k = 1, 2, 3, 4.
h = 1, 2, 3, 4.
We shall now subject the value of the differential quotient
(12) ((d(N + δN))/dλ) (λ = 0)
to a transformation. Since each δxh as a function of (x, y, z, t) vanishes for the zero-value of the parameter λ, so in general dδxk/(∂xh = 0, for λ = 0.
Let us now put (∂δxh/∂λ) = ξh (h = 1, 2, 3, 4) (13)
λ = 0
then on the basis of (10) and (11), we have the expression (12):—
= -∫∫∫∫ ∑ ωh((∂ξh/∂x₁)ω₁ + (∂ξh/∂x₂)ω₂ +(∂ξh/∂x₃)ω₃ + (∂ξh/∂x₄)ω₄)
dx dy dz dt