242 BRIDGMAN. 



bility and its change with pressure. It is shown by numerical calcu- 

 lation that the effect discussed by Schottky due to the deformation of 

 the atoms under pressure is of such an order of magnitude that it must 

 be taken into account. 



Finally, if we do not assume the specific form of the repulsive poten- 

 tial, but replace it by an arbitrary function, it is shown that the first, 

 second and third derivatives may be computed numerically from 

 experimental data now available for a number of the metals of this 

 investigation. From these numerical values the conclusion is drawn 

 that the boundaries of the atoms cannot be as definite as appeared 

 not unlikely from a study of polymorphic changes under pressure. 



I am indebted to my assistant, Mr. I. M. Kerney, for help in making 

 the greater number of the readings. 



The Jefferson Physical, Laboratory, 

 Harvard University, Cambridge, Mass. 



1 T. W. Richards, Numerous papers, summarized in Jour. Amer. Chem. 

 Soc. 37, 1643, 1915. 



2 L. H. Adams, E. D. Williamson and John Johnston, Jour. Amer. Chem. 

 Soc. 41, 1, 1919. 



3 M. Born, Numerous papers, in particular Ann. Phys. 61, 87, 1919. 



4 P. W. Bridgman, Proc. Amer. Acad. 44, 266, 1909. 



5 P. W. Bridgman, Proc. Amer. Acad. 47, 366, 1911. 



6 P. W. Bridgman, Proc. Amer. Acad. 52, 609, 1917. 



7 P. W. Bridgman, Proc. Amer. Acad. 47, 335, 1911. 



8 L. Holborn, Ann. Phys. 59, 145, 1919. 



9 P. W. Bridgman, Proc. Amer. Acad. 57, 52, 1922. 



10 P. W. Bridgman, Proc. Amer. Acad. 57, 110, 1922. 



11 C. C. Bidwell, Phys. Rev. 19, 447, 1922. 



12 Reference 10, page 101. 



13 P. W. Bridgman, Proc. Amer. Acad. 56, 93, 1921. 



14 Eeference 13, page 96. 



15 P. W. Bridgman, Phys. Rev. 3, 154, 1914. 



16 Reference 13, page 82. 



17 P. W. Bridgman, Proc. Amer. Acad. 49, 1, 1913. 

 13 Reference 10, page 114. 



19 E. Griineisen, Ann. Phys. 39, 257, 1912. 



20 A. W. Hull, Phys. Rev. 17, 42, 1921. 



21 W. Schottky, Phys. Zs. 21, 232, 1920. 



22 T. W. Richards, Jour. Amer. Chem. Soc. 36, 2417, 1914. 



23 Reference 15, page 157. 



24 p. W. Bridgman, Proc. Amer. Acad. 52, 180, 1916. 



25 On reading the galley proofs Professor Richards has been kind enough to 

 call my attention to his estimates of the decrease of compressibility with pres- 

 sure of the alkali metals on page 24 of Publication No. 76 of the Carnegie 

 Institute of Washington. He finds the average compressibility of sodium 

 between 300 and 500 kg. to be 2/150 less than between 100 and 300, and that 

 of potassium 12/300 less for the same intervals of pressure. 





