M M 



i2 = ^(2-3sin 2 0), R' = i± (2-3sin 2 f); 



e and <f>' denoting the corresponding quantities for the second 

 bar. Also, if a denote the distance between the centres of the 

 deflecting and suspended magnets, we have 



Substituting these values, and observing that sin 8 cj> = sin 2 <£', 

 very nearly, 



(2-3sin 2 0)(^+F^) = -<- 



"Now, if b denote the horizontal distance of the axis of 

 each bar from the centre of the suspended magnet, and h the 

 distance of their centres above and below the plane in which 

 the latter moves, we have 



e 2 = (a + h) 2 + b 2 , e' 2 = {a- hf + b 2 ; 

 accordingly, if we expand a 3 e~ z , a? e'~ 3 } according to the as- 

 cending powers of - , - , (stopping at the second), we find 



in which, since Fand J 7 " are nearly equal, the term 3 (V- V) — 



b 2 b 2 

 may be neglected. Also sin 2 $ = — = —,q.p. And, subsid- 

 es a, i 



tuting these values in the formula obtained above, it becomes 



a* a* J n 

 But p = (V+ V'y x cotan 6 ; wherefore, finally, 



"In my original instrument there was but one iron bar ; and 

 it was placed in the vertical plane passing through the centre 

 of the suspended magnet, and perpendicular to the magnetic 



