“In the preceding memoir on this subject, the author had confined himself to the fundamental operations leading to the differential co-efficients of various functions. In the present paper, he offers an illustration of the entrance of such coefficients into the analysis of physical and geometrical problems. Having first established a general theorm, connecting finite integrals of a certain form with fractional and negative differentials, the author adapts it to represent the integrals actually occurring in several problems. By this means he wishes to shew that the theory of General Differential Coefficients will at some future period become a powerful instrument in the hands of analysts, by furnishing them with results comprehended under general forms, and thus opening another section of the science of comprehensive memory.’