this makes the velocity greater in about the ratio of 1 to V2. |