As the whole or absolute weight, So is the specific gravity of the solid, That is, the spec. grav. w B-b B s, by cor. 6, art. 250. EXAMPLE. A piece of cast iron weighed 34.61 ounces in a fluid, and 40 ounces out of it; of what specific gravity is that fluid? Ans. 1000, 254. PROP. To find the quantities of two ingredients in a given compound. Take the three differences of every pair of the three spe. cific gravities, namely, the specific gravities of the compound and each ingredient; and multiply each specific gravity by the difference of the other two. Then say, by proportion, As the greatest product, Is to the whole weight of the compound, EXAMPLE. A composition of 112lb. being made of tin and copper, whose specific gravity is found to be 8784; re. quired the quantity of each ingredient, the specific gravity of tin being 7320, and that of copper 9000? } Answer, there is 100lb. of copper in the composition. and consequently 12lb. of tin. SCHOLIUM. 255. The specific gravities of several sorts of matter, as found from experiments, are expressed by the numbers an. nexed to their names in the following Tables. TABLES OF SPECIFIC GRAVITIES. Platina SOLIDS. 20,722 Rhodium Gold, pure, hammered 19,362 Virgin Silver : 11,000 10,744 Guinea of George III. 17,629 Shilling of George III. 10,534 Tungsten Mercury, at 32° Fahr. 13,598 Copper, wiredrawn 17,600 Bismuth, molten 11,352 Red Copper, molten 11,300 Molybdeną 9,822 8,878 8,788 8,611 ** Since a cubic foot of water at the temperature 40° Fahrenheit, weighs 1000 ounces avoirdupois, or 62+ pounds, the numbers in the preceding Tables exhibit very nearly the 994 about 14 respective weights of a cubic foot of the several substances tabulated. 256. PROP. To find the magnitude of any body, from its weight. As the tabular specific gravity of the body, EXAM. 1. Required the content of an irregular block of green marble, which weighs 1 cwt. or 112lb? Ans. 1160.6 cubic inches. EXAM. 2. How many cubic inches of gunpowder are there in 1lb. weight? Ans. 29 cubic inches nearly. EXAM. 3. How many cubic feet are there in a ton weight of dry oak? Spec. grav. 925. Ans. 38 cubic feet. 257. PROP. To find the weight of a body from its magnitude. As one cubic foot, or 1728 cubic inches, To the weight of the body. EXAM. 1. Required the weight of a block of marble, whose length is 63 feet, and breadth and thickness each 12 feet; being the dimensions of one of the stones in the walls of Balbeck? Ans. 683 ton, which is nearly equal to the burden of an East India ship. EXAM. 2. What is the weight of 1 pint, ale measure, of gunpowder ? Ans. 19 oz. nearly. EXAM. 3. What is the weight of a block of dry oak, which measures 10 feet in length, 3 feet broad, and 25 feet deep or thick? Ans. 43351lb, BUOYANCY OF PONTOONS, GENERAL SCHOLIUM. 258. The principles established in art. 250 have an interesting application to military men, in the use of pontoons, and the buoyancy by which they become serviceable in the VOL. II. 34 construction of temporary bridges. When the dimensions, magnitude, and weight of a pontoon are known, that weight can readily be deducted from the weight of an equal bulk of water, and the remainder is evidently the weight which the pontoon will carry before it will sink. Pontoons as usually constructed, are prisms whose vertical sections are equal trapezoids, as exhibited in the marginal figure. Suppose AB = L I CD=1 AI=KB = $(L-1)=δ L CI = D KB G H M Uniform width of the pontoon = 6: all in feet and parts. Suppose also CL = d, depth of the part immersed; w = weight in avoirdupois pounds of the water displaced; and c = 62 lbs. weight of a cubic foot of rain water. Then, by the following expressions, which are left for the student to investigate, d may be found when wand the rest are given, and w may be found when d and the rest are given; also the maximum value of w. 2. w when a max. = ben (l + d) = 1 bcD (L + 1) Ex. 1. Given AB = 214 feet, CD = 17+ feet, ci = 21 feet, b = 43 feet. Required the weight of the pontoon and its load, when it is immersed to the depth cL, of 11⁄2 feet. Ans. 8287 lbs. nearly. Ex. 2. Suppose the weight of such a pontoon to be 900lbs. what is the greatest weight it will carry ? Ans. 12014lbs. Ex. 3. Suppose the weight of the above pontoon and its load to be 6000lbs, how deep will it sink in water ? Ans. 1.08872 f = 13·064 inches. HYDRAULICS OR HYDRODYNAMICS. 259. Hydraulics or Hydrodynamics is that part of mechanical science which relates to the motion of fluids, and the forces with which they act upon bodies against which they strike, or which move in them, This is a very extensive subject: but we shall here give only a few elementary propositions. 260. PROP. If a fluid run through a canal or river, or pipe of various widths, always filling it; the velocity of the fluid in different parts of it, AB, CD, will be reciprocally as the transverse sections in those parts. A C B D That is, veloc. at a: veloc. atc:: CD: AB; where AB and CD denote, not the diameters at A and B, but the areas or sections there. For, as the channel is always equally full, the quantity of water running through AB is equal to the quantity running through co, in the same time; that is, the column through AB is equal to the column through co, in the same time; or AB X length of its column = CD X length of its column; therefore AB: CD :: length of column through cu: length of column through AB. But the uniform velocity of the water, is as the space run over, or length of the columns; therefore AB: CD :: velocity through CD: velocity through AB. 261. Corol. Hence, by observing the velocity at any place AB, the quantity of water discharged in a second, or any other time, will be found, namely, by multiplying the section AB by the velocity there.. But if the channel be not a close pipe or tunnel, kept always full, but an open canal or river; then the velocity in all parts of the section will not be the same, because the velocity towards the bottom and sides will be diminished by the friction against the bed or channel; and therefore a me. dium among the three ought to be taken. So, if the velo city at the top be that at the bottom and that at the sides 100 feet per minute, dividing their sum by 3, gives 70 for the mean velocity, which is to be multiplied by the section, to give the quantity discharged in a minute: and in many cases still greater accuracy will be necessary in determining the mean. 262. PROP. The velocity with which a fluid runs out by a hole in the bottom or side of a vessel, is equal to that which is generated by gravity through the height of the water above the hole; that is, the velocity of a heavy body acquired by falling freely through the height AB. |