172 MR. A. NORMAN SHAW: A DETERMINATION OF THE ELECTROMOTIVE 
take B as the directive force at the instant of deflection we may, therefore, assume that 
B is a constant quantity for values of 6 from zero up to the deflections considered 
in this investigation. As ju for our suspensions decreased rapidly with time after 
deflecting the system it was always necessary to apply a correction if the deflection 
was observed an appreciable time after it was produced. The calculation of this 
correction under the condition of continued reversals of 0 is treated fully in the place 
quoted above. 
B can be most accurately calculated from determinations of moments of 
inertia and times of oscillation of the suspended coils. The following method was 
adopted. An accurately constructed movable tube 45 cm. in length was placed 
coaxial with the coils, and into this a pair of similar cylindrical weights could be fitted 
either at the centre or at the extremities of the tube. It was thus possible to vary 
the moment of inertia of the suspended system without altering the total mass. A 
sliding support was inserted in the dynamometer to hold the suspended coils when it 
was necessary to handle the system. 
If Tj is the time of a complete infinitesimal oscillation (two transits), and K x is the 
moment of inertia with the cylinders at the outside position, and T 2 and K 3 the 
period and moment of inertia when they are at the internal position, then we have 
Tj = 2tt /\/^ and T, = 2tt /\/^ 2 > 
and hence 
B = - (K^-Ks), 
J-1 12 
and it can easily be shown that 
K 1 -K J = M{(Ky-(K) a } 
where d x and d 2 are the distances between the centres of mass of the two cylindrical 
weights and M is the total mass of the two cylinders. 
Thus 
E .. (9) 
Ty T 2 " 
It was important that the tube and especially the cylinders should be very care¬ 
fully constructed in order that the above formula should hold to the desired limits of 
accuracy. After a trial of several pairs two very satisfactory solid brass cylinders 
were made, and the series of tests outlined below will indicate that the necessary 
refinement was obtained. 
( h) The Cylindricity of the Weights. 
Forty diameters of each cylinder were measured with micrometer calipers. Each 
column in the table below represents a set taken at regular intervals from end to end 
with the cylinder in each of four equally rotated positions. 
