Attractive and Repulsive Forces. 195 



posed a mathematical theory of the generation of steady streams 

 under that condition. 



14. Respecting the or?^m«^zo?i of the gradations of atomic den- 

 sity, it will suffice for my present purpose to say that in galvanism 

 the producing cause appears to be chemical action between dis- 

 similar substances in contact ; in magnetism the act of magneti- 

 zing may be supposed to generate a gradation of atomic density 

 which is afterv/ards maintained^ with more or less persistence, 

 by the intrinsic atomic and molecular forces of the magnetized 

 body; and in frictional electricity the friction seems to superin- 

 duce an abnormal state of equilibrium of the atoms of an ex- 

 tremely thin superficial stratum of the electrified substance, 

 together with an interior gradation of its atomic density^ depend- 

 ing, as to degree and permanence, on the capacity of its intrinsic 

 atomic and molecular forces to retain the superficial atoms in the 

 abnormal positions. 



15. Now, in whatever way steady streams are generated, ac- 

 cording to hydrodynamics they will be accompanied by variations 

 of the density and velocity of the fluid from point to point of 

 space, while the density and velocity at any given point and the 

 direction of the velocity will be constant. Hence it evidently 

 follows that a small spherical atom, immersed in the sether under 

 these circumstances, will be differently pressed at difi"erent points 

 owing both to the motion and to the variation of density of the 

 fluid, and consequently that the atom will in general be acted upon 

 by an accelerative force. The exact mode of this action is now to 

 be investigated. The following mathematical reasoning employed 

 for this purpose is almost exactly the same as that I have given 

 in the solution of Example VIII. in p. 313 of the ' Principles of 

 Mathematics and Physics.' But as that reasoning is not directly 

 referred to in the Theory of Magnetism in the June Number, 

 and I have reason to think that on account of this omission 

 some difficulty may be felt in following the arguments, I propose 

 to reproduce it here. 



16. The investigation being restricted to motion for which 

 \udx] is an exact diff'erential^ the equations (b) and (c) give, by 

 the usual process, 



«^Nap.logp+f+y+/W=0; 



and as the motion is steady, -~) which is equal to I -r- ds, va- 

 nishes. Since also the fluid is by hypothesis of unlimited extent, 

 there will be distant points at which V = and the density p is 

 that which the fluid has in its undisturbed state. Calling this 



02 



