(2)

∂x = ∂xδq1 + ∂xδq2 + ..., &c., &c.,
∂q1 ∂q2

(3)

so that the expression § 1 (8) for the kinetic energy is to be replaced by

2Τ = α0 + 2α1q˙1 + 2α2q˙2 + ... + A11q˙1² + A22q˙2² + ... + A12q˙1q˙2 + ...,

(4)

where

α0 = Σm { ( ∂x) ²+ ( ∂y) ²+ ( ∂z) ²},
∂t ∂t ∂t

(5)

αr = Σm { ∂x ∂x+ ∂y ∂y+ ∂z ∂z},
∂t ∂qr∂t ∂qr∂t ∂qr