621 
S. (pi + + (pj+ <H + 
( pk + < 
or, as it may evidently be written, 
P + 2 fx , 
dP dy 
— -| 
dy dx , 
dl + <K 
dz dx 
d% dvi 
dy dx , 
P + 2 — 
dy , 
dz dy 
^| + % 
dz dx , 
dr\ d<? 
dz^ dy , 
= 0 . • ( 13 ). 
A value of p having been found from (13), the direction of the cor- 
responding axis is given by 
• (*+«.+•£) ■ ■ ( 14 ). 
III. a. As a very simple example of distortion, suppose g to repre- 
sent the position of each particle with regard to a centre attracting 
according to Newton’s law, and let cnthe vector of distortion be a 
small constant multiple of the vector force. Then 
7YI 
ip- = C (the potential). 
QUID 
Hence = p-|, where g is very small, 
9 m U 4 w ) 
when g becomes g + cn, g + w becomes g -f ea + 
T& is exceedingly small, this may be written 
gm(g+a) 
T(g + »y 
As 
Hence w 1 = w + + 3g^^ , and an originally spherical 
face Tw = e (8) becomes after distortion approximately 
a spheroid of revolution whose axis is g, as indeed is evident. 
sur~ 
IV. In this latter case we see at once that V. <d cn = 0, and it 
is easy to show that in general, if the small displacement of each 
pomt of a medium is in the direction of , and proportional to, the 
