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1. In some recent papers I have developed the theory of what I have called harmonic integrals associated with an algebraic variety. My object has been to provide an apparatus with which to investigate the properties of the classical integrals
of total differentials which are finite everywhere on an algebraic variety Vm of m dimensions
These integrals are referred to in what follows as “Abelian integrals”, as it is desirable to have a single name to denote all integrals of this type. The usual qualification “of the first kind” is omitted, and is always to be understood. In the present paper it is shown how the theory of harmonic integrals can be applied to deduce certain results concerning Abelian integrals, and a number of interesting problems are suggested by these results.
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