NEW THEORY OF SLATE. 87 



note the existence of this elongation dors not seem to me fatal to the 

 theory. Many observers have obtained satisfactory evidence of elonga- 

 tion in the direction of the grain of the slate, while few, if any, of them 

 appear to have sought for another direction of elongation not in the plane 

 of cleavage. 



The theory here advanced has the advantage of being based on some 

 of the best-established facts of natural philosophy and of connecting- 

 cleavage in the most intimate and definite manner with schistosity, joint- 

 ing, faulting, and systems of fissures. It also exhibits the cleavage of 

 slate and the master joints, which usually intersect the cleavage planes 

 at very large angles, as two features of a single strain. 



Neither Hooke's law nor any other exterpolated generalization has 

 been employed in reaching conclusions as to the origin of slaty struc- 

 ture. Poisson's hypothetical solid was assumed only in an example 

 in order that the formulas might receive a numerical and geometrical 

 illustration. 



Summary. 



The studies here presented are an outgrowth of field-work in the Sierra 

 Nevada of California. That range is intersected by faults, joints, schis- 

 tose and slaty cleavages to such an extent that, on a scale of one mile 

 to the inch, their average separation would be for the most part micro- 

 scopic. In many areas thes< ■ < ly i tamic manifestations are very systematic. 

 Such of them as can be considered as concomitants of infinitesimal 

 strain have been treated in a former paper. In a great proportion 

 of cases, however, the strains have been finite. Only such areas are 

 here considered as may be regarded as uniformly affected by finite 

 strains. 



In the first portion of the paper finite strain is considered from a 

 purely kinematical standpoint. The subject is treated rather fully be-* 

 cause, for the purpose in hand, it is needful to take an extended view 

 of the possibilities. The most important topic is that of the planes of 

 maximum tangential strain and the manner in which they range rela- 

 tively to the material of a solid which is undergoing strain. 



The relations of stress to strain are next sketched, the nature of a 

 finite shear is elucidated, and Hooke.'s law is examined. Hooke's law 

 is shown to differ from the statement that '-stress is proportional to 

 strain" when the deformations are finite. Viscosity, flow, plasticity, 

 ductility and rupture are defined, and the relation of plastic solids to 

 fluids is explained. 



XIII— Bull. Gkol. Soc. Am., Vol. i, 1892. 



