SURFACES OF DISCONTINUITY 587 



of thermodynamic texts if writers would cultivate the habit of 

 indicating by bracketed symbols just what quantities are being 

 considered as the variables upon which the physical properties 

 being discussed are dependent, — at all events in circumstances 

 where ambiguity might otherwise easily arise. For example, in 

 the present instance, a regarded as depending on t, ni, would 

 be written as cr(f, ni), meaning the function of the variables t, m 

 which is, for any given values of t and mi, equal to the value of 

 the surface tension at these values of temperature and the 

 potential of the first component. On the other hand <t regarded 

 as depending on t, p would be written as (r(f, p). Of course it 

 would be implied in such a convention that the functional form 

 of <T{t, Ml) would not be the same as (r{t, p). Actually, to satisfy 

 the requirements of a strictly rigorous use of mathematical 

 symbolism we should write the two functions, which both repre- 

 sent the same physical quantity, in different ways, say f{t, m) 

 and g{t, p); but the situation does not really demand such rigor 

 and there is an advantage in indicating just what physical 

 quantity is being represented, provided the implication referred 

 to is kept in mind. Such a symbolism when combined with the 

 modern partial differential coefficient notation (the use of d 

 instead of d, not in use when Gibbs wrote his memoir), would 

 also clearly indicate what quantities are being regarded as con- 

 stant in any particular differentiation, so that the use of the 

 subscript after a bracket (the usual method of the thermo- 

 dynamic texts) would be unnecessary. Thus in equation [593] 

 {da/dt)p would be da(t, p)/dt and {da/dp)t in [595] would be 

 d<T{t, p)/dp. In [587] and [592] the differentials are total differ- 

 ential coefficients. Gibbs makes a special reference to this 

 point at the top of page 271. With only one component, say 

 a liquid and its vapor, p is a function of t, and <r can be re- 

 garded either as a function of p only or as a function of t only 

 and written accordingly a{p) or ait) as the case may be; so that 

 in [587] the total differential coefficient symbol would still be 

 correct and we would write it as 



