9 PROFESSOR GC. V. BOYS ON THE 
Parr I, 
Preliminary. 
In a paper on the CavENDISH experiment, published in the ‘ Proc. Roy Soc., vol. 46, 
p- 253, I showed how the famous experiment of CAVENDISH could be transformed in 
several particulars, so that greatly increased delicacy and accuracy would be obtainable. 
The experiment is-so well known that there is no occasion to describe the apparatus 
which CAVENDISH employed, or the subsequent work of Reicu,t Barty,{ or Cornu 
and Bariie.§ It is sufficient to state that, owing to the extremely small value of the 
Newtonian constant of gravitation, all these experimenters made use of balls as large 
as they conveniently could, so as to increase the force of attraction as much as 
possible, and of a lever as long as they could, so as to increase the effect of the force 
in producing torsion. However, Cornv realized that if he could keep the period the 
same by the use of a sufficiently fine torsion wire, and reduce the dimensions of the 
whole apparatus, the angle of deflection would not be reduced but would remain the 
same. Cornu also introduced refinements which have made the behaviour of his 
apparatus far more consistent than that of any which had preceded it. 
Soon after I had made and found the value of quartz fibres for producing a very 
small and constant torsion, I thought that it might be possible to apply them to the 
CAVENDISH apparatus with advantage, which opinion I found was also held by 
Professor TynpAuLL. Before employing them for this purpose I examined the theory 
of the apparatus with a view to using them in the most suitable manner. 
The sensibility of this kind of apparatus is, if the period is maintained always the 
same, independent of its linear dimensions ; for in two similar instruments, in which 
all the dimensions of one are n times the corresponding dimensions of the other, the 
moments of inertia of the beams and their appendages are as n° : 1, and, therefore, if the 
period is to be unchanged, the torsional couples must be as 7? : 1 also. The attracting 
masses, both fixed and movable, are as 1°: 1, and their distances apart asm: 1; there- 
fore, the attractions are as n°/n”, or as n*: 1, and these, acting on arms n times as long 
in one as in the other, produce moments as “> : 1; that is, in the same proportion as 
the torsional rigidities, and so the angles of deflection are the same in the two cases. 
If, however, the length of the beam only is changed, and the attracting masses are 
moved until they are opposite to and a fixed distance from the ends of the beam, then 
the moments of inertia will be altered in the ratio 2* : 1, while the corresponding 
moments will only change in the ratio n : 1, and thus there is an advantage in 
reducing the length of the beam until one of two things happens, either it is difficult 
to find a sufficiently fine torsion thread that will safely carry the beam and produce the 
required period—and this, no doubt, has prevented the use of a beam less than that 
* ¢ Phil. Trans.,’ 1798, p. 469. 
+ ‘Comptes Rendus,’ 1837, p. 697. 
t ‘Phil. Mag.,’ vol. 21, 1842, p. 111. 
§ ‘Comptes Rendus,’ vol. 76, p. 954; vol. 86, pp. 571, 699, 1001. 
