of Magnetic Moments in Absolute Measure. 325 



Then for equilibrium we have 



^f 1___JL_ 1 = Htanfl; 



2a\(r-ay (V + a) 2 / 



therefore 



Hence jj 2r 



M = (r-«y(r + ay Ht||nft 

 lr 



Again, 



M —{r-af (r + a) 2 tan 6' 



or 



T 2 = 



H = 



47rV 



Ml' 



47T 2 /^ 



T 2 M* 



Substituting the value found above for M and squaring, 



W6 gGt W - BttV, 



" T 2 <V-a) 2 (r + a) 2 tan<9* 



These formulas were used in preference to the approximate 

 formulas which they become when a is struck out, and which 

 are generally employed. 



The distance between the poles of a magnet, or its virtual 

 length 2a in the above formulas, may be determined by 

 observing the deflections 6 and d f of the magnetometer-needle 

 produced by the magnet when placed at distances r and 

 / from the centre of the needle. 



For we have the equations 



2M_ (r 2 -a 2 ) 2 tanfl 

 H ~ r ' 



(r' 2 -a 2 ) 2 tan0' 



= ? ' 



from which we obtain by reduction 



•'Vrtanfl'-rV/tan 6 



v r tan 0' — 



The average of a number of determinations of a made by 

 this method agreed almost exactly with the actual half-length 

 of the magnet ; and as the effect of a slight error in the value 

 of a does not sensibly affect the value of M, the actual half- 

 length was used in all the calculations. 



The values found from each of the five magnets are given 

 in the following Table. These results, as well as all those 

 which follow, are given in C.G.S. units. 



