Dynamical Theory of the Electromagnetic Field. 155 



force ; and if the lines in any one part of their course are so distri- 

 buted that the number of lines enclosed by any closed curve is pro- 

 portional to the " electric momentum " of the field referred to that 

 curve, then the electromagnetic phenomena may be thus stated : — 



The electric momentum of any closed curve whatever is measured 

 by the number of lines of force which pass through it. 



If this number is altered, either by motion of the curve, or motion 

 of the inducing current, or variation in its strength, an electromotive 

 force acts round the curve and is measured by the decrease of the 

 number of lines passing through it in unit of time. 



If the curve itself carries a current, then mechanical forces act on it 

 tending to increase the number of lines passing through it, and the 

 work done by these forces is measured by the increase of the num- 

 ber of lines multiplied by the strength of the current. 



A method is then given by which the coefficient of self-induction 

 of any circuit can be determined by means of Wheatstone's electric 

 balance. 



The next part of the paper is devoted to the mathematical expres- 

 sion of the electromagnetic quantities referred to each point in the 

 field, and to the establishment of the general equations of the electro- 

 magnetic field, which express the relations among these quantities. 



The quantities which enter into these equations are : — Electric 

 currents by conduction, electric displacements, and Total Currents ; 

 Magnetic forces, Electromotive forces, and Electromagnetic Momenta. 

 Each of these quantities being a directed quantity, has three com- 

 ponents ; and besides these we have two others, the Free Electricity 

 and the Electric Potential, making twenty quantities in all. 



There are twenty equations between these quantities, namely 

 Equations of Total Currents, of Magnetic Force, of Electric Cur- 

 rents, of Electromotive Force, of Electric Elasticity, and of Electric 

 Resistance, making six sets of three equations, together with one 

 equation of Free Electricity, and another of Electric Continuity. 



These equations are founded on the facts of the induction of cur- 

 rents as investigated by Faraday, Felici, &c, on the action of cur- 

 rents on a magnet as discovered by Oersted, and on the polarization 

 of dielectrics by electromotive force as discovered by Faraday and 

 mathematically developed by Mossotti. 



An expression is then found for the intrinsic energy of any part 

 of the field, depending partly on its magnetic, and partly on its 

 electric polarization. 



From this the laws of the forces acting between magnetic poles 

 and between electrified bodies are deduced, and it is shown that the 

 state of constraint due to the polarization of the field is x such as to 

 act on the bodies according to the well-known experimental laws. 



It is also shown in a note that, if we look for the explanation of the 

 force of gravitation in the action of a surrounding medium, the con- 

 stitution of the medium must be such that, when far from the pre- 

 sence of gross matter, it has immense intrinsic energy, part of which 

 is removed from it wherever we find the signs of gravitating force. 

 This result does not encourage us to look in this direction for the ex- 

 planation of the force of gravity. 



