Action of a Galvanic Coil on an external small Magnet. 361 



into account (see art. 52) ; and in Ampere's theory the same 

 thing is done by making the hypothesis of a magnetic sheet. 

 This probab]y explains why that theory agrees with experiment 

 in some degree better than the hydrodynamical theory when the 

 latter does not include the direct action. 



The hydrodynamical theory admits also of the application of 

 a different arithmetical test, based on the following considera- 

 tions. The theoretical quantities ^X, and /tY x are velocities of 

 the ather • and supposing X' and Y' to be the directive forces 

 acting on the small magnet, expressed numerically by inference 



Y Y' 



from the experiments, we have seen that quam proxime —• = vr?* 



This equality would be generally true if the ratio of Y x to Y' 

 were the same as that of Xj to X', even if that ratio were differ- 

 ent for different positions of the magnet. But the argument in 

 art. 19 shows that the directive forces in the two rectangular 

 directions are equal to the quantities X t and Y l multiplied by a 

 constant factor, which, although dependent on the dimensions 

 and atomic constitution of the small magnet, is independent of 

 its position and the direction of its axis. Consequently for each 

 set of corresponding values we have Y' = kY^ and X^^Xj, k 

 being absolutely constant ; and by summing all these equalities, 



S.Y'+S.X'r^S.Yj + S.X,), 



which equation may be supposed to give the value of k with as 

 much accuracy as the character of the experiments allows of. 

 By calculating X 2 and Yj from the expressions within brackets 

 in the formulae of art. 15, taking X' and Y' as given numerically 

 by the experiments, and using all the values of X„ Y ]} X', Y', I 

 find that the value of k which satisfies the above equality is 6973*7. 



Assuming that in Ampere's theory X' = /v'X 2 , Y^k'Y^, and 

 that the values of X 2 , Y 2 are those obtained for X and Y by Mr. 

 Stuart's calculation, I have found, by a process exactly analogous 

 to that indicated above, that /c'= 1*6373. 



The values of the constant factors k and k 1 being thus deter- 

 mined, we may proceed to test both theories by comparing the 

 several values of kX } and kY v and those of k'X 2 and A'Y 2 , with 

 the corresponding values of X' and Y'. In this way the follow- 

 ing results have been obtained : — 



