58 PROFESSOR C. V. BOYS ON THE 
Fig. E. 

and m, m— that of displaced air. Then the moments are for any one attraction 
out of the four possible, 
GMmpr 
Diez 
These are most readily obtained from the observations in the manner set forth 
on the last page, where every figure made use of isset down. Single multiplications 
are performed on the arithmometer more quickly than by logarithms, hence natural 
sines and cosines are employed. Continued multiplications are more conveniently 
performed by logarithms, and the change from D? to D® can only be so effected. 
The angle, @, is the amount through which the lead balls are turned from the 
neutral position — the angle through which the gold balls are deflected. 
R, the radius of motion of either lead ball, is half the distance between the axes of 
the wires, and they are taken in the calculation as being identical, 7.¢., there is 
supposed to be no eccentricity. In Experiment 5 I calculated the result both on 
this supposition and more laboriously giving the true and slightly different values to 
Ry and R,, the radius of motion of the upper and of the lower ball respectively. The 
difference in the result only amounted to 3 parts in 2,000,000, and so, as I explained 
on p. 26, a small eccentricity, if it exists, is of no consequence. 
r, the radius of motion of either gold ball, is half the distance between the axes of 
the fibres. The next few lines explain themselves; they simply give intermediate 
quantities required for the solution of the different triangles. h, and hy are the 
differences of levels of the centres of the lower gold and lead balls and upper gold and 
lead balls respectively. H, is the difference of level of the lower lead and upper gold 
ball and H,, the other great difference of level. The four couples obtained are those 
due to the attraction of the two pairs at the same level and of the two pairs at 
different levels. The latter are in the opposite direction to the former, and are 
therefore subtracted. The result, 1942°625, when multiplied by G, is the actual 
moment produced upon the torsion fibre by the action of the balls upon one another 
