The object of the paper was to point out that the theory of variables has a third branch, bearing to the Differential and Integral Calculus a relation somewhat analogous to that which the theory of Logarithms bears to Involution and Evolution.

In the theory of Functions there are three connected variable quantities, viz., the Primary, the Function, and the Derivative. When the relation between the primary and the function is given, the discovery of the derivative belongs to the Differential Calculus. When that between the primary and the derivative is given, the function is found by help of the Integral Calculus. And the general problem to find the primary when the relation between the function and its derivative is given, belongs to a third branch, which may be called the Calculus of Primaries.