- ∂F₂₄/∂xh f₂₄ - ∂F₃₄/∂xh f₃₄),
(h = 1, 2, 3, 4)
By using the fundamental relations A) and B), 90) is transformed into the fundamental relation
(91) lor S = -sF + N.
In the limitting case ε = 1, μ = 1, f = F, N vanishes identically.
Now upon the basis of the equations (55) and (56), and referring back to the expression (82) for L, and from 57) we obtain the following expressions as components of N,—
(92) Nh = - ½ Φ[=Φ]∂ε/∂xh - ½ ψ[=ψ]∂μ/∂xh
+ (εμ - 1)(Ω₁ ∂ω₁/∂xh + Ω₂ ∂ω₂/∂xh + Ω₃ ∂ω₃/∂xh + Ω₄ ∂ω₄/∂xh)
for h = 1, 2, 3, 4.
Now if we make use of (59), and denote the space-vector which has Ω₁, Ω₂, Ω₃ as the x, y, z components by the symbol W, then the third component of 92) can be expressed in the form