J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’

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                                If there are many bodies connected with A and B in a 
similar way but with different values of p and q we may 
treat the question in the same way by assuming 
[equations]
where the summation is extended to all the bodies with their 
proper values of C, p, and q. Then the momentum of 
the system referred to A <s>and B<\s> is 
Lu + Mv 
and referred to B MU + Nv 
and we shall have 
[equations] (2) 
where X and Y are the external forces acting on A & B. 
(25) To make the illustration more complete we have only to suppose 
that the motion of A is resisted by a force proportional to its 
velocity which we may call Ru and that of B by a similar 
force which we may call Sv, R and S being coefficients of 
resistance Then if [xi] and [eta] are the forces on A and B 
[equations] (3) 
If <s>u<\s> the velocity of A be increased at the rate du/dt then in order to prevent 
B from moving a force [eta]=d/dt(Mu) must be applied to it 
This effect on B due to an increase of the velocity of A corresponds 
to the electromotive force on one circuit arising from an increase 
in the strength of a neighbouring circuit. 

This dynamical illustration is to be considered merely as assisting the 
reader to understand what is meant in mechanics by Reduced Momentum. 
The facts of the induction of currents as depending on the variations 
of the quantity called Electromagnetic Momentum or Electrotonic State rest on the 
experiments of Faraday*, <s>and<\s> Felici+ 
* Exp Res. Series I, IX 
+ Annales de Chimie XXXIV (18 ) p64  
                            
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Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
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Cite as

J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7

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