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

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                                Part VI. Electromagnetic Theory of Light 

(91) At the commencement of this paper we made use of the optical 
hypothesis of an elastic Medium through which the vibrations 
of light are propagated in order to show that we have warrantable 
grounds for seeking, in the same medium, the cause of other phenomena 
as well as those of light. We then examined electromagnetic 
phenomena seeking for their explanation in the properties of the 
field which surrounds the electrified or magnetic bodies. In this 
way we arrived at certain equations expressing certain properties 
of the electromagnetic field. We now proceed to investigate whether 
these properties of that which constitutes the electromagnetic field, 
deduced from electromagnetic phenomena alone, are sufficient 
to explain the propagation of light through the same substance. 

scored out by mistake (92) Let us suppose that a plane wave whose direction cosines are 
l m n is propagated through the field with a velocity V 
Then all the electromagnetic functions will be functions of 
w = lx + my + nz - Vt 
The equations of Magnetic Force will become 
[mu][alpha] = m dH/dw - n dG/dw 
[mu][beta] = n dF/dw - l dH/dw 
[mu][gamma] = l dG/dw - m dF/dw 
If we multiply these equations respectively by l, m, n and add, 
we find l[mu][alpha] m[mu][beta] + n[mu][gamma] = 0 (62) 
which shows that the direction of the magnetization must be in 
the plane of the wave. 

                            
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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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