532 



Mr. W. Sutherland on 



errors in the value of k given by the formula for perfect 

 isotropy. 



The following Table contains in the row k ± the values of k 

 calculated from my average values of n and q given in 

 Tables III. and VII., in k 2 Torulinson's values, in & 3 Amagat's, 

 and in # 4 the values found from equation (7) above, using 

 Fizeau's values of b. The temperature is 15° C. in all. In 

 the last row are given the values of the ratio of k 4 to the 

 mean of k x , k 2 , and k 3 . 





Cu. 



Ag. 



Au. 



Mg. 



Zn. 



Al. 



Sn. 



Pb. 



Fe. 



Pt. 



io- 6 ^.. 



. 2500 



690 



1370 



325 



900 



810 



imp. 



86 



2000 



. 990 



10- 6 £ 2 .. 



. 980 



930 







350 



320 



130 



76 



1500 



590 



io- 6 & 3> . 



. 1170 















360 



1470 





io-% 4 .. 



. 970 



520 



980 



190 



250 



325 



264 



134 



2000 



2800 



Ratio .. 



. 63 



64 



71 



59 



40 



58 



203 



77 



120 



350 



There are large discrepancies in the quasi-experimental 

 values of k ; for example, in the case of tin k x is impossible, 

 because 9n — 3q is negative; accordingly tin is so far from 

 being reliably isotropic as to make attempts at calculating k 

 illusory. If, besides tin, we reject platinum, we find fairly 

 good agreement amongst the values of the ratio of & 4 , the 

 theoretical value, to the mean quasi-experimental value. The 

 mean value of the ratio, leaving out iron, is 62, and including 

 iron is 69 ; so that we can say that the theoretical values of 

 the bulk-modulus of the metals, on the assumption that the 

 molecules do not change in size with changing temperature, 

 are about 70 times the actual values. Thus, while the 

 assumption of constant size in molecules is proved by this 

 comparison to be untenable, the general form of our equation 

 receives some partial verification from it, as it shows kb 2 0?n/p 

 to be nearly the same for 8 out of 9 metals, and this is what 

 the form of our equation demanded. 



But fortunately there is a more satisfactory comparison to 

 be made between theory and experiment in the matter of 

 latent heats of melting. We cannot imagine our equation to 

 bridge the gap in continuity between the solid and liquid 

 states and calculate the latent heat by the formula 



\= i'&bpl^ddv, 



where v 2 and v l are the volumes of unit mass in the liquid 

 and solid states. But without any bridging of the gap in 

 continuity we have the thermodynamic relation 



k=(v 2 ->-v 1 )0dp/d0, 



