Then

(15) P(-An^2 + Kn + 2Ta) - QTa[e^(ci) + 1] = 0,

(16) -LMn^2 - QT[e^(ci) - 1] = 0,

(17) L[e^(ci) - 1] -Pa[e^(ci) + 1] - 2Qle^(ci) = 0,

leading, on elimination of L, P, Q, to

(2 Ta + Kn - An^2) (1 - Mn^2l/T) - Mn^2

(18) cos c = ---------------------------------------,

2Ta + Kn - An^2 + Mna^2

M n^2 2Ta(a + l) + KNl - An^2l

(19) 2 sin^2 1/2c = -- ----------------------------.

T 2Ta + Kn - An^2 + Mn^2a^2

With K = 0, A = 0, this reduces to Lagrange's condition in the

vibration of a string of beads.

Encyclopaedia Britannica, 11th Edition, "Gyantse" to "Hallel" Volume 12, Slice 7 · 第 33 / 53 题