# J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’ ```                                k[del operator]<sup>2<\sup>[mu][alpha] = 4[pi][mu] d<sup>2<\sup>/dt<sup>2<\sup> [mu][alpha]
k[del operator]<sup>2<\sup>[mu][beta] = 4[pi][mu] d<sup>2<\sup>/dt<sup>2<\sup> [mu][beta]
k[del operator]<sup>2<\sup>[mu][gamma] = 4[pi][mu] d<sup>2<\sup>/dt<sup>2<\sup> [mu][gamma]

(95) If we assume that [alpha] [beta] [gamma] are functions of lx+my+nz - Vt = w
the first equation becomes

k[mu] d<sup>2<\sup>[alpha]/dw<sup>2<\sup><s>[mu][alpha]<\s> = 4[pi][mu]<sup>2<\sup>V<sup>2<\sup> d<sup>2<\sup>[alpha]/dw<sup>2<\sup> (70)
V = [plus or minus][square root] k/4[pi][mu] (71)

The other equations give the same value for <s>v<\s>V so that
the wave is propagated in either direction with a velocity <s>v<\s>V
This wave consists entirely of magnetic disturbances, the direction
of magnetization being in the plane of the wave. No magnetic
disturbance whose direction of magnetization is not in the plane
of the wave can be propagated as a plane wave at all.
Hence magnetic disturbances propagated through the electromagnetic
field agree with light in this, that the disturbance at any point
is transverse to the direction of propagation, and such waves
may have all the properties of polarized light.

96 The only medium in which experiments have been made to
determine the value of k is air, in which [mu] = 1
and therefore, by equation (46)

Y = v (72)

By the electromagnetic experiments of MM. Weber and Kohlrausch
v = 310 740 000 meters per second

is the number of electrostatic units in one electromagnetic unit of
electricity and this according to our result should be equal to the
velocity of light in air or vacuum

Velocity of light in air by M. Figeau’s+ experiments

V = 314.858 000

* Leipzig Trans V (1857) p260 or Poggendorff's Annalen Aug 1856 p10
+ Comptes Rendus vol XXIX (1849) p90

```
images

## 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