708 
MR,. A. McAULAY ON THE MATHEMATICAL 
and a similar equation would hold with regard to x s + which, however, requires 
definite information as to the velocities involved in x s . £ is supposed (Rodth, ibid .) 
expressed as a function, not of the variables (17), but of 
6, ©Va: ; dq idx ; K Va:, H Vx.(19). 
It is best at first to regard x as a function, not of K, but of C and c [§ 24, eq. (10)]. 
When later we make the assumption that, so far as it depends on these last two, it is 
a function of their difference (K) only, it will only have to be noticed that 
c V.r = K Vx = — c Vx .. . . (20). 
Note that this gives 
SK K Vtc = SC c Vaj + Sc c Vx.(21), 
which shows [eq. (18)] that the statement that £ is the reciprocal of x with regard to 
© and the velocities is still true. 
Similarly, if it were assumed, as on a future occasion it will be assumed, that Xs 
was a function of 
0; [p']a-b, % u dq; TSUrK.(22), 
it would be best first to regard it as a function of 
0 ; p a \ pb, dq, dq ; C a , C i} c a , c b .(23), 
and later make the necessary restrictions. 
36. We shall now suppose that the symbols Q, F, F*, <f>, E, E,., e, e,. stand for 
those parts only of the external forces of the various types, which are owing to 
friction and the like. To determine their values we shall use the principle* 
present paper and F and q in the former paper [paragraph, following eq. 40)] when nsed as affixes. 
There are objections from the printer’s and proof-reader’s point of view when the affix is anything other 
than a mere letter. For instance, *CI in the present case, and, still more, g V in eq. (2), § 44, below, are 
objectionable on these grounds. Is it not, then, desirable to have, at any rate, an alternative notation ? 
As an alternative to ^.V, let me here suggest any one of the following: V|<r| |V<r| [Vcr] V|er V;<r 
V a Vo-1 V<r;. Of these I should personally be inclined to favour [Vo-] or Vc ; , the latter rather than 
the former. For instance, in this notation, eq. (18) would become 
SB + f = - Seve; x - SKVK; * - SHVH ; x - S*£ a *; 
which, I think, shows that the notation is sufficiently striking, while it has the advantage of great- 
simplicity. 
* I have not been able to reduce this to simpler form or to substitute a simpler principle leading to 
the same results. I merely wished to make all the phenomena of the kind now being considered depend 
cn some single scalar function X, much as the reversible phenomena depend on the single scalar 
