48 JOURNAL OF the; WASHINGTON ACADEMY OF SCIENCES VOL. 11, NO. 3 



(in absolute units), the atomic weight A, the density p, and the vi- 

 bration frequency v of the atoms : 



i^ = 3.3 X 10^ A-^>-'^ ^-'^ (2) 



Lindemann,^ on the other hand, calculates p from the equation: 



V =3.1 X 10'^ A-^' p^' T^' (3) 



in which T^ is the melting point on the absolute scale. Eliminating 

 V from these two equations, and multiplying by 10^ in order to change 

 the units of (3 from cmVdyne to cm-/megadyne, we have: 



/3 = 1.13 X 10-"— (4) 



This equation closely resembles the empirical equation used by 



A 

 Richards, ^^ namely, /3 = 2.1 X 10~" ^,^ . rr:, and yields for 



many elements values of /3 which are in fair accord with the observed 

 A^alues. The melting point of diamond is not known, but assuming 

 that it is 4000°, and taking p as 3.51, the value of /S calculated from 

 equation (4) is 0.10 X 10"". As calculated from Richards' formula, 

 the value is 0.13 X 10 "^ 



Another equation may be obtained from Griineisen's formula ■} ^ 



v = 2.^ + wi'-n 'a-^p^ (5) 



in which c^ is the specific heat per gram, and a is the cubical expansion 

 coefficient. Eliminating v from equations (2) and (5) and multiplying 

 by 10^ as before, we have 



a 



^ = 1.29 X 10-2 — . (6) 



c„p 



This equation clearly illustrates the fact that low compressibility 

 tends to be accompanied by low thermal expansibility. In using 

 equation (5) or (6) for numerical calculation, however, for the ratio 



-- must be taken its limiting value as the temperature is decreased. 



Cv 



It may be noted, nevertheless, that if the values of c^ and a for diamond 

 at 25° C. {c, = 0.12 cal. per g.; « = 3.5 X lO"^) be substituted in 

 equation (6), 13 is found to be 0.11 X 10 "^ 



9 F. A. LiNDEMANN, Phys. Zeitschr. ii: 609. 1911. 



1" Op. cit., p. 1653. See also W. D. Harkins and R. E. Hali,, Journ. Amer. Chem. Soc. 

 8: 209. 1916. 

 " E. GRiJNEisEN, Ann. Phys. (4) 39: 293. 1912. 



