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 ξh is to satisfy the condition
w₁ξ₁ + w₂ξ₂ + w₃ξ₃ + w₄ξ₄ = 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 | = | Xx Yx Zx -iTx |
| S₂₁ S₂₂ S₂₃ S₂₄ | = | Xy Yy Zy -iTy |
| S₃₁ S₃₂ S₃₃ S₃₄ | = | Xz Yz Zz -iTz |
| S₄₁ S₄₂ S₄₃ S₄₄ | = | -iXt -iYt -iZt Tt |