which cannot be obtained by a finite chain of functions of only two arguments.
By employing auxiliary movable elements, nomography succeeds in constructing functions of more than two arguments, as d'Ocagne has recently proved in the case of the equation of the
th degree.[31]
[30] d'Ocagne, Traité de Nomographie, Paris, 1899.
[31] "Sur la resolution nomographiqne de l'équation du septième degré." Comptes rendus, Paris, 1900.
14. PROOF OF THE FINITENESS OF CERTAIN COMPLETE SYSTEMS OF FUNCTIONS.
In the theory of algebraic invariants, questions as to the finiteness of complete systems of forms deserve, as it seems to me, particular interest. L. Maurer[32] has lately succeeded in extending the theorems on finiteness in invariant theory proved by P. Gordan and myself, to the case where, instead of the general projective group, any subgroup is chosen as the basis for the definition of invariants.
An important step in this direction had been taken already by A. Hurwitz,[33] who, by an ingenious process, succeeded in effecting the proof, in its entire generality, of the finiteness of the system of orthogonal invariants of an arbitrary ground form.