352 



c^— 0-625 e + 0-0i25 =0; 

 from which we deduce c = '078. 



The following Table contains the values of h thus calcu- 

 lated, together with the means of the observed results. The 

 diiFerences barely exceed the probable errors of the latter ; 

 and the corresponding error in the calculated value of q is 

 less than the probable error of the same quantity, as deduced 

 in the ordinary method from the observed deflections at two 

 distances. 



I 



I' 



k (obs.) 



k (calc.) 



Diff. 



•5 



•5 



- 0-189 



- 0-178 



+ •011 



•5 



•375 



+ 0-067 



+ 0-092 



+ •025 



•5 



•313 



+ 0-180 



+ 0-191 



+ •011 



•375 



•5 



- 0-333 



- 0-358 



-•025 



•375 



•375 



- 0-063 



- 0-088 



-•025 



•375 



•313 



+ 0-007 



+ 0-011 



+ •004 



It follows from the preceding formula, that the relation 

 between the half lengths of the two magnets, which will cause 

 the coefficient of the fifth power of the distance to vanish, is 



l-c= l-224{l'-c); 

 orj substituting for c its value, 



1+ -0175= 1-224 /'. 



It will appear evidently from the foregoing results, that 

 on account of the large probable error of A, its value should 

 be determined in each case from the mean of a much greater 

 number of observations, before we can obtain thereby a sa- 

 tisfactory verification of any formula for its calculation. As 

 far as the comparison has been here carried, the results ap- 

 pear to indicate that the value of h cannot be obtained a 

 priori, in the case of large magnets, with that precision 

 which would justify us in superseding observation, although 

 we may obtain thereby an approximate value, comparable in 

 exactness with the result of a single observation. 



