= Po(l- 



196 Prof. Challis 07i the Hydro dynamical Theory of 

 density pQy we shall have a'^ Nap. log |0q+/(/) =0. Consequently 



_V2_ 



P = Po^ ^«'. (d) 



which is an exact equation, applying to the fluid at every point 

 of space it occupies, provided it is acted upon by no extraneous 

 force. It will be seen that I have not here substituted the con- 

 stant a' for a, as in art. 8 of the Theory of Magnetism, the reason 

 being that, according to the hydrodynamical principles which I 

 have long maintained, the substitution is not required when the 

 motion is steady. 



17. Respecting the above expression for p, it is to be ob- 

 served that it not only applies to the whole of the fluid in steady 

 motion, but applies also whether the steady motion be simple or 

 be compounded of two or more steady motions. For, according 

 to hydrodynamics, such motions may coexist, and the resultant 

 is consequently steady motion. (See ' Principles of Mathematics 

 and Physics,^ pp. 242 & 243.) As V will always be very small 

 compared with a, instead of equation (d) we may use 



2«V 



18. Let us conceive, at first, the spherical atom to be fixed, 

 and to be acted upon by a stream of the aether in steady motion. 

 Then if the lines of motion were parallel, the distribution of 

 density on the surface of the sphere, due to the sphere^s reaction, 

 would be symmetrical with respect to a plane through its centre 

 perpendicular to the direction of the stream. (For proofs of this 

 proposition I may refer to an article in the Philosophical Maga- 

 zine for November 1859 (p. 323), and to the argument con- 

 cluded in p. 302 of the ^ Principles of Mathematics &c.'') Con- 

 sidering that the atom is of extremely small dimensions, and 

 consequently that the lines of motion in the very slender portion 

 of fluid incident upon it must originally be very nearly parallel, 

 it may be admitted that the above-mentioned symmetrical dis- 

 tribution of density will not be sensibly affected by their con- 

 vergency or divergency. Thus, so far as regards any modification 

 of the pressure arising from the reaction of the atom, we may 

 suppose that no accelerative action upon the atom is thereby pro- 

 duced. There remains only the accelerative force resulting from 

 that variation of pressure from point to point of the spherical 

 surface, which is due exclusively to the steady motion, and would 

 be sensibly the same at the same points if the motion were not 

 interfered with by the reaction of the atom. 



19. Suppose now that trajectory to the surfaces of equal pres- 

 sure to be drawn the direction of which passes through the 



