72 



Prof. W. M. Thornton on the 



The equation of the upper line of density is 

 and the minima of the curves of atomic volume lie on the 



(1) 

 The 



curve 



Y[ = w/{0-62 + 0-1146 w), . . . , 

 asymptotic to a volume 8*72, osmium being at 8*5. 

 maxima lie on the curve 



V m = W(0-62 + (M)083to), .... (2) 

 asymptotic to 120. The slope of the line of mean density 

 isf'0'057, and for the corresponding volumes 



V n = w/(0-62 + 0-057u>), (3) 



asymptotic to a value of 17*5. This line passes between 

 thallium and lead, so that when the region of elements at 

 present radioactive is reached, the mean atomic volume is 

 rather below than above that of lead. 



3. Superposed upon the lines of mean density of volume 

 there is an oscillation which, since the change from maximum 

 to minimum takes place in a regular periodic manner, and so 

 that the rate of change is never discontinuous, may be assumed 

 to be caused by a simple periodic variation of cohesive force. 

 Using now the conception that there is structural hysteresis 

 in taking up new atomic formations, we have the following 

 interpretation of the curves, considering first atomic volumes. 



Fig. 3. 



Assume for the moment that the mean central force is 

 constant, represented by the line AB (fig. 3), and that the 



