466 RICE 



ART. K 



being equivalent to a rotation simply recalls the fact that in the 

 analysis of strain the e^ and 621 coefficients involved the strain 

 through their sum and a rotation around the axis OZ through 

 their difference. (See equations (7) of this article.) 



The reader may at this point feel a little mystified about 

 making the states of reference and of strain coincide ; for in such 

 case he may well ask, how can one have stresses at all. If he 

 will refer to the top of page 185, and read over the remarks on 

 this point by Gibbs, he will feel once more that they are too 

 brief to be very illuminating. The essential point is this. 

 We are after all not treating the state of strain itself and its 

 relation to a state of reference which is physically an unstrained 

 state; we are treating other states of strain obtained by slight 

 deformations from the state of strain in question, involving 

 variations of an, etc.; and for that purpose it does not matter 

 what particular state, strained or not, we take for a state of 

 reference. The position is similar to the treatment of the 

 geometry of a surface. There we are considering the relations 

 of points on a given geometrical locus to some other geometri- 

 cally relevant point (e.g., spherical surface to center, cone to 

 apex, etc.) and it does not matter theoretically what particular 

 set of axes we set up for assigning coordinates to the points in 

 question. We choose in each case a set which is practically the 

 most convenient. To give as wide a theoretical basis as possi- 

 ble to his analysis, Gibbs does not confine himself to any partic- 

 ular set of axes or any particular state of reference; but he does 

 at this point make a passing reference to those axes and states 

 which in practice are the most convenient by reason of the 

 simplifications which they make possible, and to which we con- 

 fined ourselves, for that reason, at the outset of our discussion 

 of elastic solid theory. 



Before we go on to comment on pages 191-207 in which Gibbs 

 goes into certain details connected with equations [374], [381] 

 and [383], it will be as well to dispose of the question of discon- 

 tinuity referred to at the bottom of page 189. We have already 

 mentioned that in deriving [369] from [367] Green's theorem is 

 used. This theorem states that, if <^(a:', y', z') is a function which 

 is continuous, one-valued and finite throughout a region of 



