222 



and u, and may therefore be neglected in comparison with pu 

 andjaV. Hence, approximately, 

 p'u = pu. 



But, if a and a 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 = a — a; 



and eliminating u between this and the preceding equation, 

 the error in the position of the magnet is 



p (a - a) 



u = ^^ ; — . 



P-P 



Finally, the error of the plane of detorsion is 



^ pp'(a'-a) ^ 



P-P 



The angles a and a are given by the formulae 



a = k(n - no), a = k' {n - no) ; 



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

 magnets, and no and no the readings corresponding to the 

 zero-points. 



It appears that the method above described, in which the 

 value of j9 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 w, 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 oip may be diminished by increasing H, 

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

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



