58 G. F. BECKER — STRUCTURE OF THE SIERRA NEVADA. 



As was pointed out, the distortious are supposed to be so small that their 

 squares may be neglected, and this is certainly the case with such material 

 as granite ; for suppose such a substance under pressure to undergo so great 

 a linear contraction as 1 per cent, before rupture, then the square of this 

 distortion would be only to^oo, which it would be very difficult to detect ex- 

 perimentally. Neglecting the distortions of the second order, the above 

 formula reduces to — 



2d= PjZn, 



so that the elongation oi o x and o z per unit length in consequence of the 

 pressure is Pl^n. 



Turning now to the traction acting on the incompressible cube, it is evi- 

 dent that its effect is exactly analogous to that of the pressure with contrac- 

 tion substituted for elongation. Hence the traction will decrease o z and o y 

 each by Pl^n per unit length. The line o is thus increased by the press- 

 ure and decreased by the traction in precisely the same proportion, or, in 

 other words, this line is not affected in length by the system of forces repre- 

 sented in figure Zh. 



Hence a compression P/3 accompanied by a traction P/3 at right angles 

 to it, acting on a compressible cube, alters neither the volume of the body 

 nor the length of lines perpendicular to the plane of the forces. The only 

 effect is to diminish the height by P/Bn -|-P/67i=P/2/i and to increase the 

 breadth by the same amount. 



Now the northeasterly and southwesterly forces of figure 1, if they could 

 act alone (or if the mass were capable of deformation only in this direction), 

 would tend to drag the mass into an oblique form, as shown in figure 4a, by 

 shifting of layers. No change of area would accompany this distortion. 



l^'iGURE 4 — Analysis of a Shear. 



Similarly the other couple would by itself tend to produce the distortion 

 shown in figure 4b, again without change of area. Neither couple would 

 have any tendency to change the volume. Acting simultaneously they 

 would produce the distortion shown in figure 4c. 



Thus the effect of the balanced couples of figure 1 is exactly the same as 

 that of a pressure accompanied by an equal traction as shown in figure Sb, 

 and these different diagrams are merely different methods of representing one 

 and the same strain — a simple shear. 



