4 PROFESSOR C. V. BOYS ON THE 
whereas the other three quantities can be measured, as will appear later, with the 
highest degree of precision. 
It will be evident that, as the size of the attracting balls is increased with the 
object of increasing the deflection, their action on the opposite suspended balls increases 
in a very high ratio, so that very soon a practical limit is reached, beyond which any 
increase of size produces an insignificant effect. For instance, if the distance between 
the centres of the attracting balls is five times the length of the beam, and they are 
set at the angle (58° 20’) at which their action is a maximum, the counteracting 
couple due to the far ball is § of that due to the near one, so that the resultant couple 
is only & of that which would be produced if the attraction on the remote end of the 
beam could be annulled. This, in effect, I practically accomplished by arranging the 
two sides of the apparatus at very different levels. In this way, if only the exact 
position of the balls can be determined, or rather their co-ordinates can be ascertained 
with degrees of accuracy in proportion to their importance, then the arrangement is 
eminently suitable for the purpose of finding the gravitation constant. 
The preliminary apparatus that I made on this principle in 1889 worked so well, . 
even under the unfavourable conditions met with at South Kensington, that I felt 
satisfied that an instrument built on the same lines, but in which the necessary 
geometrical measurements could be made, would enable me to make a more accurate 
measure of the Newtonian constant than had been considered possible hitherto. I 
even felt satisfied that it could be determined with an accuracy of 1 in 10,000; and 
this extreme degree of precision I now feel certain may be attained by a skilled 
experimentalist, if the very small modifications suggested by my recent work, which 
are described at the end of this paper, are adopted, and if, above all, the experimen- 
talist,, whoever he may be, has time and place at his command, and is not driven by 
necessity to steal as much time for observation from his holidays and nights as his 
physical strength will allow. 
In the design of any apparatus, it is necessary to have some definite idea as to the 
degree of accuracy which is to be aimed at, so that trouble may not be taken in 
attaining an absurd degree of precision in one part, while some other part is glaringly 
in defect. The aim which I made, and which my preliminary experiments showed 
to be reasonable, was one of 1 in 10,000 in the result; for this purpose the large 
masses would have to be determined 
to 1 in 10,000; 
times) ,, Las Z0s0008 
some lengths ,, 1 ,, 20,000 about ; 
other * Bole se TOMOKO) |. 
1 ,, 10,000. 
I gathered from conversation with some physicists of note, whose judgment and 
experience I fully appreciated, that there was some doubt whether I was doing right 
in persisting in making small apparatus where absolute determinations were the 
object, for though I had clearly enough shown that so far as sensibility and constancy 
an angle ,, 
