170 
Proceedings of the Royal Society of Edinburgh. [Sess. 
He did so by showing that Bonty’s formula is a particular case of his 
own. For since 
e~ yt =1 - yt + V-t 2 - V * + etc., 
' 1.2 1.2.3. 
we have, for sufficiently small values of t, 
e~ yt = 1 - yt . 
Substituting this expression for e~ yt into Wiedeburg’s formula, we have 
P = f- 
a -h( \ - yt) 
which is of the same form as Bouty’s. We may write Bouty’s formula as 
V 
+PP = <*■ , 
and in this form it indicates that if ^ be plotted against p, the graph 
obtained should be rectilinear within the time to which this law is 
applicable. 
Fig. 3 shows the curves of ~ against p, as given by my observations 
for the two anodes No. 1 and No. 2 of fig. 2. It will be seen that between 
the points corresponding to 01 and Ctl 8 min. on the one curve, and 01 and 
02 min. on the other, the curvature is not appreciable. Above this the 
curves begin to bend as we might expect. Difficulty of observation both of 
time and polarisation makes it impossible for me to take points on my 
curves corresponding to smaller values of the time, but from these curves 
we can conclude that Bouty’s form of Wiedeburg’s formula holds in the 
cases investigated within a time range of about a fifth of a minute. 
For larger values of the time which necessitate the inclusion of the term 
J , but allow of the term y 7 being excluded from the expansion of e~ yt , 
2x3 
we have 
e yt = 1 - yt + 
//V 2 
Wiedeburg’s formula becomes, in that case, 
V 
t - At 2 
B + C t- Dif 2 ’ 
by 
where A = Mr ■ B = — — - ; C = 6 ; D = 
2 y z 
My observations enable me to make at least a partial test of the 
applicability of this formula within time ranges which are beyond the 
