16 G.F.BECKER — FINITE STRAIN IN ROCKS. 



to consider finite strains as well as infinitesimal ones.* Now, to discuss 

 such strains completely it would he needful to know the relation between 

 finite strains and the forces which produce them. This relation is not 

 yet known. 



One might infer that until it were ascertained discussion would he 

 useless. I hope to show, however, that many relations of finite strain 

 can he elucidated without the assumption of any law connecting stress 

 and strain, and that these relations are of great assistance in the study 

 of orogeny. 



The general principles governing finite distortion have, of course, heen 

 indicated by natural philosophers; hut little attention has heen given 

 to their development, because the theory of finite strain is needless for 

 computation of machinery, while this subject will not offer much purely 

 mathematical interest until the stress-strain law is known experimentally. 

 In particular, but little attention has been paid (so far as I am aware) 

 to the planes of maximum strain, which turn out to be those in which 

 geologists have a special interest. f 



In the following pages the attempt will lie made to develop all the 

 manifestations of uniform or homogeneous finite strain in rock masses 

 regarded as isotropic, exhibiting viscosity and capable of flow, which can 

 be elucidated without assuming a law connecting stress and strain. For 

 this purpose finite strain must first be discussed by itself; then it must 

 he considered just how far the relations of stresses are capable of coor- 

 dination with those of strain. The influence of viscosity and solid flow 

 must next be shown. Readers willing to assume that these subjects 

 have been logically treated will probably skip them and proceed to the 

 geological applications which follow. Finally, the results will be com- 

 pared with actually observed phenomena and with the experiments 

 which several investigators have made on slaty structure. 



FlNITli ROTATIONAL STRAIN. 

 LIMITATIONS OF THE PROBLEM. 



The mechanical effects short of rupture which force can produce in 

 any mass are translation, rotation, dilation and deformation. The effects 

 of mere translation may be considered separately from the other effects of 

 force, or, in other words, one may consider these other effects relatively 

 to some chosen point of the body itself. 



* I have previously endeavored t" show that some fissure systems are satisfactorily explained on 

 the hypothesis of small strains : Bull. Geol. Soc. Am., vol. 2, 1891, p. 49. 



f < tn finite strain consult Thomson and Tait, Nat. Phil., 1879, sec. L81 ; and Ibbetson, Math. Theory 

 of Elasticity, 1887, p. 09. 1 am much indebted t" l><ith authorities. 



