1889.J 



On the Cavendish Experiment. 



259 



effect in the nearer ball only is considered, then it is easy to find the 

 best position for any distance of the attracting mass from the axis of 

 motion. Let P (fig. 2) be the centre of the attracting ball, N" that of 



Pig. 2. 



the nearer attracted ball, the axis of motion, c and a the distances 

 of P and N from 0, and x the distance from 1ST of the foot of the per- 

 pendicular from P on ON produced. Then the moment of N about O 

 will be greatest when 



a v J 



or what comes to the same thing when 



2 _i_ 2 



cos 2 0+°-^- cos 9 = 3. 

 ca 



The solutions of these equations are given in the following table : — 



9 



cja. 





-* > 



xja. 



1 



0° 



0' 







2 



27 



45 



0-77 



3 



42 



16 



1-22 



4 



51 



19 



1-50 



5 



58 



20 



1-62 



6 



63 



, 15 



1-70 



7 



66 



44 



1-76 



8 



69 



23 



1-82 



9 



71 



17 



1-88 



10 



72 



50 



1-95 



oo 



90 







2-00 



