Page:The principle of relativity (1920).djvu/96

 Then the fundamental Equations can be written as

[part][function]_{1 2}/[part]x_{2} + [part][function]_{1 3}/[part]x_{3} + [part][function]_{1 4}/[part]x_{4} = s_{1} }

(A) [part][function]_{2 1}/[part]x_{1} +    + [part][function]_{2 3}/[part]x_{3} + [part][function]_{2 4}/[part]x_{4} = s_{2} }

[part][function]_{3 1}/[part]x_{1} + [part][function]_{3 2}/[part]x_{2} +  + [part][function]_{3 4}/[part]x_{4} = s_{3} }

[part][function]_{4 1}/[part]x_{1} + [part][function]_{4 2}/[part]x_{2} + [part][function]_{4 3}/[part]x_{4}    = s_{4} }

and the equations (3) and (4), are

[part]F_{3 4}/[part]x_{2} + [part]F_{4 2}/[part]x_{3} + [part]F_{2 3}/[part]x_{4} = 0 }

[part]F_{4 3}/[part]x_{1} +    + [part]F_{1 4}/[part]x_{3} + [part]F_{3 1}/[part]x_{4} = 0 }

[part]F_{2 4}/[part]x_{1} + [part]F_{4 1}/[part]x_{2} +  + [part]F_{1 2}/[part]x_{4} = 0 }

[part]F_{3 2}/[part]x_{1} + [part]F_{1 3}/[part]x_{2} + [part]F_{2 1}/[part]x_{3}    = 0 }

§ 8..

We are now in a position to establish in a unique way the fundamental equations for bodies moving in any manner by means of these three axioms exclusively.

The first Axion shall be,—

When a detached region of matter is at rest at any moment, therefore the vector u is zero, for a system