STRAINED ELASTIC SOLIDS 455 



treatment consult Geiger and Scheel's Handbuch der Physik, 

 Vol. VI, Chap. 2, pp. 47-60 (Springer, Berlin). 



We have now completed this long exposition of elastic solid 

 theory. It has been necessary to go into it in some detail, since 

 without some modicum of knowledge concerning it, this section 

 of Gibbs' treatment, brief as it is, would be utterly unintelhgible. 

 Indeed its very brevity renders the task more difficult; for 

 although Gibbs, in his treatment of heterogeneous phases con- 

 sisting of solids and fluids, does not employ in every detail the 

 analysis of stress and strain in a solid usual in the texts of to-day, 

 every now and then he interposes a short remark which would 

 puzzle a reader unacquainted with that analysis. The very 

 first page of the section is a case in point. Moreover, this 

 analysis usually forms part of one of the more specialized courses 

 in the physics or mathematics department of a university, and 

 even students of physics, not aiming at a highly specialized 

 degree in that subject, might well find their knowledge of stress 

 and strain too rudimentary to follow Gibbs at this point. 



We now take the section itself and give a commentary upon it 

 page by page. 



II. Commentary 



7. Commentary on Pages 184~190. Derivation of the Four 

 Equations Which Are Necessary and Sufficient for the Complete 

 Equililrium of the System. We have already in the preceding 

 exposition dealt extensively with the introductory defini- 

 tions and formulations of Gibbs, I, pp. 184-186. We would 

 remind readers that in [354] the usual practice of to-day would 

 replace a differential coefficient such as dx/dz' by dx/dz', since 

 it is implied that x, regarded as a function of x' , y', z', is being 

 differentiated ^partially with respect to z', with the condition 

 that x' and y' do not change in value. Actually it will probably 

 be more convenient if we keep the notation introduced above 

 and refer to dx/dx' as an, dx/dy' as an, dy/dx' as a^i, etc. If the 

 strain is homogeneous these ars strain-coefficients are independ- 

 ent of the particular values of x', y', z'; they are constant 

 throughout the soHd body. In general, however, the strain 

 may be heterogeneous, and in that event any a^g is a function 



