Action of a Galvanic Coil on an external small Magnet, 195 



parallels to the axis the angle whose tangent is — . The motion 



is thus completely determined if only the forms of the functions 

 f(r) and F(r) can be found. In my work already cited I have 

 expressed (in p. 566) a doubt as to the practicability of doing 

 this in the existing state of hydrodynamics. I have, however, 

 since discovered the following argument, which I consider to be 

 adequate to this purpose. 



33. Suppose the straight galvanic current to be cut by a plane 

 transversely, and on the plane three concentric circles to be de- 

 scribed having the common centre on the axis, and let their 

 radii be r + a, r, and r — «, a being very small. Also let there be 

 drawn in the plane from that centre two straight lines separated 

 by the small angle B0. Then the space bounded by these lines 



and the first and second circles is C(r-}-a) 2 — ^ 2 ))-«-> and that 



bounded by the same lines and the second and third circles is 



&0 

 (V 2 — (r—a)*) — . Now, according to the foregoing investigation, 



these spaces may be considered to be transverse sections of ele- 

 mentary channels in which the galvanic current is constrained to 

 move. Let V be the mean velocity of the current through the 

 space furthest from the axis, and V that of the current through 

 the other. Then, inclusively of small terms of the second order, 



V' = E (r+ |YandV=]?(r— gY Hence the excess of fluid 



which in a second of time passes through the larger space above 

 that which in the same time passes through the other is 



which, omitting terms containing a 3 &c, becomes 

 F(f) d.Y{ry 



jm d.b\r) \ 

 \ r dr )' 



34. We have now to take into account the principle adverted 

 to in art. 11, according to which the inertia of an unlimited mass 

 of incompressible fluid opposes an insuperable obstacle to any 

 alteration of the quantities of the mass on the two sides of any 

 unlimited fixed plane. Since in the case of the galvanic current 

 fluid is being transferred every instant across the above-men- 

 tioned transverse plane, not only must the rheophore furnish a 

 channel for the circulation of the fluid, but there must also be a 

 general stress, like hydrostatic pressure, which, taking effect 

 always in the directions of any channels of circulation, maintains 



02 



