Curves of the Periodic Law, 



73 



curve C is the change of cohesive force caused by the suc- 

 cessive removal of nuclear electrons from the atomic structure. 

 Ordinates Pa of the latter curve from the base-line are the 

 effective forces of cohesion. The result of there being a 

 minimum atomic density is to move the curve of hysteresis 

 to the right, clear of the vertical axis ; a steady component 

 of the force of cohesion moves the centre of the loop vertically 

 downwards. The ordinates of the line of densities in the 

 right-hand figure are obtained by projecting any points 

 P, P', on to the hysteresis curve, and setting up vertically 

 lengths ap, ap', which, if there is lag, are the values corre- 

 sponding to the force aP. The resultant curve resembles 

 closely that of observed densities, fig. 1. 



The period decreases with loss of atomic weight. To a 

 first approximation the maxima of cohesive force occur at 

 the cubes of the first six natural numbers. 



Element. 



Atomic 

 Weight. 



n. 



n\ 



w 3 /A.W. 



H.... 



1 

 11 

 27-1 

 635 



101-5 



191 



1 

 2 

 3 

 4 

 5 

 6 



1 



8 



27 



64 

 125 

 216 



Mean ratio 



10 



0-72 

 1-00 

 1-00 

 1-22 

 113 



B 



Al 



Ou 



Ru 



Os 



1-01 



Superposing a series of such oscillations, of increasing 

 amplitude, upon the curve of equation (3), with minima of 

 force at l 3 , 2 3 , 3 3 , . . . ., we obtain a fair approximation to the 

 full curve of fig. 2. The equation of the density curve if 

 there were no hysteresis would be 



p = p Q + kw{l + ae m $ sin <j>) , 



where <j) is proportional to w. 



The change of atomic volume with atomic weight, gene- 

 rally taken to illustrate the periodic law, can then be built 

 up from two components: — 



(1) An asymptotic rise of mean volume to a maximum 

 which coincides with the radioactive elements. 



(2) A periodic oscillation, giving a displacement modified 

 by structural hysteresis, increasing in amplitude and period, 

 there being six known minima which in the absence of 

 abnormal forces correspond approximately with the cubes of 

 the first six natural numbers. 



The last maximum of cohesive force appears to be at a 

 weight of 6 3 = 2I6, and it is to be remarked that although 



