If, as in § 1 (30), we write this in the form
Τ = ⅋ + K,
(11)
then (3) may be written
R = ⅋ − K + β1q˙1 + β2q˙2 + ...,
(12)
where β1, β2, ... are linear functions of κ, κ′, κ″, ..., say
βr = αrκ + α′rκ′ + α″rκ″ + ...,
(13)
the coefficients αr, α′r, α″r, ... being in general functions of the co-ordinates q1, q2, ... qm. Evidently βr denotes that part of the momentum-component ∂R / ∂q˙r which is due to the cyclic motions. Now