238 



BRIDGMAN. 



TABLE VI. 



The First Three Derivatives of the Repulsive Potential. 



compressible metals. This is what we would expect, the atoms of the 

 less compressible metals being less deformable. 



The order of magnitude of these derivatives now gives a little 

 further information. We would expect that if / is one of the more 

 ordinary mathematical functions the natural sphere of variability of / 

 would have the radius 8, so that the proportional change of / and its 

 various derivatives in a distance 8 would be of the order of small 

 numbers. This is true for the first derivative, as we see from the 

 table, for 8of'(8 )/f(8o) is of the order of a small number. We can, 

 if we like, reverse this principle, and get the order of magnitude of the 

 unknown / by putting 5o/'(5 )//(5o) equal to a small number. We 

 shall find /(<5o) of the order of 10~ ]0 . This is what we would expect on 

 other grounds, for it is also the order of a/8o. The same is true of the 

 second derivative, for 8of"(8o)/f"(8 ) is also of the order of a small 

 number. 



The fact that/'(5 ), which measures roughly the force of repulsion 

 between adjacent atoms, changes only a few fold in the range of 8o, has 

 an important bearing on our picture of the nature of the atomic boun- 

 daries. The meaning is that the atoms do not behave, when pushed 

 into contact, as if they had rigid boundaries, like two bricks, for 

 example. If this were the case, the relative increase of /'(<5 ) would be 

 very much more rapid. In my previous work on polymorphic changes 

 under pressure, 24 I found it useful to think of the atoms as more or 



