3 A 14 NOTES. 245

that, if p is the density, and X the force acting on the element
in the direction of x, we have

When w, v, w are very small, we may neglect the terms «*-«— etc.,
and add the term **-?—-, which is likewise of the second order of

magnitude, because in the case of slow motions, the change of the
density per ainit of time is very small. It follows that

th.e mathematical expression for the statement made in the text.

13 (Page 35). The value cp of the scalar potential that exists
at the time t at the point (#, y, z] of the ether, will be found at
the time t -f- dt at a point whose coordinates are x -f- wdt} y, z. As
the value of the potential for these new values of the independent
variables may be represented by

we have

.
at

n

Applying the same reasoning to the function J?-, one finds

14; (Page 36). Let Sf be a system without translation, and let
two points, the one in the moving system S, with the coordinates
SGy y, z, and the other in 'S' with the coordinates u?', y, 2 — the re-
lation between x and xf being as shown in (58) — be said to cor-
respond to each other. Then corresponding elements of volume,
and dS', are to each other in the same ratio as x and x', so that

dS' - (1 - ft

and. if they are to have eq^al charges, the density $' in dSf must be
related to the density p in dS as follows:- [fc - A]}dS - ij([d • h] + [d • b]}dS