152 Notices respecting New Books. 



notice for which we should look iu vain in the earlier treatise. In 

 the advanced parts the additions are still more numerous, as in 

 the chapter on tortuous curves, where the subject of their curva- 

 ture, their normal and osculatiug planes, and the connected lines 

 and developable surfaces are admirably worked out. Here the 

 subjects discussed are perhaps twice as numerous as those in the 

 corresponding chapter of the earlier work. A similar remark 

 applies to the discussion of surfaces of the second degree, which, 

 of course, occupies a large part of the volume. Thus the reduc- 

 tion of the general equation of the second degree is not only 

 effected by modern methods, but the discussion is very complete, 

 while the chapters on confocal surfaces and on the modular and 

 umbilical generation of " Conicoids " contain parts of the subject 

 which have been worked out only of late years. 



It will be observed that Mr. Frost uses — or, as he puts it, 

 persists in using — the word conicoid for the locus of the equation 

 of the second degree. "We will state his reasons for doing so. 

 After objecting to the word quadric for what seems a cogent 

 reason, he proceeds thus : — 



" The useful word ' conic ' being well established, the term 

 ' conicoid ' seems to suggest all that can be required, when it is em- 

 ployed to designate the locus of the equation of the second degree 

 in three dimensions, at least so long as the analogous words sphe- 

 roid, ellipsoid, and hyperboloid are in use; at all events it is not open 

 to the great objection of being equally applicable to plane curves, 

 as is the term quadric, cubics and quartics being actually so em- 

 ployed in Salmon's ' Higher Plane Curves' (p. viii)." 



The work is designed for the use of students of a high class, 

 who wish to obtain a thorough acquaintance with the subject; and 

 consequently it presupposes on their part a knowledge of the 

 ordinary processes of analysis. Those who come to the study of 

 it thus prepared will find few difficulties but such as are inherent 

 in a somewhat abstruse subject. The author seems to have done 

 all that could be desired in the way of removing the difficulties that 

 yield to clear and brief exposition. To each chapter is added a col- 

 lection of examples and exercises — between four and five hundred 

 in all. Examples are very useful in such a work as the present ; 

 but to frame them successfully requires the exercise of mathema- 

 tical knowledge and ingenuity of a high order. In the first edition 

 these exercises were mainly due to Professor "VVolstenholme, whose 

 skill in that department of mathematics is well known. In the 

 present edition the collection has been enlarged by contributions 

 supplied by many Cambridge mathematicians, as "well, we presume, 

 as by the author himself. 



