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LVII. The Hydrodynamical Theory of the Action of a Galvanic 

 Coil on an external small Magnet. — Part III. By Professor 

 Challis, M.A. } F.R.S. 



[Continued from p. 363.] 



TO complete the arguments contained in Parts I. and II. 

 relative to the action of a galvanic coil, it remains to em- 

 ploy the hydrodynamical theory of galvanism to account for the 

 experimental basis of the explanation of that action given by 

 Ampere's theory. The facts and hypotheses that will be referred 

 to for this purpose are for the most part contained in Lecons 70 

 and 71 of Jamin's Cours de Physique, vol. iii., and for the sake 

 of convenience will be adduced by citation from that work. The 

 articles in this third Part are numbered in continuation of those 

 of Part II. 



55. Two parallel rheophores are mutually attracted or repelled 

 according as the currents along them are in the same or oppo- 

 site directions (see Jamin, p. 198). Before proceeding to give 

 a theoretical demonstration of this law, a few preliminary re* 

 marks are required. 



It may be first stated that since according to one of the fun- 

 damental hypotheses enunciated in art. 1 "the size of the atoms 

 is supposed to be so small that even in dense bodies they fill a 

 very small portion of a given space/' it will be assumed that the 

 steady motions that will come under consideration are not sen- 

 sibly modified by the mere occupation of space by the atoms. 

 Again, it will be admitted, as before in art. 19, that in steady 

 motion the accelerative action of the fluid on an atom has a con- 

 stant ratio to the accelerative force of the fluid itself at the po- 

 sition of the atom, and is in the same direction. Hence, since 

 in the case of the parallel rheophores the mutual action may be 

 assumed to take place in directions transverse to the axes, if p 

 be the pressure at any position distant by r from a fixed line of 

 reference parallel to the axes and in the same plane, the accele- 

 rative action on an atom in that position will be proportional to 



-~. It is further to be remarked that the law arrived at in art. 

 <lr 



35, according to which the velocity parallel to the axis of a 

 straight rheophore varies inversely as the distance from the axis, 

 does not apply to positions within its cylindrical surface, because 

 otherwise the velocity would be infinite along the axis. Also, 

 for a like reason, there cannot be within that surface trans- 

 verse motion varying as some inverse power of the distance 

 from the axis. Hence it is necessary to conclude that at 

 distances from the axis less than the radius of the rheophore the 



