43P> Prof. Challis on the Hydrodynamical Theory of the 



the sum of the values -~- for the positions of all the atoms of 

 dr r 



the element acted upon, is composed of the factors V sin f cos e, 



aV 



a ds' and the differential coefficient of — — ds sin 6 with 



r- r 



respect to r, together with a constant factor F . Hence, putting 

 F for the value of the expression, we have 



— ■=—— g — sin 6 sin 6 ] cos e ds ds' (c) 



It is plain from the form of this formula that by a change of 

 the constant F it would express the action of the element 

 whose intrinsic intensity is V 7 on that whose intrinsic intensity 

 is V, although investigated only with reference to the action of 

 the latter. 



F 



64. The above expression for -^ is identical with the first 





 term of the well-known formula obtained by Ampere for the 



mutual action between two galvanic elements. That formula, 



as given in Jamin, p. 207, contains an additional term, involving 



a constant factor k, the numerical value of which is subsequently 



determined by means of a certain analytical process. The reason 



assigned for adding this term, and the analysis employed for 



determining the value of k, rest upon two experimental facts, 



which, as I propose in the next place to show, admit of being 



accounted for by the hydrodynamical theory. 



65. The first experiment, made originally by Ampere, is that 

 represented by a figure in Jamin, p. 200, according to which a 

 current entering at one end, and issuing at the other, of a bent 

 movable rheophore the terminals of which point towards the 

 same quarter in parallel directions, is caused to move in the 

 direction of the entering of the current. In ' The Principles 

 of Physics/ p. 591, I have given an explanation on hydrody- 

 namical principles of a very similar experiment made by Fara- 

 day. According to this explanation, which is equally applicable 

 to the present instance, the current enters the rheophore con- 

 vergently and with increasing velocity, and consequently, by the 

 hydrodynamics of steady motion, with diminishing pressure, 

 in the direction of entering, whilst it issues divergently with 

 diminishing velocity, and increasing pressure, in the direction of 

 issuing; so that within certain portions of the rheophore at 

 both ends the decrements of pressure are in the same direction, 

 and have consequently the effect of a repulsive action in that 

 direction. 



66. It is evident, however, that this result depends on the 

 rheophore being bent. In the case of a straight rheophore, or 



