492 



by grapliical iiitegraliüii tVom a c'ur\e which has been dra\vn thi'Oiigh 

 • lie experimental points of fig. d, with an exirapolalion below 14° K. on 

 the basis of the assumption that the T'-haw is the ulliniate limiting law. 



T' 

 being derived from Debije's formula for the energy: 



1 ré'dï. 

 .r'J é—l 



The change of 6,, with T has the effect of making the values of 

 6, which are derived directly from the atomic heats, differ some- 

 what from those of 6'„. 



For cop|)er 6,, appears to decrease with increasing temperature in 

 the region of 20 to 70 K., the rate of decrease being more rapid 

 at the lower than at the higher temperatures of this region. 



§ 5. The values of 0,, fouiul in § 4 (and also those of 6, ^ 3) 

 are smaller than ihose following from the formula given by Debije 

 I.e., which with ilie value found by Milmkan for the Avogadro 

 iniiiib'r (cf. Suppl. N" 'MMi, March 'J4) changes to: 

 3,657.10-3 1 



V z. for 18 C. : ^9=13:^3, for —191° C. : ^ = 344 '^ 

 111 Lindeman.n's formula'"): 



h 7V/q 



one (iiids for ( n from 61 = 315: /t. = 2.72.10'' 



whereas for I'h from /9 =: 88 follows: //,= 2.81.10'', where for 



v„ ilie values at 7'^ 0,2 Tg have been used. 



T = 120 , 160 , 200 240 , 280 , 



C^, = 4.22, 4.85. 5.28, 5.60, 5 SU' , from which we fiud: 

 5 = 331 , 343 . 3-^6 

 On Ihe contrary tl'e results of E. H. and Ezkr Grtffiths, Phil Trans. 214 A 

 (1914), p 319, cannot be reconciled so easily with ours as can be seen from the 

 fact that they give: at 138= K. 6 = 278, at 149.5^ K. 5 = 285. 



1) Calculated from : 18 C. : « = 8,94, k = 0.74.10-12, ^ ^ o,35 

 -191' C: 9,' 2, 0,69.10-12, 0,35. 



The value of y at 18' C. has been taken from E. Grüneisen Ann. d. Phys. (4) 

 25 (1908), p. 848, the change of with temperature from E, Grünkisen, Ann. 

 d. Phy.. (4) 33 (191U), p. 1264. 



a- has been assumed to change inappreciably with the temperature according to 

 E. Grü.neiskn, Ann. d. Phys. (4) 33 (1910), p. Ii72. 

 '-} F. A. LusDEMAKN, Physik. ZS. U (1910), p. G09. 



