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

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                                Note on the Attraction of Gravitation 

82 After tracing to the action of the surrounding medium both the 
magnetic and the electric attractions and repulsions, and finding them 
to depend on the inverse square of the distance we are naturally led 
to enquire whether the attraction of gravitation which follows the 
same law of the distance is not also traceable to the action of a surrounding 
Gravitation differs from magnetism and electricity in this, that the 
bodies concerned are all of he same kind, instead of being opposite 
signs lie magnetic poles and electrified bodies and that the force between 
these bodies is an attraction not a repulsion as is the case between 
like electric and magnetic bodies. 

The lines of gravitating force near two dense bodies are exactly 
of the same form as the lines of magnetic force near two poles of the 
same name, but whereas the poles are repelled, the bodies are 
attracted. Let E be the intrinsic energy of the field surrounding two gravitating 
bodies M<sub>1<\sub>M<sub>2<\sub> and let E' be the intrinsic energy of the field surrounding 
two magnetic poles m<sub>1<\sub>m<sub>2<\sub> <s>proportional<\s> equal in numerical value to 
M<sub>1<\sub>M<sub>2<\sub> and let X be that gravitating force during the displacement [delta]x 
and X' the magnetic force 
X[delta]x = [delta]E x'[delta]x = [delta]E' 
Now X and  X' are equal in numerical value but of opposite signs 
so that [delta]E = - [delta]E' 
or E = C - E' 
= C - [capital sigma]1/8[pi]([alpha]<sup>2<\sup> + [beta]<sup>2<\sup> + [gamma]<sup>2<\sup>)dV 
where [alpha] [beta] [gamma] are the components of magnetic intensity. If R be the 
resultant gravitating force and R' the resultant magnetic force at a 
corresponding part of the field. R - R' and 
[alpha]<sup>2<\sup> + [beta]<sup>2<\sup> + [gamma]<sup>2<\sup> = R<sup>2<\sup> = R'<sup>2<\sup> 
Hence E = C = [capital sigma]1/8[pi] R<sup>2<\sup> dV  47 
The intrinsic energy of the field of gravitation must therefore be 
<s>diminished<\s> less wherever there is a resultant gravitating force 

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James Clerk Maxwell
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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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