306 ./. W. Glbbs — EquiUhrium of Heterogeneous iSnbstances. 



1'=°' £=«• '^'^ 



■ ^(^•'^) (K^~) ^{^^) .• .1 !•«• .-1 ^ 



Moreover, it we write -\-r^ -\rr •, -\-r lor the ditterential coetti- 

 da dp dy 



cients obtained from (420) by treating a', p\ y' as independent 



variables, 



d{r^) , , , f?(r2) ^ . , (/(r2) ^ , 



(423) 



Therefore a line of the element which in the unstrained state is per- 

 pendicular to X' is perpendicular to Jl in the strained state. Of all 

 such lines we may choose one for which the value of r is at least as 

 great as for any other, and make the axes of Y' and 1^ parallel to 

 this line in the unstrained and in the strained state respectively. 

 Then 



|,= 0; (4.4) 



and it may easily be shown by reasoning similar to that which has 

 just been employed that 



1 = 0. (42,,) 



Lines parallel to the axes of X', F', and Z' in the unstrained body 

 will therefore be parallel to X, Y^ and Z in the strained body, and 

 tlie ratios of elongation for such lines will be 



dx dy dz 

 dx" ty" ffe'* 



These lines have the common property of a stationary value of 

 the ratio of elongation for varying directions of the line. This 

 'appears from the form to which the general value of r^ is reduced by 

 the positions of the co-ordinate axes, viz.. 



