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1 XXXVI. A New Periodic Property of the Elements. 

 By William Suthekland, if. A, B.Sc>* 



TO help towards getting some insight into the physical 

 basis of the periodicity in the properties of the elements 

 unfolded by NewJands, Mendelejeff, Meyer, Carnelley, and 

 others, it occurred to me to investigate some property in 

 which the period would be a real time-period. With the 

 same object in view many workers have attacked the spectra 

 of the elements ; but though interesting results have been 

 obtained, the complications of the subject have proved too 

 entangled to unravel to a simple issue as yet. But if we start 

 from the usual idea that in solids the molecules vibrate about 

 a mean position, then at some characteristic temperature each 

 solid ought to have a period of vibration characteristic of its 

 molecule. The question is, At what temperature? At the 

 melting-point in each case the vibratory motion just breaks 

 down, so that we ought to expect some simple relation 

 amongst the periods of vibration of the elements at their 

 melting-points. To find relative values of these periods we 

 may proceed thus : — Suppose a molecule of mass, M, and 

 specific heat (mean), C, heated up from rest at absolute zero 

 to its melting-point, T. It receives heat, MCT, which we 

 will take to be proportional to its kinetic energy J Mv 2 , where 

 v is the velocity of the molecule at the melting-point : this 

 would be strictly true only if we kept the body from expand- 

 ing while being heated. Now, by Dulong and Petit's law, 

 MC is approximately constant for the elements, so that v, the 

 mean velocity of the molecule in its vibrations at the melting- 

 point, is proportional to \/T/M. Knowing thus the mean 

 velocity of the vibration, if we can find its length L then its 

 time or period ~L/v is obtainable. Let d be the density of the 

 substance, then M/d represents the volume occupied by the 

 molecule ; and if a is the mean coefficient of linear expansion 

 of the substance between absolute zero and T, then «T(M/d) 5 

 represents the increase in the linear dimensions of the space 

 occupied by a molecule when heated from zero to T, and 

 therefore represents the length or amplitude of the vibration 

 just as the molecule is going to leave the vibratory state cha- 

 racteristic of the solid. Hence the periodic time p of the 

 molecule at the melting-point is proportional to 



aT(M/d)VMCT/M. 



* Communicated by the Author. 



