"Mr Gregory devoted to it a chapter of his work, and noticed particularly some of the more remarkable applications of definite integrals to the expression of the solutions of partial differential equations. It is not improbable that in another edition he would have developed this subject at somewhat greater length. He had long been an admirer of Fourier’s great work on heat, to which this part of mathematics owes so much; and once, while turning over its pages, remarked to the writer,—“ All these things seem to me to be a kind of mathematical paradise.""