Kinetic Theory of Solids. 549 



measured directly for a few metals by Mallock (Proc. Roy. 

 Soc. xxix.) by one method, and by Amagat [Compt. Rend. 

 cviii.) by a quite distinct method, and also by an indirect 

 method. We will compare the values given by the first 

 equation for a at 15° C. with these experimental values. 



Values of cr at 15° C. 



Ou. Zn. Pb. 



Theory "38 '17 '33 



Mallock -35 -18 -37 



Amagat '32 ... *43 



For iron theory gives a value *41, while Mallock found for 

 steel the value '25, and Amagat for steel *27, but Okatow 

 (Pogg. Ann. cxix.) has shown that steel according to its 

 treatment gives values of cr ranging from '275 to *40. If we 

 calculate cr according to the second equation above, using the 

 mean experimental values of q and n at 15°, as given in 

 Tables III. and VII. of the introduction, we get the follow- 

 ing values:— Cu -42, Zn -33, Pb '13, Fe -33. These 

 values for zinc and lead are in complete disaccord with the 

 experimental values, that for zinc being much too large, and 

 that for lead much too small. Now in studying the values of 

 the ratio Q/N, which ought theoretically to be 3, we found 

 for zinc 3*5, and for lead 2*3; but as the values of Q and N 

 are both calculated from the mean values of q and n at 15° C. 

 it is very likely that there is experimental error in q and n 

 as individual experimenters differ greatly in their values. 

 Hence if 3 is the true value for Q/N for all the metals, q/n is 

 wrong in the same proportion as Q/N; and if we multiply our 

 values of q/n by 3, and divide by Q/N, and use the result 

 in our second equation for cr, we shall see whether theory will 

 thus eliminate the discrepancy above for zinc and lead as due 

 to experimental uncertainty in q/n. Doing this, we get for 

 Cu '38, Zn 14, *Pb -47, and Fe 42, which agree well with 

 the values given by the first equation for cr, and with the 

 directly observed values of Mallock and Amagat. 



This agreement of theory and experiment shows that all 

 idea of a constant value for cr in the case of isotropic bodies 

 must be abandoned, and, what is much more important, that 

 the metals are at least approximately isotropic. Amagat has 

 already shown by some fine experimental work ( Compt. Rend. 

 cviii.) that some metals and alloys are isotropic, although 

 his method of calculation makes the proof a little more per- 

 fect than it actually is. His method is to measure Young's 

 modulus directly by statical experiments ; let P be the pressure 



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