676 PROFESSOR TAIT ON 
if V.¢ be the impure part of the strain 
~=2aSh() . : ° : : (4) 
Hence if ¢ be put (as can always be done) in the normal form 
GSe( ) + Sy(_) + SKC ), 
where 7, 7, & form a rectangular unit system ; we have 
K=2VBa= V(il +jn +40) : ; : (5) 
In the particular case which we shall chiefly require, it will be found that there 
is a certain vector @ such that 
p8=0. 
Hence we may write ¢ in the form 
7Sy(_)+8'S0C ) 
where y, 5 are any two unit vectors perpendicular to each other and to Bethe 
now, we change 
y to ycos9+ésin9 , 
and 6 to —ysind+dcos$ , 
(which are still unit vectors, perpendicular to one another, and to £) 
y becomes y'cos}—s'sind , 
and 5 ‘5 y'sind + 6’cos? . 
These are at right angles to one another if 
28/8’ 
tan 2.9 = Feo 
This always gives real values of 9, corresponding to two definite directions at 
right angles to one another. Hence we may always take 
p=ySy( )+dS8() ' (4’) 
where y and § are as before, and y’ and 6’ are vectors at right angles to one 
another. 
Another point to be borne in mind is that rotation of a rigid system may 
