198 Prof. Challis on the Hydrodynamical Theory of 



tive action will not be altered ; and as under these circumstances 

 a uniform stream is incident on the sphere at rest, from what 

 has already been said in art. 18, no change in the accelerative 

 action of the steady stream on the sphere is thereby produced. 



21. If, however, the sphere be free to move in obedience to 

 the pressure of a steady stream, it will in general be continually 

 accelerated, and the acceleration will give rise to resistance due 

 to the inertia of the surrounding fluid, which will in turn be 

 impelled by the acceleration of the sphere. The amount of this 

 retardation may be calculated just as in Poisson^s solution of the 

 resistance of the air to a ball-pendulum. Hence it follows, if 



-tJ be the actual acceleration of the sphere, that the retarding 



force is — ^~ • -7^'- (Principles &c. p. 266), and consequently 

 that 



Therefore 



d% ^Pq V,dY, _ Pq cl^Si 

 df^ A ds^ 2A dt^ 



dt'^ ~"2A + Po* ds^ 



It thus appears that, whether the atom be fixed or moveable, 

 its acceleration by the pressure of the fluid in steady motion has 

 a constant ratio to the acceleration of the fluid where the atom 

 is situated. It may be observed that the acceleration is inde- 

 pendent of the magnitude of the atom. 



22. This result furnishes a general rule for ascertaining the 

 mode arid the direction of the motive action of magnetic and 

 galvanic currents. It is required for that purpose to deduce 

 from the given circumstances under which the steady motion, 

 whether simple or composite, is produced, the values of p and V 

 expressed as functions of coordinates, and also the courses of the 

 trajectories to the surfaces of equal pressure. When by means of 

 these deductions the accelerative force of the fluid is determined 

 at each point as to magnitude and direction, in virtue of the 

 foregoing equation both the magnitude and direction of the ac- 

 celerative action on any atom are also determined. In illustra- 

 tion of this conclusion it may be added that by the above-men- 

 tioned trajectories the theory accounts for the lines of magnetic 

 force, the courses of which are exhibited by the distribution and 

 arrangement of iron filings submitted to the attraction of a mag- 

 netized bar. 



It may now be stated that the many theoretical explanations 

 of magnetic and galvanic phenomena given in the article in the 

 June Number all depend on principles the consequences of 



