248 Effects of Motion of Electrified Bodies. 



with similar expressions for the components of the force 

 parallel to the axes of y and z. 



From this we see that if q x be the acceleration of the second 

 sphere, the forces on the first sphere are an attraction 



v^p2^</cos e along the line joining the centres of the spheres, 



a force ^jj- q\ in the direction opposite to the acceleration of 



the second sphere, and a force ^- q 1 -j ( ^ J in the direction 



opposite to the direction of motion of the second sphere. 

 There are, of course, corresponding forces on the second 

 sphere ; and we see that, unless both spheres move with equal 

 uniform velocities in the same direction, the forces on the two 

 spheres are not equal and opposite. If we suppose that the 

 two spheres are moving with uniform velocities q in the same 



direction, the repulsion between them is -fF^pJl— y J; 



or if c be the velocity of light in the medium through which 



ee' ( q 2 \ 

 they are moving, the repulsion = ^r^M — to]. Hence, if 



the repulsion between two electrified particles is to be changed 

 into an attraction by means of their motion, their velocities 

 must exceed *j3c; hence we should expect the molecular 

 streams in a vacuum-tube to repel each other, as we could not 

 suppose that the velocity of the particles forming these streams 

 is as great as that of light ; and Mr. Crookes has, in fact (see 

 Phil. Trans. 1879, part ii.), experimentally determined that 

 they do repel each other. 



It is remarkable that the law of force between two moving 

 charged particles, which we have deduced from Maxwell's 

 theory, agrees with that assumed by Clausius, in his recent 

 researches on Electrodynamics (see Phil. Mag. Oct. 1880); 

 but it differs from Weber's well-known law materially. Ac- 

 cording to Weber's law, the force does not depend on the 

 actual velocities of the particles, but only on their velocity 

 relative to each other, whereas, according to the laws we have 

 investigated, the forces depend on the actual velocities of the 

 particles as well as on their relative velocities : thus there is 

 a force between two charged particles moving with equal 

 velocities in the same direction, in which case, of course, the 

 relative velocity is nothing. It must be remarked that what 

 we have for convenience called the actual velocity of the par- 

 ticle is, in fact, the velocity of the particle relative to the 

 medium through which it is moving : thus, in equation (6), 

 g, q r are the velocities of the first and second partieles respec- 

 tively relative to the medium whose magnetic permeability is jjl. 



