738 
MR. A. Me AULA Y ON THE MATHEMATICAL 
“ If we now write E 0 ' the electromotive force instead of — V'z, we find 
W = _i|f|sd'E 0 W. 
“ Hence, the electrostatic energy of the whole field will be the same if we suppose 
that it resides in every part of the field where electrical force and electrical displace¬ 
ment occur, instead of being confined to the places where free electricity is found.’' 
Were it not for this last statement, the interpretation I should put on the whole of 
the above passage would be expressed thus :—In the particular case of electrostatics 
E 0 ' = — V'z and W = —- JjjSd'EQ'cfc'. In the general case, where the electricity 
is not stationary, E 0 ' cannot be put in the form — Y'z ; but we shall nevertheless 
assume that the equation 2W = — |||Sd / E u , c?s / is still true. This seems to me the 
interpretation that presents least difficulty, but it seems hard to reconcile it with the 
last sentence quoted, which implies that the equation 2W = JJJSd' V'zcW is exactly 
the same as the equation 2W = —|||Sd'E (J V?s'. There seems only one other possible 
interpretation of the passage, but that lands us in hopeless difficulties. This expla¬ 
nation is that the E 0 ' which occurs in § 598, where it cannot be put in the form — Y’z, 
has a different meaning from the E 0 ' which occurs in §§ 630, 631, where it is = — Y'z. 
If he has changed the meaning of E 0 ', we may presume that matters have not been 
further complicated by a change in the meaning of 2 . In this case §§ 630, 631 may 
be put thus :— 
(1) It is assumed that the energy of the field can be divided into two parts, 
electrostatic and electromagnetic. 
(2) The former of these, in the absence of electric currents, can be put in the 
form \ JJJSd'VW where e is a scalar. It is assumed that this statement 
is also true when there are electric currents present. 
(3) It is assumed that the z appearing in this expression is the same as the z 
which occurs in the general equation E 0 ' = Yp B' — a A '/dt — Y'z ; and it 
is convenient to give it the name electric potential. 
It will he acknowledged that these assumptions are more unwarrantable than the 
one required for the first interpretation, and therefore I shall understand the passage 
to be thus, as at first, correctly interpreted. But if this be so, we are as far off as 
ever from the conclusion that z has a definite value which can appropriately be called 
the electric potential. 
66. This is no mere question of terms, for [equation (12), above] Maxwell asserts 
that in the expression for the force due to the field occurs a term — D'Yz, and here 
the indefiniteness is not counterbalanced by the corresponding indefiniteness of dA'fdt. 
There are more ways than one of compromising to get out of the difficulty.* The 
* For instance, we may (arbitrarily) render A' definite by tbe equations SV'A' = 0 [Sd2'A'] a+ i = 0, 
and tbus render Vz definite; and we may then assert that equation (12) is correct. 
