456 RICE ART. K 



of x', ij', z', and a^, implies a functional form and is really a con- 

 traction for a„ {x', y', z'). 



Care should be exercised also to retain a clear idea of the 

 meaning of the variational symbol 5. We have already used it 

 in the exposition in the sense in which it is employed by Gibbs; 

 thus b{dx/dx') or, as we shall write it, 6an refers to an infini- 

 tesimal variation of the strain-coefficient, at a given -point, i.e., 

 in a given physically small element surrounding the point which 

 was originally at x' , y', z'. The reader must guard himself 

 carefully against the misconception that he is to think of a 

 point neighboring to x' , y', z', say x' + 8x', y' + W, z' + hz' , 

 and to regard han as short for 



9aii 9aii ha^ , 



^ ax' + ^ iy' + - &', 



i.e., as the difference between the strain-coefficient at a point and 

 at a neighboring point. Such a blunder would be fatal to any 

 understanding of [355] . Indeed it was to avoid giving the reader 

 any unconscious bias toward such an idea, that the writer, in re- 

 ferring in the exposition to a point near to x' , y' , z' employed 

 the notation x' + ^', y' + t]',z' + f ' and not x' + bx' , etc. 



In the exposition we used e and -q as symbols for the energy 

 and entropy of the amount of material which occupies the unit 

 of volume in the state of strain from which an infinitesimal 

 variation is made; there was no need for suffixes as there was no 

 ambiguity involved at that point. It is, however, the general 

 practice of Gibbs to refer the material to its state of reference 

 when considering magnitudes of measured properties per unit 

 length, area or volume. Hence his use of the suffix v to bring 

 that clearly before the reader's mind. Occasionally when he 

 wishes to make a statement concerning magnitudes measured 

 per unit of volume in the state of strain he employs the suffix v 

 without the accent. 



In the exposition we saw that 



dtv = td7}v + ^Xrdf. 



Now a unit of volume in the state of reference becomes the 



