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Pornt-INVARIANTS FOR THE LIE GROUPS OF THE PLANE. 
By Davip A. RotHRocK. 
Among the many interesting and important applications of Lie’s Theory of 
Transformation Groups none deserves more prominent mention than the applica- 
tion to invariant theory. Whether the invariants dealt with be functions or 
equations, surfaces and curves or points, equally interesting results are obtained. 
The present paper has to do with the determination of the point-invariants for 
the finite continuous groups of the plane as classified by Lie in Vol. XVI. of 
the Mathematische Annalen. In the first part of the paper is sketched a brief 
outline of the Lie theory leading up to the point-invariant, then follow the 
calculations of the invariant functions. 
An infinitesimal point-transformation gives to x and y the increments 
Oxo & (x, y) ot, dy ai (x, y) ot, 
