730 
MR. A. Me AULA Y ON THE MATHEMATICAL 
with Maxwell’s resuits. With the exception of (1) the expression for current in 
terms of displacement for a moving body, and (2) certain of his mechanical results 
which I hold to be inconsistent with certain others of his own, it will be found that 
his results flow from the equations now established. 
We put down, then, simple forms of l and x, the first involving as independent 
variables % d and H, and the second \P and K only, and compare the results with 
Maxwell’s. Besides Maxwell’s results we shall find that this form of l is sufficient 
to take account of the interdependence of magnetisation and strain, and of specific 
inductive capacity and strain. After that we add certain terms to, and otherwise 
generalise l and x , still, however, regarding them as involving no independent vari¬ 
ables except such as occur in the lists (25), (26), of § 27. Thermoelectric, thermo- 
magnetic, and the Hall phenomena are thereby accounted for and discussed in 
detail. Finally, to account for electrostatic contact-force (and incidentally capillary 
phenomena), we shall assume l to contain certain independent variables not in the 
list (25) of § 27, and shall adopt a certain form for l s . 
59. For Maxwell’s results it is only necessary to assume 
l = 2ttS dK ” 1 d - SH/xH/Stt - SI 0 H.(1), 
x = - SKRK/2 ..(2), 
where I 0 is a flux, /x and K # are self-conjugate functions of Class I. of § 9, and It is 
one of Class II, all four being functions of strain and temperature. From these 
statements, and § 9, it follows that 
* I did not notice when first [former paper, p. 119] using K in this signification that it already had a 
special quaternion meaning (conjugate of a quaternion). As this meaning is never required in the 
present paper, and very rarely in physical applications, I have nevertheless retained the present meaning 
for K. 
I take this opportunity of apologising for the apparent want of system in my notation. It has been 
brought about by an attempt to compromise between accepted notation and a system of notation more 
suitable for quaternion methods. May I suggest the following system F First, let the Greek alphabet 
be left as a happy hunting ground for symbols of every denomination (vectors, scalars, linear vector 
functions, &c.) ; secondly, let the ordinary alphabets, A, B . . a, b . . be used for scalars and linear 
vector functions of a vector (which so often in important cases reduce to scalars) only; thirdly, let bold 
type be used for vectors only and write i, j, k instead of i, j, 1c ; fourthly, let Hamilton’s K, S, T, U, Y 
be transferred to the German alphabet; fifthly, let the rest of the two German alphabets be retained for 
mathematicians who are hard pressed for suitable symbols ; sixthly, let the symbols of differentiation be 
quite independent of the above restrictions. The following somewhat chaotic but classified list of some 
of the chief symbols used in the present paper may serve to convince the sceptic that some such system 
is necessary. (1.) Linear vector functions of a vector (20), A B, C K, R, a, b, c, r, Y, 4>, F, 0, y, p, w, v , 
0) X. 0- ( 2 9 Vectors (31), i, j, Tc, A, B, C, D, E, F, H, I. K, L, N, P, a, b, c, d, e, h, 0, d2, a, e, y, Ui', p, 
a, t, ilk (3.) Scalars (32), D, E, F, H, P, Q, W, X, Y, Z /, g, In, l, m, n, q, s, t, u, v, x, y, z, 0, \, 
T>, S, 93, t. (4.) Symbols of differentiation and variation, G, d, d, A, V. £, (5.) Symbols of peculiar 
quaternion meaning , S, T, U, Y. 
