It will be observed that in the first process the value of the **modulus** is in fact calculated from the formula.

Hesse's canonical form shows at once that there cannot be more than two independent invariants; for if there were three we could, by elimination of the **modulus** of transformation, obtain two functions of the coefficients equal to functions of m, and thus, by elimination of m, obtain a relation between the coefficients, showing them not to be independent, which is contrary to the hypothesis.

Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of **modulus** sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.

The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being R = P/M = (B 2 -H2)/87-M, where M is Young's **modulus**.

In nickel the maximum change of the elastic constants is remarkably large, .amounting to about 15% for Young's **modulus** and 7% for rigidity; with increasing fields the elastic constants first decrease and then increase.