223 



efficient, H, may be increased without removing the magnet, 

 simply by loading it with an additional weight, care being 

 of course taken that the total weight is within the limit which 

 the thread is capable of sustaining. The method is simpler, 

 and easier in practice, as well as more accurate than the re- 

 ceived one ; and if the position of the magnet, when loaded 

 and unloaded, be observed for several alternations, and in rapid 

 succession, the result may be obtained with very great preci- 

 sion. The difference of the angles, a - a, is, in this case, 

 simply the diflPerence of the observed scale-readings reduced 

 to angular value ; or, 



a - a = k (n - n). 



The following are the details of a series of observations 

 made according to this plan. The last columns in the follow- 

 ing Tables contain the differences between each reading, as 

 given in the second columns, and the mean of the preceding 

 and subsequent readings. The additional weight was 10 oz., 

 being about one-half the weight of the magnet itself and its 

 appendages. 



Obs, I. 



Obs. II. 



Magnet. 



Reading. 



Diffs. 



Magnet. 



Reading. 



Dififs. 



Unloaded 



81-9 





Unloaded 



90-9 





Loaded 



80-6 



- 1-65 



Loaded 



88.3 



- 1-9 



Unloaded 



82-6 



-2-0 



Unloaded 



89-5 



-2-4 



Loaded 



80-6 



-2-65 



Loaded 



85-9 



-2-4 



Unloaded 



83-9 



-2-4 



Unloaded 



87-1 



-20 



Loaded 



82-4 



-2-35 



Loaded 



84-3 





Unloaded 



85-6 











M 



ean diff. = 



= - 2-21 



Mean diflf. = 



= -2-18 



Hence n -n = - 2-20 ; and a-a=k(ri-n) = - r-58. 

 In determining the values of/) and p, the arm of the torsion 



