Action of a Galvanic Coil on an external small Magnet. 437 



one slightly curved, the hydrodynamical pressures in directions 

 along the axis and at c the ends would neutralize each other, and 

 no motion would result from the passage of a galvanic current 

 through it. This theoretical inference is proved to be true by 

 means of the second of the two experiments referred to above, 

 the method of performing which, as originally arranged by 

 Ampere, is exhibited by figure 564 in p. 207 of Jamin's 

 work. 



67. It thus appears that both experiments are explainable by 

 the hydrodynamical theory; and hence, if Ampere has legiti- 

 mately deduced from them the second term of the expression 

 for F, and the numerical value of the constant k, these results 

 may be claimed as properly belonging to that theory. I must, 

 however, say that I do not see how the two experiments taken 

 together justify the supposition of a repulsive force between 

 elements having their axes in the same straight line; they 

 rather seem to me to point to the conclusion that the action 

 between elements under these circumstances does not come 

 into account as respects the production of motion of translation, 

 because the resulting forces at the extremities of a finite rheo- 

 phore are equal in opposite directions, and those between 

 elements in juxtaposition are neutralized. On the principles of 

 the hydrodynamical theory it may be argued that the parts 

 V cos 6 and V cos ! of the original elementary currents, resolved, 

 as stated in art. 61, along the line joining their middle points, 

 give rise to no action between the elements of the rheophores, 

 because the motions which, according to the principles of the 

 resolution of galvanic currents explained in arts. 59 and 62, 

 belong to these resolved parts are incapable of producing by 

 composition variations of pressure at the positions of the atoms 

 of either of the elements of the rheophores. 



68. The course of the general argument now requires the 

 solution, by means of the hydrodynamical theory, of a problem 

 which may be thus enunciated (see Jamin,p. 205) : — A conductor 

 consisting of straight portions of fine wire which, being con- 

 nected, form two rectangles, the planes of which make any angle 

 with each other, is supported so as to be movable about a 

 vertical axis with which a side of each rectangle is coincident ; the 

 horizontal sides are equal, the vertical sides are of given lengths 

 I and /', and between them is fixed a straight vertical rheophore 

 of indefinite length, the current of which is opposite in direction 

 to the currents of the vertical sides ; the effect of the earth's 

 magnetism being eliminated, and the distances a and a' of the 

 indefinite current from the vertical sides in the case of equili- 

 brium being measured, it is found that j = - r The solution of 



