524 PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
Let us suppose that e is a strain coordinate ; then it follows, by Lagrange’s equations, 
that there is a force due to this term, tending to increase e, equal to 
Since f according to our view, changes very rapidly, we must find the mean value of 
this term, that is, we must find the value of 
J o 
If the electric field breaks down and gets established n times in a second, this will 
equal 
i 
AT <->TTT 
n f n fhlt. 
Jo 
J.\ ow 
{*fdt =/ 
J 0 
Let 
(V = £.(«/)* 
J o 
where, as before, af is the maximum value of f and /3 is a quantity which will depend 
upon the way f reaches its maximum ; then 
where u is the current through unit area of the section of the conductor. Then the 
O 
average force tending to increase c.equals 
“ . ( 81 ) 
4 de' ' n 
If neither n nor a depend upon e, then this equals 
— olR — u~". 
de 
(82) 
Thus, if the specific resistance increases with the strain, there will be a tendency to 
diminish that strain when a current traverses the conductor. 
