1873] 
first read through Faraday’s ‘Experimental Researches 
on Electricity.’ I was aware that there was supposed to 
be a difference between Faraday’s way of conceiving phe- 
nomena and that of the mathematicians, so that neither 
he nor they were satisfied with each other’s language. 
Thad also the conviction that this discrepancy did not 
arise from either party being wrong. I was first con- 
vinced of this by Sir William Thomson, to whose advice 
and assistance, as well as to his published papers, I owe 
most of what I have learned on the subject. 
“ As I proceeded with the study of Faraday, I perceived 
that his method of conceiving the phenomena was also a 
mathematical one, though not exhibited in the conven- 
tional form of mathematical symbols. I also found that 
these methods were capable of being expressed in the 
ordinary mathematical forms, and this compared with 
those of the professed mathematicians. 
“ For instance, Faraday, in his mind’s eye, saw lines of 
force traversing all space where the mathematicians saw 
entres of force attracting at a distance: Faraday saw a 
medium where they saw nothing but distance: Faraday 
sought the seat of the phenomena in real actions going 
on in the medium, they were satisfied that they had found 
itin a power of action at a distance impressed on the 
electric fluids.” 
It certainly appears, at least at first sight, and in com- 
parison with the excessively simple distance action, a very 
formidable problem indeed to investigate the laws of the 
propagation of electric or magnetic disturbance in a 
medium. And Maxwell did not soon, or easily, arrive at 
the solution he now gives us. It is well-nigh twenty 
years since he first gave to the Cambridge Philosophical 
Society his paper on Faraday’s Lines of Force, in which 
he used (instead of Thomson’s heat-analogy) the analogy 
of an imaginary incompressible liquid, without either 
inertia or internal friction, subject, however, to friction 
against space, and to creation and annihilation at certain 
sources and sinks. The velocity-potential in such an 
imaginary fluid is subject to exactly the same conditions 
as the temperature in a conducting solid, or the potential 
in space outside an electrified system. In fact the so- 
called equation of continuity coincides in form with what 
is usually called Laplace’s equation. In this paper 
Maxwell gave, we believe for the first time, the mathe- 
matical expression of Faraday’s Electro-tonic state, and 
greatly simplified the solution of many important elec- 
trical problems. Since that time he has been gradually 
developing a still firmer hold of the subject, and he now 
gives us, in a carefully methodised form, the results of his 
long-continued study. 
A sentence like the following has a most cheering effect 
when we meet with it in a preface ; and we need only add 
that our author has been thoroughly successful in the 
endeavour he promised :— 
“J shall avoid, as much as I can, those questions 
which, though they have elicited the skill of mathe- 
maticians, have not enlarged our knowledge of science.” 
He might with truth, and with propriety, have added 
that he would also avoid, as far as possible, those so- 
called experimental illustrations which require in the 
operator training akin to that of a juggler, and which are 
calculated to mystify, and to retard the progress of, the 
real student, while gratifying none but the mere gaping 
sight-seer. 
It is quite impossible in such a brief notice as this to 
enumerate more than a very few of the many grand and 
479 
valuable additions to our knowledge which these volumes 
contain. Their author has, as it were, flown at every- 
thing ;—and, with immense spread of wing and powet of 
beak, he has hunted down his victims in all quarters, and 
from each has extracted something new and invigorating 
—for the intellectual nourishment of us, his readers. 
The following points, however, appear to us to be 
especially (we had almost said exceptionally) worthy of 
notice :— 
1, Though not employing the Quaternion Calculus, 
Maxwell recognises its exceeding usefulness in exhibiting 
(merely by the extraordinary simplicity and comprehen- 
siveness of its notation) the mutual relations of variotis di- 
rected, or vector, quantities ; together with their derivation 
from scalar quantities, such as potentials, by the use of 
the Hamiltonian V7, the operator whose square is the 
negative of the scalar operator in Laplace’s equation. 
There can be little doubt that in this direction must lie 
the next grand simplification of the somewhat complex 
mathematics of electro-dynamic investigations. — 
2. The notion of electric Zwertia, first clearly pointed 
out by Helmholtz and Thomson, is here developed in a 
most splendid style. The mechanism whose inertia has 
to be overcome before a steady current of electricity can 
be started or stopped in a conductor, and which opposes a 
resistance exactly analogous to the inertia equivalent of 
an ordinary train of wheels, is treated by means of the 
general equations of motion in the forms given respec- 
tively by Lagrange and by Hamilton. Maxwell has 
adopted from Thomson and Tait’s “ N atural Philosophy My 
the idea of commencing with the impulse required to 
produce a given motion of a system, and has developed 
in this way the general equations in a form suitable for 
electric problems where the mechanism is as yet entirely 
unknown, 
3. The chapter dealing with Electrolysis we may 
specially refer to, as containing, not merely an admirable - 
summary of what was previously known but also, several 
new ideas apparently of great value. 
4. Another curious feature of the work is the amount 
of labour bestowed upon the exceedingly uselul, but dry 
and uninteresting, pursuit of accuracy in the tracing of 
the forms of Lines of Force anddeterminations of strensths 
of electric and electro-magnetic fields, and their deviation 
from uniformity under various conditions, some of exces- 
sive complexity. For the theory of the newer instru- 
ments, especially Thomson’s electrometers and galvano- 
meters, and also for their applicability to problems in 
quite different branches of physics, these results are very 
valuable. 
5. Another feature in which this differs from all but a 
very few of the very best scientific works is the particular 
care bestowed upon the modes of measurement, the units 
employed, and the Dimenstons (in terms of these units) of 
the various quantities treated of—such as, for instance, 
Electric Quantity, Electric Potential, Electric Current, 
Electric Displacement, &c. 
6. The subject of Evectric Jmages is developed at 
considerable length, and the reader is led up by easy steps 
to a sketch of the grand problem which, thougn solved in 
simple finite terms a quarter of a century ago by Thom- 
son, has remained unnoticed till very recently, viz., the 
statical distribution of electricity upon a spherical bowl. 
