182 ME. A. NOEMAN SHAW: A DETEEMINATION OF THE ELECTEOMOTIYE 
was a gradual increase of the deflection which reached a limiting value according to an 
expression of the type 
y — a + b log (l +ct), 
where y represents the distance from an arbitrary origin at the time t after producing 
a given deflection and a, b, and c are constants. Deflections were observed only when 
the temperature of the whole circuit was quite constant, and it was found that the 
variation was due to a decrease in the controlling couple while the system was 
maintained in a deflected position. As the measurement of this couple depends on 
observing small oscillations of the suspended system, it is necessary to obtain the 
instantaneous value for a deflection reading. An investigation was undertaken by the 
writer for the purpose of examining this effect in bifilar suspensions, and the results, 
which have special application to the present work, have been published in the article 
already quoted. It is shown there how the behaviour of these suspensions may be 
subjected to accurate calculation. The direction of the deflection was reversed every 
five minutes throughout all the series of final observations and the readings were made 
in each case three and a half minutes after producing a reversal. All auxiliary 
observations were performed between each reversal and it was planned that any 
desired series of readings could be performed continuously in this way. A manipula¬ 
tion of the reversing commutators made it possible to bring the suspended system to 
rest in a few seconds. The object of this method was to maintain the wires in a known 
elastic state which could be referred to the initial one. The problem thus arose to 
find the equation representing the variation of the deflection after its direction had 
been reversed every T minutes for a comparatively long period, and to express this 
with reference to the instantaneous position of the first deflection. The general 
solution to this was shown to be 
x = b log (l+ct + nT) — 2b log (l +ct + (n— l)T) 
+ 2 b log (l +ct + (n — 2)T)— ... +( — l) n 2 b log (l +ct), 
where x is the distance from the initial instantaneous deflection, t is the time after the 
last reversal, n is the number of previous reversals, and b and c are constants. The 
application of this formula is not practicable, but when T < 15 and n very large, it 
was found that a much simpler formula could be deduced which was tested 
experimentally and found to be perfectly satisfactory. The formula obtained was 
^ = D_D T+f = ^’ e "" i .- n) 
where D was shown to be the distance of the asymtotic limit of the creep from the 
position of the instantaneous deflection and k a constant depending on the rigidity of 
the suspensions and the dimensions of the system. D depends on the magnitude 
of the deflection. The formula was tested for different values of T, and curves were 
