Action of a Galvanic Coil on an external small Magnet. 353 



the resolved parts of the velocities in three rectangular direc- 

 tions, the pressure^ at any point is given by the equation 



p = C-i(U 2 + V 2 + W 2 ). 



In this equation TJ, V, W may represent the resolved parts of 

 impressed velocities, such as the longitudinal and transverse 

 velocities which, according to the present theory, constitute 

 the galvanic current which is produced and maintained, by the 

 action of a battery, along a fine cylindrical conductor. Hence, 

 since the value of p, by reason of these velocities, varies from 

 point to point of space, they give rise to motions of the fluid 

 which, for distinction, may be called secondary ; and the varia- 

 tions of pressure producing such motions, inasmuch as they result 

 from impressed velocities, are to be regarded as externally im- 

 pressed moving forces. The motions thus produced will be 

 steady because the originating primary motions are steady ; and 

 consequently these secondary motions can coexist with the 

 primary. 



49. In the problem before us U, V, W may be taken to ex- 

 press the sums of the resolved parts of all the motions, as well 

 those parallel to, as those transverse to, the axes of the conduct- 

 ing wires. But it is evident that the former may be left out of 

 consideration, because they tend to produce equal and opposite 

 motions on the opposite sides of the plane of the axis of each 

 circular conductor, and therefore, on the whole, have no effect 

 in generating secondary motions. Thus we have only to take 

 account of the transverse motions about the circular axes. 



50. Directing attention at first to a single circular rheophore 

 and to the motions about its axis which cross the enclosed plane 

 circular area, it will be seen that at each point of this area two 

 motions about two elements of the axis, which are at the extre- 

 mities of a diameter passing through the point, have the same di- 

 rection. The sum of the velocities at or immediately contiguous 



to the centre is ~, and is a minimum ; it increases from the 



centre up to the conductor ; but on the other side of the con- 

 ductor in the extension of the same plane the two velocities 

 are opposed to each other, and their sum rapidly decreases. 

 Thus, the motion being steady, the mean of the motions cross- 

 ing the circular area will be in excess, and the mean of the 

 pressures in defect, within the area ; and the contrary will be 

 the case outside. The consequence will be that a current of 

 the circumambient fluid will set through the area, entering at 

 one side and issuing at the other, as being necessarily a cir- 

 culating current. Each circla cf the coil will have the same 

 Phil. Mag. S. 4. Vol. 48. No. 319. Nov, 1874. 2 A 



