(9) _d_(_x__{_h_} + δ_x__{_h_}) = _dx__{_h_} + ∑_{_k_}
∂δ_x__{_h_}/∂_x__{_k_} + ∂δ_x__{_h_}/∂λ _d_λ
_k_ = 1, 2, 3, 4
_h_ = 1, 2, 3, 4
Now on the basis of the remarks already made, it is clear that the value
of N + δN, when the value of the parameter is λ, will be:—
(10) N + δN = ∫∫∫∫ ((ν_d_(τ + δτ))/_d_τ)_dx_ _dy_ _dz_ _dt_,
the integration extending over the whole sichel _d_(τ + δτ) where _d_(τ
+ δτ) denotes the magnitude, which is deduced from
√(-(_dx₁_ + _d_δ_x₁_)² - (_dx₂_ + _d_δ_x₂_)² - (_dx₃_ + _d_δ_x₃_)² -
(_dx₄_ + _d_δ_x₄_)²)
by means of (9) and
_dx₁_ = ω₁ _d_τ, _dx₂_ = ω₂ _d_τ,
_dx₃_ = ω₃ _d_τ, _dx₄_ = ω₄ _d_τ, _d_λ = 0
therefore:—
(11) (_d_(τ + δτ))/_d_τ = √( -∑(ω_{_h_} +
∑(∂δ_x__{_h_}/∂_x__{_k_})ω_{_k_})²)
_k_ = 1, 2, 3, 4.
_h_ = 1, 2, 3, 4.