1889.] 



On the Cavendish Experiment 



255 



excess of the constancy of the effect actually produced. The observa- 

 tions of Cornu are the only ones which are comparable in accuracy 

 with other physical measurements, and these, as far as the few figures 

 given enable one to judge, show a very remarkable agreement between 

 values obtained for the same thing from time to time. 



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. 

 Professor Tyndall, in a letter to a neighbour written some months 

 ago, expressed the conviction that it would be possible to make a 

 much smaller apparatus in which the torsion should be produced by 

 a quartz fibre. Last summer I began to prepare an instrument with 

 a working beam five millimetres long, but other experimental work 

 obliged me to put this on one side for a time. I have lately examined 

 the theory of this instrument in some detail, and as I find that in many 

 particulars there is an advantage in departing from the arrangement 

 that has always been employed, I have lately prepared two pieces of 

 apparatus, which on trial fully bear out the results of this inquiry. 



I shall, therefore, first give a short account of the principles that 

 should be followed in the design of the Cavendish apparatus, and 

 then describe the results which I have obtained up to the present 

 time. 



As I have already stated, the sensibility of the apparatus is, if the 

 period of oscillation is always the same, independent of the linear 

 dimensions of the apparatus. Thus, if there are two instruments in 

 which all the dimensions of one are n times the corresponding 

 dimensions of the other, then the moment of inertia of the beam and 

 its appendages will be as n 5 : 1, and, therefore, the torsion also must 

 be as n 5 : 1. The attracting masses, both fixed and movable, will be 

 as n s : 1, and their distance apart as n : 1. Therefore, the attraction 

 will be as nPjrfi or # : 1, and this is acting on an arm n times as long 

 in the large instrument as in the small, therefore the moment will be 

 as n h : 1, that is, in the same proportion as the torsion, and so the 

 angle of deflection is unchanged. 



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 moment of inertia will 

 be altered in the ratio n 2 : 1, while the corresponding moment will 

 only change in the ratio of nil, 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, I 

 believe, has up to the present time prevented the use of a beam less 

 than 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 



VOL. xlvi. u 



