1888.] Mr W. Peddle on Transition- Resistance, 119 
represent the total increase of transition-resistance in time, t this 
gives 
E = Ko(l-s-‘% (A) 
where Eq is the final value of E. Hence, if we delete the suffix, 
and write for the value of the total resistance in the circuit when 
^ = 0, we get for the value of the total resistance at any time 
r = ro + E(l-s-'^). 
So, if we assume the capacity to be constant, the equations of. 
conduction give approximately with this value of r , 
= .... (B) 
where 
_E ,_1 
“ ^ c(K + r,)’ 
e being the capacity of the condenser. The approximation is 
obtained by assuming that the reciprocal of the quantity ch(r^ E), 
is very small compared with unity. Since C and E are very large 
quantities, while h is not very small, this assumption may safely be 
made. 
This equation contains four unknown constants, and their 
numerical value cannot be determined by elimination, for the degree 
of the resulting equation is too large. So I have obtained them by 
giving probable values to a and a?Q, and then calculating h and k. In 
this way, by giving different values to a and curves were obtained 
between which the observed curve lay, and so by varying a and 
satisfactory values were finally obtained. The curve to which I 
liave applied the equation is that drawn through the group of 
points marked a in the plate which accompanies my paper already 
referred to on transition-resistance. The value of the constants were 
a =10, aTQ = 420, & = 0‘3924, /t = 0‘0404. The calculated and 
observed values of x for different values of t are given below. 
t 
1 
2 
4 
8 
12 
16 
x{ohserved), 
93 
60 
40-4 
28-4 
23 
20-2 
x{calculated)^ 
95 
60-2 
40-8 
28-8 
23-7 
20 
The coincidence is obviously extremely close. I also applied the 
equation to the curve marked h in the plate alluded to, assuming 
the same values for h and k, which is at least approximately correct. 
The values of a and Xq are 5*3 and 230. The results are 
