THIS is a book thoroughly worthy of the great name of its author. It is difficult to know which to admire most, the grasp of the subject, the extreme simplicity of its exposition, or the neatness of its notation. It will, we think, at once take its proper place as the leading text-book on the subject. Elementary Treatise on Elliptic Functions. By Arthur Cayley. (Cambridge: Deighton, Bell, and Co.).