NEWTONIAN CONSTANT OF GRAVITATION. 3 
half a metre in length—or else, when the length becomes nearly equal to the diameter 
of the attracting balls, they then act with such an increasing effect on the suspended 
balls at the other end of the beam, that the balance of effect begins to fall short of that 
which would be due to the reduced dimensions if the opposite ball did not interfere. 
I showed, in the paper already referred to, that when the attracting balls have been 
brought as near to the equatorial plane, or plane perpendicular. to the length of the 
beam, as they are to the plane of the beam, so that the line joining them makes an 
angle of 45° with the beam, that is that the azimuth is 45°, the ultimate sensi- 
bility is still further increased by shortening the beam to half the length that would 
bring the ends opposite the attracting balls. After that the sensibility very slowly 
begins to fall. 
Since, with such small apparatus as the quartz fibre seemed to make practicable, it 
is easy to provide attracting masses which are very large in proportion to the length 
of the beam, while with the usual long beam relatively small masses must be made 
use of, it is clear that much greater deflections can be produced with small than with 
large apparatus. For instance, to obtain the same effect in the same time in an 
instrument with a 6-foot beam that I was able to realize in my preliminary apparatus, 
in which the beam was 2 inch in length, as seen from above, with attracting balls 
2 inches in diameter, it would be necessary to provide and deal with a pair of balls 
each 25 feet in diameter, and weighing 730 tons, instead of about 1 lb. apiece. 
There is the further advantage in small apparatus that if, for any reason, the greatest 
possible effect is desired, attracting balls of gold would not be entirely unattainable. 
The use of attracting bails which are themselves very large compared with the 
beam length makes it convenient to hang the beam in a cylindrical tube, instead of in 
the long box almost universally employed hitherto. Several advantages follow from 
this. In the first place, if the beam is hung centrally, neither the gravitational 
attraction of the tube nor any minute difference of potential between the tube and the 
beam and its accessories, produce any effect. In the second place, the attracting balls 
may be carried round outside the tube through a complete circle, and yet be placed 
but little further from the attracted balls than would be necessary if no intervening 
tube existed. For this purpose they are conveniently supported by a common 
metallic structure, symmetrical in form, about the axis of the tube, and able to rotate 
about this axis also. If, following the usual arrangement, all four balls are on one 
level, there are obviously two planes, one containing and one normal to the beam, in 
which the centres of the attracting balls may be placed so as to produce no deflection. 
At some intermediate position the deflection will be a maximum, The use of this 
position has the obvious advantage that, besides the fact that this gives the greatest 
effect, the accuracy with which the angle of azimuth is measured is of little conse- 
quence, the geometrical measurements of real importance being the distance between 
the centres of the large balls, the corresponding distance between the centres of the 
sinall balls, and the angle of deflection. This is all the more important since it would 
be extremely difficult to make a really accurate determination of the azimuth, 
B 2 
