in the Motion of the Magnetic Field. 321 



course, a periodic motion round the axis of the vector J. 

 Arising inside matter, it must produce there a kind of 

 pressure, counterbalanced by the elastic forces of matter, 

 and must therefore be accompanied by certain deformations. 

 We suppose that this pressure is kinetic in character, i e., it 

 passes on by collisions from particle to particle. 



Now it is easy to prove that such a kinetic pressure must 

 be proportional to the square of the velocity J, and that at 

 the moment of the change of this pressure forces of reaction 

 appear which act backward on the vector J. 



Actually, the hypothesis of the existence of kinetic pressure 

 produced by the magnetic motion of matter is dynamically equi- 

 valent to supposing that a connexion exists between this motion 

 of matter and the motion arising at its deformations. There- 

 fore, if we denote the coordinates fixing magnetic deformations 

 by the letters/) jPq, • • >■, then the above hypothesis will mean 



that terms exist in the formula of Lagrange's function of the 

 following kind : — 



where p a , p^, . . . are coefficients defining the connexion be^ 



tween the two motions. 



Therefore, in Lagrange's equation for the vector J, besides 

 the forces contained already in formula (12), new forces 

 appear and the equation is : — 



j t (XI + .J) + J t < Pa P a +P&0 + '...)- ^ [P. P a J 



+/yyJ+ ...]=0, . (18) 



if we denote by © the coordinate the velocity of which is 

 J, L e. : 



'-? ™ 



Besides this we shall get the following equations relating to 

 coordinates p a , p„, ■ . . : — 



J 



(20) 



Phil. Mag. S. 5. Vol. 42. No. 257. Oct. 1896. 2 A 



