MINDING’S THEOREM. 679 
Let the tensors of y’ and & be e,, e, respectively, and let B’ be a unit vector 
perpendicular to them, then we may write 
bip=x2B+e,e.8 —oB, . ' (8) 
Operating by («—~)~', and noting that 
we have 
biw—a)"p=—-B-“~,.  .  . (8’) 
Taking the scalar of the product of (8) and (8’) we have 
BSp(o—2) ‘p= —= (#B + e10,6')?—SBah . 
But by (7’) we have 
?=SPoB + e+ &—2¢,e,SBR : : (9) 
so that, finally, 
i 2_ 2) (a— 
Peg(e@—2) p=-14; 4 a Ct. «CCG 
5. Equation (10), in which 7? is given by (9) in terms of 8, is true for every 
point of every single resultant. But we get an immense simplification by 
assuming for w either of the particular values ¢,? or ¢,”.. For then the right 
hand side of (10) is reduced to negative unity, and the equation represents one 
or other of the focal conics of the system of confocal surfaces 
Sp(a—h) p=—p, 
a point of each of which must therefore lie on the line (8). This is 
Minpine’s Theorem. 
6. A singular form, in which it can be expressed, appears at once from 
equation (5’). For that equation is obviously the condition that the linear and 
vector function 
—bpSB( )+7'Sy(_)+8'S8( ) 
shall denote a pure strain. 
Hence the following problem :—Given a set of rectangular unit vectors, 
which may take any initial position : let two of them, after a homogeneous strain, 
