8 PROCEEDINGS OF THE AMERICAN ACADEMY. 



sion already existing in any given substance. But the comparison of 



different substances involves the dangerous assumption that all substances 



would be alike compressible if freed from self-affinity, — an assumption 



which seems more probable than the last, but which nevertheless must 



be rejected. A much safer measure of the stress under which a single 



substance rests is the work which heat is able to do upon it. The 



changing of a simple substance from t° to t° + dt° Centigrade must 



involve the addition to it of an amount of internal work which is 



represented by the rise of temperature multiplied by the heat capacity 



of the substance, or C dt. In a simple elementary substance, when this 



work does not involve the alteration of crystalline form or any other 



apparent change except increase in size, it seems reasonable to consider 



no other variables, at least as a working hypothesis. If this is the case, 



we may write C dt = P dc, in which P is the internal stress against 



which the heat-energy is doing work, G the molecular heat capacity, t 



temperature, and v volume. The stress against which this work is 



being done is due only to the internal stress and to atmospheric pressure 



(which latter may be neglected by comparison with the very large value 



G dt 

 of the former), hence the stress = P =— — ■• This can apply precisely 



only to infinitesimal changes, because in all probability P will vary with 

 the volume. While it cannot be claimed that the expression just given 

 certainly expresses a single pressure pitted against temperature-work, the 

 expression certainly represents a resultant tendency which opposes 

 expansion by heat, and therefore, by inference, opposes all other forms of 

 expansion.* It is the inward tendency, the opposite to the driving 

 tendency f or fugacity.J 



While then this stress, represented by the quotient of energy divided 

 by change of volume, can hardly represent anything very definite, it 

 must nevertheless be supposed in a general way to increase when the 

 self-affinity increases. Hence, while giving no certain knowledge, its 

 study may give an indication of affinity. 



A typical comparison may be made of the two elements zinc and 

 mercury. They are simple, similar, and yet widely different as to their 

 power of holding oxygen. In each case the atomic contraction on union 

 with oxygen is about the same. If we take as the atomic volume of 



* All the slight data which we possess upon compressibility seem to run 

 parallel with the coefficients of expansion. 

 1- Richards, These Proceedings, 35, 471. 

 % Lewis. 



