63. The following are reduced from the results obtained by Amaury and Descamps, Comptes Rendus,' tom. lxviii. p. 1564 (1869), and are probably more accurate than the foregoing, especially in the case of mercury: 64. The following values of the coefficients of resilience for solids are reduced from those given in my own papers to the Royal Society (see 'Phil. Trans.,' Dec. 5th, 1867, p. 369), by employing the value of g at the place of observation, namely 9814. 65. The resilience of volume was not directly observed, but was calculated from the values of "Young's modulus" and "simple rigidity," by a formula which is strictly true for bodies which have the same properties in all directions. The contraction of diameter in lateral directions for a body which is stretched by purely longitudinal stress was also calculated by a formula to which the same remark applies. The ratio of this lateral contraction to the longitudinal extension is called "Poisson's ratio," and the following were its values as thus calculated for the six bodies experimented on.:- Kirchhoff has found for steel the value 294, and Clerk Maxwell has found for iron 267. Cornu ('Comptes Rendus,' Aug. 2, 1869) has found for different specimens of glass the values 225, 226, 224, 257, 236, 243, 250, giving a mean of 237, and maintains (with many other continental savants) that for all isotropic solids (that is, solids having the same properties in all directions) the true value is 1. 66. The following are reduced from Sir W. Thomson's results ('Proc. Roy. Soc.,' May, 1865), the value of g being 981'4: Other specimens of copper in abnormal states gave results ranging from 3.86 × 10" to 4'64 × 10". 67. The following are reduced from Wertheim's results (Ann. de Chim.,' ser. 3. tom. xxiii), g being taken as 981 : Different Specimens of Glass (crystal). Young's modulus,...... 341 to 4'34, mean 3'96 Volume resilience, I'26 to 1.66, I'48 3.89 X 1011 68. Savart's experiments on the torsion of brass wire ('Ann. de Chim.' 1829) lead to the value 3'61 × 1011 for simple rigidity. Kupffer's values of Young's modulus for nine different specimens of brass, range from 796 x 1oll to 11*4 × Ioll, the value generally increasing with the density. For a specimen, of density 8:4465, the value was 10'58 × 1011. For a specimen, of density 8:4930, the value was 11:2 × Ioll. The values of Young's modulus found by the same experimenter for steel, range from 202 x 10ll to 214 × I011. 69. The following are reduced from Rankine's 'Rules and Tables,' pp. 195 and 196, the mean value being adopted where different values are given : The tenacity of a substance may be defined as the greatest longitudinal stress that it can bear without tearing asunder. The quotient of the tenacity by Young's modulus will therefore be the greatest longitudinal extension that the substance can bear. 57 CHAPTER VI. ASTRONOMY. 70. Size and Figure of the Earth. ACCORDING to the latest determination, as published by Capt. Clarke in the Philosophical Magazine' for August, 1878, the semiaxes of the ellipsoid which most nearly agrees with the actual earth are, in feet, a = 20926629, b = 20925105, c = 20854477, which, reduced to centimetres, are à = 6·37839 × 103, b=6·37792 × 10°, c=6·35639 × 108, giving a mean radius of 6.3709 × 108, and a volume of 10832 × 1027 cubic centims. The ellipticities of the two principal meridians are The longitude of the greatest axis is 8° 15′ W. The mean length of a quadrant of the meridian is 1'00074 × 109. The length of a minute of latitude is approximately 185200-940 cos. 2 lat. of middle of arc. The mass of the earth, assuming Baily's value 5.67 for the mean density, is 6.14 × 1027 grammes. |