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

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                                Measurement of Electrical Phenomena by Electrostatic Effects 

(80) The quantities with which we have had to do have been 
hitherto expressed in terms of the Electromagnetic System 
of measurement, which is founded on the mechanical action 
between currents. The electrostatic system of measurement 
is founded on the mechanical action between electrified bodies 
and is independent of, and incompatible with the electromagnetic 
system, so that the units of the different kinds of quantity 
have different values according to the system we adopt, and 
to pass from one system to the other, a reduction of 
all the quantities is required. 

According to the electrostatic system, the repulsion 
between two small bodies charged with quantities y<sub>1<\sub>y<sub>2<\sub> of 
electricity is  y<sub>1y<sub>2<\sub>/r<sup>2<\sup> 
where r is the distance between them 
Let the relation of the two systems be such that one 
electromagnetic unit of electricity contains v electrostatic 
units then e<sub>1<\sub> = vy<sub>1<\sub> and e<sub>2<\sub> = vy<sub>2<\sub> 
and k/4[pi] e<sub>1<\sub>e<sub2<\sub>/r<sup>2<\sup> = v<sup>2<\sup> e<sub>1<\sub>e<sub2<\sub>/r<sup>2<\sup> (45) 
whence k the coefficient of "electric elasticity" in the medium 
in which the experiments are made i.e. common air, is 
related to v the number of electrostatic units in one 
electromagnetic unit, by the equation 
k = 4[pi]v<sup>2<\sup> (46) 
The quantity v may be determined by experiment in several ways 
According to the experiments of M.M. Kohlrausch 2 and Weber 1 
v = 310.740.000 meters per second 

                            
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Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
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J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7

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