256 



Prof. C. V. Boys. 



[June 20, 



increasing effect on the opposite suspended balls, so as to tend to deflect 

 the beam in the opposite direction, 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. Fig. 1 will make the meaning 

 more clear, ab is the beam of the ordinary apparatus with a ball at 



Fig. 1. 













/ % 



b b' b" 



O a," tit' a. 



each end. M is one of the attracting masses, and the other one 

 occupies a symmetrical position on the opposite side of the centre 0, 

 but as the relations of each with the moving system are identical, it 

 will be sufficient to consider only one. 



As the beam is supposed to become shorter, the small balls will 

 occupy successively the places ab' and a"b", while the large mass M 

 will take the corresponding places shown by the dotted circles at M' 

 and M". When it has reached the position M", at which the line 

 joining its centre with makes an angle of 45° with ab, the sensi- 

 bility of the combination is still increasing, but not quite so fast as it 

 would do if the attraction on the ball b did not partly counteract the 

 attraction on the ball a. Should this position be chosen for the mass 

 M, then the beam of the length a"b" is not the best that can be used, 

 if it is further shortened the sensibility will be still further increased, 

 and will become a maximum when the beam has a length equal to 

 half a"b", that is, when the distance between the large balls is 2«/2 

 times the distance between the small ones. If the length of the beam 



is made successively equal to 1, 2, 3 10 tenths of the distance 



a"b", then the corresponding deflections will be represented by the 

 numbers in the following table : — 



ah. 



Deflection. 



o-i 



1-050 



0-2 



1-070 



0-3 



1-077 



0-4 



1-082 



0-5 



1-088 



0-6 



1-080 



0-7 



1-066 



0-8 



1-037 



0-9 



0-982 



1-0 



0-911 



