482 Dr. H. S. Allen on Atomic 



in Table II. the results given by Lindemann's formula are 

 nofc in agreement with the proposed relation. Various 

 suggestions might be made to account for these discrepancies. 



Table II. 



Atomic Frequency by Lindemann's Formula. 



Element. 



N. 



*>xio- 12 . 



N^XlO- 12 . 



1 

 Element. 



N. 



rxio- 12 . 



N„xl0- 13 . 



B 



5 



(28-1) 



7x20-1 



Em 



45 



7-01 



15X211 







6 



(36-4) 



10x21-8 



Pd 



46 



6-16 



14x20-2 







8 



2-54 



1x20-3 



Ag 



47 



4-792 



11x20-48 



Al 



13 



8-33 



5x21-7 



Cd 



48 



301 



7X20-6 



Si 



14 



10-5 



7x210 



; Sn 



50 



2-50 



6x20-9 



Ca 



20 



4-28 



4x21-4 



1 Sb 



51 



3 22 



8x20-5 



Sc 



21 



(6-84) 



7x20-5 



Te 



52 



(2-69) 



7x20-0 



Ti ...... 



22 



917 



10x20-2 



Cs 



55 



1-12 



3x20-6 



V 



23 



9-26 



10x21-3 



Ba 



56 



2-66 



7x21-3 



Cr 



24 



(9-23) 



11x20-2 



La 



57 



3-04 



8x21-7 



Mn 



25 



8-35 



10x20-9 



Oe 



58 



2-86 



8x20-7 



Fe 



26 



911 



11x21-5 



Pr 



59 



3-24' 



9x21-2 



Co 



27 



8-87 



11x21-8 



Nd 



60 



311 



9x20-8 



Ni 



28 



8-86 



12x20-7 



Sa 



62 



3-76 



11x21-2 



Ou 



29 



7-397 



10x21-45 



Ta 



73 



5-72 



20x20-9 



Zn 



30 



4-79 



7x20-5 



W 



74 



(6-06) 



22x20-4 



Ga 



31 



2-82 



4x21-8 



Os 



76 



5-96 



22x20-6 



Ge 



32 



(5-23) 



8x20-9 



Ir 



77 



5-47 



20X21-1 



Se 



34 



(2-94) 



5x20-0 



Pt 



78 



4-75 



18x20-6 



Sr 



38 



(3-44) 



6x21-8 1 



Au 



79 



3-69 



14x20-8 



Yt 



39 



(4-07) 



8x21-7 1 



Tl 



81 



2-00 



8x20-3 



Zr 



40 



(4-63) 



9x20-6 



Pb 



82 



1-99 



8x20-4 



Ob ...... 



41 



(6-73) 



13x21-2 



Bi 



83 



1-80 



7x21-3 



Mo 



42 



7-57 



15X212 



Th ... . 



90 



(3-06) 



13x21-2 



Ru 



44 



6-99 



15x20-5 



U 



92 



(4-67) 



20x21-4 



In the first place it has heen assumed in the application of 

 Lindemann's formula that the solid is monatomic. If the 

 molecule contains several atoms the result must necessarily 

 be modified, and it would obviously be possible by properly 

 choosing the number of atoms to be assigned to the molecule 

 to obtain agreement with the proposed relation. In the 

 present state of our knowledge of the constitution of the 

 solids in question little would be gained from such a 

 procedure, and to the writer it appears better to adopt, 

 tentatively at least, a suggestion made in the earlier paper, 

 and admit that in certain cases simple submultiples of the 

 fundamental frequency, v A , may occur. This has been done 

 in the following Table (III.) in which fractions J, \, or f 

 have been introduced into the frequency number to secure 

 agreement between the values o£ v A . It is significant that 

 the table includes four alkali metals, which are peculiar in 

 their large atomic volume, and three or four elements which 

 are known to exist in allotropic modifications. 



