to the axes whose thicknesses are dr and dr. Then the force 

 exerted by the former upon the latter is 



MI drdr 

 ~* ' 



s denoting their mutual distance. The portion of this force 

 contained in the plane of the deflected magnet, and perpendicular 

 to its axis, is 



and the moment of this force to turn the magnet is obtained by 

 multiplying by r. But 



s 2 = D 2 + r 2 + r\ 



T) being the distances of the centres of the two magnets; and 

 accordingly the total moment of the acting forces is 



fir dr . f/r'dr 



nurdr.f, 

 (D 2 + r 



Expanding the denominator, and making, for abridgment, 



= i)h, &c., 

 = ' a , &c., 



in which the integrals are to be taken between the limits = + /, 

 r =T 9 I and I' being half the lengths of the two magnets, this 

 becomes 



-i/r -j o K JJ 



- " 3 mm' - (m 3 m r + mm' 3}-- + -^-7 (rn^ti + 2m 3 m\+mm f ,}^ + &c. j , 



or mm'U, in which 



15 



Now it is to be observed, that the variations of the ratios 



^ ^ & c arising from the variations of v, are of a lower order 

 m m 



of magnitude than that of m, and may be disregarded in then- 

 effect upon the value of U* On the supposition that the quantity 



* This circumstance was first pointed out by Dr. Lament. 



