The first sum vanishes in consequence of the continuity equation (_b_). The second may be written as (∂ω_{_h_}/∂_x₁_)(_dx₁_/_d_τ) + (∂ω_{_h_}/∂_x₂_)(_dx₂_/_d_τ) + (∂ω_{_h_}/∂_x₃_)(_dx₃_/_d_τ) + (∂ω_{_h_}/∂_x₄_)(_dx₄_/_d_τ) = _d_ω_{_h_}/_d_τ = (_d_/_d_τ)(_dx__{_h_}/_d_τ) whereby (_d_/_d_τ) is meant the differential quotient in the direction of the space-time line at any position. For the differential quotient (12), we obtain the final expression (14) ∫∫∫∫ ν((∂ω₁/∂τ)ξ₁ + (∂ω₂/∂τ)ξ₂ + (∂ω₃/∂τ)ξ₃ + (∂ω₄/∂τ)ξ₄) _dx dy dz dt_. For a virtual displacement in the _sichel_ we have postulated the condition that the points supposed to be substantial shall advance normally to the curves giving their actual motion, which is λ = 0; this condition denotes that the ξ_{_h_} is to satisfy the condition _w₁_ξ₁ + _w₂_ξ₂ + _w₃_ξ₃ + _w₄_ξ₄ = 0. (15) Let us now turn our attention to the Maxwellian tensions in the electrodynamics of stationary bodies, and let us consider the results in § 12 and 13; then we find that Hamilton’s Principle can be reconciled to the relativity postulate for continuously extended elastic media. At every space-time point (as in § 13), let a space time matrix of the 2nd kind be known (16) S = | S₁₁ S₁₂ S₁₃ S₁₄ | = | X_{_x_} Y_{_x_} Z_{_x_} -_i_T_{_x_} | | S₂₁ S₂₂ S₂₃ S₂₄ | = | X_{_y_} Y_{_y_} Z_{_y_} -_i_T_{_y_} | | S₃₁ S₃₂ S₃₃ S₃₄ | = | X_{_z_} Y_{_z_} Z_{_z_} -_i_T_{_z_} | | S₄₁ S₄₂ S₄₃ S₄₄ | = | -_i_X_{_t_} -_i_Y_{_t_} -_i_Z_{_t_} T_{_t_} | where X_{_n_} Y_{_x_} .....X_{_z_}, T_{_t_} are real magnitudes. For a virtual displacement in a space-time sichel (with the previously applied designation) the value of the integral (17) W + δW = ∫∫∫∫ (∑S_{_h k_} (∂(_x__{_k_} + δ_x__{_k_}))/∂_x__{_h_} _dx dy dz dt_ extended over the whole range of the _sichel_, may be called the tensional work of the virtual displacement. The sum which comes forth here, written in real magnitudes, is X_{_x_} + Y_{_y_} + Z_{_z_} + T_{_t_} + X_{_x_} (∂δ_x_)/∂_x_ + X_{_y_} (∂δ_x_)/∂_y_ + ... Z_{_z_} (∂δ_z_)/∂_z_ - X_{_t_} (∂δ_x_/∂_t_ - ... + T_{_x_} (∂δ_t_)/∂_x_ + ... T_{_t_} (∂δ_t_)/∂_t_ we can now postulate the following _minimum principle in mechanics_. _If any space-time Sichel be bounded, then for each virtual displacement in the Sichel, the sum of the mass-works, and tension works shall always be an extremum for that process of the space-time line in the Sichel which actually occurs._ The meaning is, that for each virtual displacement, ([_d_(·δN + δW)]/_d_λ)_{λ = 0} = 0 (18) By applying the methods of the Calculus of Variations, the following four differential equations at once follow from this minimal principle by means of the transformation (14), and the condition (15). (19) ν ∂_w__{_h_}/∂τ = K_{_h_} + χ_w__{_h_} (_h_ = 1, 2, 3, 4)