222 



and u, and may therefore be neglected in comparison with /)m 

 and/)V. Hence, approximately, 

 Ipu = pu. 



But, if a and d denote the angles which the magnetic axes of 

 the two magnets form with the line of collimation of the ob- 

 serving telescope, supposed fixed, 



u - u = d - a; 



and eliminating u between this and the preceding equation, 

 the error in the position of the magnet is 



V (a' - a) 



n = ^-^ ; — . 



P-P 



Finally, the error of the plane of detorsion is 



P-P 

 The angles a and d are given by the formulae 



a = k(n - Wo), d = k' («' - no') ; 



n and n denoting the actual readings of the scales of the two 

 magnets, and Wo and Wq' the readings corresponding to the 

 zero-points. 



It appears that the method above described, in which the 

 value off is altered by the substitution of a weaker magnet, 

 is only approximate. But a much weightier objection to it 

 is, that the plane of detorsion, and therefore the angle v, is 

 liable to be altered by the removal of the magnet ; and thus 

 the assumption upon which the value of that angle is inferred 

 fails altogether. 



It is easy to avoid both these sources of error. It is ob- 

 vious that the value of^ may be diminished by increasing H, 

 as well as by diminishing ?m ; and that the effect upon the 

 angle ?< will be the same in both cases. Now the torsion co- 



