FORMULAS FOR SCISSION. 25 



rived, but this has been transferred to the simpler deformation. The 

 name scission would aptly indicate the "shearing-motion" strain, which 

 consists in the relative movement of imdistorted material planes, each 

 sheet of infinitesimal thickness remaining in its own mathematical plane, 

 as shown in figure 1. The motion can be well illustrated with a pack of 

 cards. 



Scission or shearing motion is that case of strain already referred to in 

 which there is a single line of unchanged direction in the xy plane, and 

 it consists of a simple shear compounded witli a rotation of the axes of the 

 strain ellipsoid. 



The most important case of scission is that in which the direction of 

 the planes of constant direction and no distortion coincide with one of 

 the axes. If this axis is o x the displacement formulas may be written 

 simply — 



•''' = •'' — 2 ys ; if = y.* 



Here 2s = '/ —a -1 , the amount of the shear involved. The rotation is 

 given by — 



tan {? — ft) = s ; 



and since tan 2 ^ = tan (y + //) = oo, the axes of the ellipse at the incep- 

 tion of strain were at 45° to the fixed axes. The quantity 4 ah -j- (e —f) 2 

 becomes zero by the simultaneous disappearance of its two terms. If # 

 is the angle by which a line originally parallel to o y is deflected by the 

 strain, 



. tan K = b = 2s , 



so that the amount of shear may be defined as " The relative motion per 

 unit distance between planes of no distortion." f 



Two Shears in the same Plane. — The most frequent combination of two 

 shears in the same plane is that in which the axes of one of these strains 

 makes angles of 45° with those of the other. If the contractile axis of 

 one of the shears makes an angle of 45° with o x, displacing .c to ./ and 

 y to y', the ratio of shear being «, and if the contractile axis of the other 



* If the planes of constant direction and no distortion make an angle, </>, with o ./-, the displace- 

 ments are given by— 



x' = x (I +s sin 2 <(>) — ys (1 + cos 2<j>) ; y' = y (1 — s sin 2 <j>) + x s (1 — cos 2 <£). 



The product, a b = — s" sin'- 2 0, is an essentially negative quantity. Hence the signs of a and b arc 

 necessarily different. Compare tin' discussion of formula (7). 

 -(■Thomson and Tait, Nat. Phil., see. 17"). 



