and therefore on the present supposition as to the nature of Q
| q = | Q | . |
| c − σ2a |
(27)
This solution has been discussed to some extent in § 12, in connexion with the forced oscillations of a pendulum. We may note further that when σ is small the displacement q has the “equilibrium value” Q/c, the same as would be produced by a steady force equal to the instantaneous value of the actual force, the inertia of the system being inoperative. On the other hand, when σ2 is great q tends to the value −Q/σ2a, the same as if the potential energy were ignored. When there are n degrees of freedom we have from
(3)
(c1r − σ2a2r) q1 + (c22r − σ2a2r) q2 + ... + (cnr − σ2anr) qn = Qr,
(28)
and therefore
Δ(σ2) · qr = a1rQ1 + a2rQ2 + ... + anrQn,
(29)