Kinetic Theory of Solids. 223 



In the case of tin and lead I made experiments on a larger 



scale on the same pieces of pipe as were used in the Rigidity 



experiments. For a pipe of external radius r 2 and internal r x 



Young's modulus is given by the formula 



_ 87r^V(n 1 2 + rz 2 2 ) 



q ~l'S751 i (r 2 2 + ri 2 )' 



With the tin pipe of length 119*6 centim. and at a tempe- 

 rature of 18°, 7i 1 = 8'82 J ?i 2 = 3*73, whence 10~ 6 q = 4:21 and 

 n 1 2 — n 2 2 = 'Q8, while according to theory n 2 — n 2 2 = '64:. 



With the lead pipe of length 121*9 and at temperature 23° 

 ^ = 2*53, rc 2 = 2-40, whence 10- 6 2 = 161*7 and n 1 2 -n 2 2 = '64:l, 

 while the theoretical value of n 2 — n 2 is *635. 



2. Compilation of Data. — As regards the variation of 

 Young's modulus with temperature, Kupffer's vibrational 

 method is so superior in accuracy to the static method, that 

 even rough experiments like my own by Kupffer's method 

 give far more trustworthy results than even the most 

 careful and refined measurements yet made by the static 

 method. Kupffer's own temperature-range was too small to 

 give weight to his measurement ; and as I know of no other 

 measurements by his method, I must regard the data just 

 given as the most trustworthy yet published. It is therefore 

 hardly worth while quoting other results except those of 

 Kiewiet, who (Wied. Ann. xxix.) applied a much more sensi- 

 tive static method than the usual one, namely, the method of 

 bending to zinc, tin, and copper. Kiewiet's values, in the 

 case of tin, for the ratio of q at 60° and 101° to q at 16° are 

 *82 and *67. while mine are '83 and *73 ; in the case of zinc 

 at 60° and 103° and 16° the ratios found by Kiewiet are *92 

 and *87, while my values are *92 and *83. At 102° and 16° 

 Kiewiet finds for rolled copper the ratio *967, and for electro- 

 lytic copper *93I/ while my number is *914. 



Except for copper the agreement of the two methods is 

 good, all things considered. 



In the following compilation as to the absolute values of 

 Young's modulus at ordinary temperatures, these are the 

 sources : — Wertheim, Ann. de Ch. et de Ph. 3 ser. t. xii. ; 

 Zoppritz's recalculation of KupfFer's data, Pogg. Ann. cxxviii.; 

 Kupffer, Cosmos, 1860 ; Pisati, Wied. Beibl. i. ; Tomlinson, 

 Phil. Trans. 1883, and Proc. Roy, Soc. xlii. & xliii. ; Mac- 

 farlane, Encyc. Brit., article Elasticity ; Miller, Wied. Beibl. 

 xi. ; Katzenelsohn, Wied. Beibl. xii. ; Kiewiet, Wied. Ann. 

 xxix. ; Mercadier, Compt. Rend, cviii.; Amagat, Compt. Rend. 

 cviii. ; Cantone, Wied. Beibl. xiv. 



When a specimen is known to have been unannealed it is 

 marked (w). 



