Action of a Galvanic Coil on an external small Magnet. 431 



motion is such that udx + vdy + wdz-is integrable of itself and 

 not by a factor, and consequently that at all such distances the 

 velocity parallel to the axis is the same. If Vi= that velocity in 

 the interior and at the surface and j3= the radius of the rheo- 

 phore, the velocity at any distance r from the axis greater than 



/3 may be assumed to be -~. Hence, since $ is in general very 

 " •■- : r .: 



small, in order that the exterior velocity parallel to the axis may 

 be of considerable magnitude, it is necessary that Vi should be 

 large. 



56. These conclusions being admitted, if at the position of 

 any atom of the rheophore within which the velocity parallel to 

 the axis is Y v the longitudinal velocity due to the other rheo- 

 phore be v u and the transverse velocity due to the same be v 2 , 

 we shall have by hydrodynamics 



i? = C-i((V 1 + ^ 1 ) 2 + ^> 



Hence, if r be the distance of the atom from the fixed line of re- 

 ference mentioned in the preceding article, we shall haye, Y x 

 being constant, 



dp nT . dv x dv Q 



s r--(V,+« 1 )- s -.i S r 



i--v,((i + |;)* + ^> 



Consequently, since from the foregoing argument the ratio ^- 



is very small if the distance between the rheophores be a large 



multiple of the radius of that to which the velocity v x pertains, 



v 

 and since a fortiori this is the case with respect to the ratio *f- 



because v 2 varies inversely as the square of that distance, it fol- 

 lows that, under the circumstances in which the experiments to 

 which the argument applies were made, we have very approxi- 

 mately 



dp _ y. dv l 



dr 1 dr 



If the distance of the axis of the nearer rheophore from the re- 



V 6 

 ference line be h, we may put ~~r for v r ; and we thus get 



dr (r-hf' 

 It thus appears that if Y l and V, have the same sign,, or the 



