and imagine R to be expressed by means of (2) as a quadratic function
of q`1, q`2, ... q`_m, [kappa], [kappa]', [kappa]", ... with
coefficients which are in general functions of the co-ordinates q1,
q2, ... q_m, then, performing the operation [delta] on both sides, we
find
dPR dPR dPR dP[Tau] dP[Tau]
-----[delta]q`1 + ... + ---------[delta][kappa] + ... + ----[delta]q1 + ... = -------[delta]q`1 + ... + -------[delta]q1 + ...
dPq`1 dP[kappa] dPq1 dPq`1 dPq1
dP[Tau] dP[Tau]
+ --------[delta][chi]` + ... + --------[delta]q1 + ... - [kappa][delta][chi]` - [chi]`[delta][kappa] - .... (4)
dP[chi]` dP[chi]1