FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
427 
into prominence in 1884, by making use of it to determine the electromagnetic flux of 
energy. Professor Lodge* gave very distinct and emphatic expression of the principle 
generally, apart from its electromagnetic aspect, in 1885, and pointed out how much 
more simple and satisfactory it makes the principle of the conservation of energy 
become. So it would, indeed, could we only understand gravitational energy ; but in 
that, and similar respects, it is a matter of faith only. But Professor Lodge attached, 
I think, too much importance to the identity of energy, as well as to another principle 
he enunciated, that energy cannot be transferred without being transformed, and 
conversely; the transformation being from potential to kinetic energy or conversely. 
This obviously cannot apply to the convection of energy, which is a true flux of 
energy; nor does it seem to apply to cases of wave motion in which the energy, 
potential and kinetic, of the disturbance, is transferred through a medium unchanged 
in relative distribution, simply because the disturbance itself travels without change 
of type; though it may be that in the unexpressed internal actions associated with 
the wave propagation there might be found a better application. 
It is impossible that the ether can be fully represented, even merely in its trans¬ 
missive functions, by the electromagnetic equations. Gravity is left out in the cold ; 
and although it is convenient to ignore this fact, it may be sometimes usefully 
remembered, even in special electromagnetic work ; for, if a medium have to contain 
and transmit gravitational energy as well as electromagnetic, the proper system of 
equations should show this, and, therefore, include the electromagnetic. It seems, 
therefore, not unlikely that in discussing purely electromagnetic speculations, one 
may be within a stone’s throw of the explanation of gravitation all the time. The 
consummation would be a really substantial advance in scientific knowledge. 
On the Algebra and Analysis of Vectors without Quaternions. Outline of Author s 
System. 
§ 6. The proper language of vectors is the algebra of vectors. It is, therefore, 
quite certain that an extensive use of vector-analysis in mathematical physics 
generally, and in electromagnetism, which is swarming with vectors, in particular, is 
coming and may be near at hand. It has, in my opinion, been retarded by the want of 
special treatises on vector analysis adapted for use in mathematical physics, Professor 
Tait’s well-known profound treatise being, as its name indicates, a treatise on 
Quaternions. I have not found the Hamilton-Tait notation of vector operations 
convenient, and have employed, for some years past, a simpler system. It is not, 
however, entirely a question of notation that is concerned. I reject the quaternionic 
basis of vector-analysis. The anti-quaternionic argument has been recently ably 
stated by Professor Willard Gibbs.! He distinctly separates this from the question 
* Lodge, ‘ Phil. Mag.,’ June, 1885, “ On the Identity of Energy.” 
t Professor Gibbs’s letters will he found in ‘Nature,’ vol. 43, p. 511, and vol. 44, p. 79; and Professor 
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