Action of a Galvanic Coil on an external small Magnet, 357 



different positions we may calculate from this formula as many 

 different values of C t as we please ; and it will be a criterion of 

 the truth of the theory to find that these values differ but little 

 from each other, Cj being, according to the theory, absolutely 

 constant. Taking the mean of the values of Ci thus obtained to 

 be a sufficiently close approximation to its true value, we may 

 proceed to calculate for any given position of the centre of the 

 small needle the angular position of its axis resulting from the 

 total action of the coil, by means of the formula 



Z, + Z', M + dN 



X^X'^M'-j-C^'' 



M, N, M', N' being calculated for the given position by means 

 of the known formulae. By comparisons] of angular positions 

 of the needle calculated in this manner with a large number of 

 observed positions, the theory may be fully tested. 



54. Since I arrived at this solution of the problem, I have not 

 had leisure for going through the arithmetical calculation which 

 would be required for making the above-mentioned comparisons, 

 and I am consequently unable to say whether the theory is 

 capable of satisfying such a test. This omission, however, does 

 not materially affect the argument, because, as I shall afterwards 

 show, the theory may be tested in another way. I have already 

 intimated in arts. 5 and 24 that on the principles of the method 

 of philosophy I have adopted it should be possible to account 

 theoretically for the facts and hypotheses on which Ampere's 

 galvanic theory of magnetism is founded. If this were effected 

 by means of the hydrodynamical theory of galvanism, it is evi- 

 dent that any confirmation which Ampere's theory might receive 

 by satisfying an applied test, would at the same time be a con- 

 firmation of the hydrodynamical theory. For instance, the com- 

 putations undertaken by Mr. Stuart for the purpose of account- 

 ing for, on Ampere's theory, the results of the Astronomer 

 Royal's experiments on the Directive Power of Galvanic Coils in 

 their action on external small magnets (given in the memoir 

 cited in art. 52), and the comparisons contained in an Appendix 

 to the memoir, might, in the case supposed, be claimed for the 

 hydrodynamical theory. Accordingly I propose to give in a 

 third part a theoretical discussion of the empirical foundations 

 of Ampere's theory, with particular reference to its application 

 in the problem of the galvanic coil. 



Cambridge, September 29, 1874. 



Postscript, Oct. 7, 1874. — In the last paragraph of the fore- 



