76 Notices respecting New Books, 



transformation would or would not lead to a new theorem, or 

 merely, as is possible, to a repetition, with a new set of constants, 

 of theone already obtained. 



It is hardly necessary to point out how strongly the analogies 

 established in the preceding investigations point to the exist- 

 ence of some simple dynamical theory of the Cartesian ovals 

 under the attraction of forces directed to their foci. The inves- 

 tigation of such theory cannot but tend materially to the eluci- 

 dation of the essential properties of these most interesting and as 

 yet little-understood curves, the natural parents of the conic 

 sections viewed as focal curves. 



In conclusion it may be observed that, in the foregoing paper, 

 it has been seen how a single orbital force passing through a 

 fixed centre may be resolved into others of a more simple form. 

 This suggests a more general subject of investigation, where the 

 force to be so resolved, instead of passing through a fixed point, 

 is tangential, or, better, normal to a fixed curve or surface. 



Such an inquiry by no means belongs to ideal mechanics; for 

 it would correspond to the case of the motion under the earth's 

 attraction of a body near the earth's surface, considered as a 

 surface of fluid equilibrium. 



K, Woolwich Common. 



20th December 1865. 



VIIT. Notices respecting New Books. 



The Mathematical Writings of D. F. Gregory, M.A., late Fellow of 

 Trinity College, Cambridge. Edited by W. Walton, M.A. Cam- 

 bridge : Deighton, Bell, and Co. 1865. 



IT is very difficult for the outside world to do justice to the wri- 

 tings of a man removed by an early death. It is not that what he 

 has produced is intrinsically unimportant (it may or may not be so), 

 but that even when it is important it is still altogether dispropor- 

 tioned to the power to which it owes its origin, and consequently is 

 inadequate to sustain the reputation in which the writer was held by 

 the small circle of friends to whom he was intimately known. And 

 this is true in the present case, although some of the articles which 

 compose the ' Mathematical Writings ' of Mr. Gregory evince great 

 originality, and at the time of their publication powerfully contri- 

 buted to the advancement of mathematical science. Still it is very 

 desirable that the original memoirs of a man like Mr. Gregory should 

 be brought together and competently edited, both as a memorial of 

 one who ought not soon to be forgotten, and as being in themselves 

 interesting and suggestive articles, and in some cases of first-rate im- 

 portance. 



Mr. Gregory was the youngest son of Dr. James Gregory, the 

 distinguished professor of medicine in the University of Edinburgh. 

 He was born in April 1813, and died in February 1844, having not 



