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is unaltered by any infinitesimal transformation of a certain group of the tenth order, and that all stuch transformations which leave the equation unaltered are contained in the above group. It is at once evident that any equation which by a point transformation can be reduced to the above formi will also be unaltered by the transformatiolns of a group of the tenth order of like composition with the above. In the present paper a more general proposition is considered, viz., the form to which linear partial differential equations, of the second order in three independent variables, can be reduced which have the property of beinlg unaltered for some infinitesimal transformations. Such equations form a class by themselves, the potential equation above and equations redulcible to it by point transformation being only particular types of this class; it is here shown that the infinitesimal transformations which leave unaltered the equations of this class form in all cases a finite group of the eleventh order at highest; and certain types are tabulated to which all equations of the class may be reduced.

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