Notices respecting New Boohs. 237 



the equation to the base, the ridge-lines will be determined 

 by the intersection of the surface (23) and the surface whose 

 equation is 



d$d$d$ fcP±__ 4!*1_#{#!_# 2 ) d °'4> 

 dx dy dz \ dx 2 dy 2 J dz \ dx 2 dy 2 J dx dy 



fd£ # 2 *) (d*<H__ #_^!i_*l =0 . (24) 

 { dx 2 dy 2 J \ dx dy dz dy dx dz J 



The proof need not be given as it may be very easily supplied. 

 It may be remarked that this is satisfied wherever 



dj> = a$ = J± =0 (25) 



dx dy dz 7 

 so that all conical points lie on the ridge-lines, a result which 

 is, however, obvious geometrically. If (23) is rational and 

 integral and of the degree n, (24) will be of the degree 4n — 5, 

 and therefore the ridge locus will be a curve of degree 4?i 2 — 5n. 



XX. Notices respecting New Books. 



A Treatise on the Mathematical Theory of Elasticity (in two 

 Volumes). By A. E. H. Love, M.A., Fellow and, Lecturer of 

 St. John's College, Cambridge. Cambridge : at the University 

 Press, 1893. 



SOME apology would seem becoming for a delay of six months 

 in noticing the first volume of this important contribution to 

 our higher text-books in Mathematical Physics, were it not that 

 there is always an advantage in considering at once the complete 

 work. It speaks much for Mr. Love's devotion to the task he set 

 himself, that the second volume has appeared so soon after the 

 first — when a longer delay might well have been excused, or even 

 expected. 



The author informs us in the preface to vol. i. how this treatise 

 originated in a suggestion of Mr. E. E. Webb that they should 

 jointly prepare a work on Elasticity, but Mr. Webb's important 

 avocations having prevented his cooperating, Mr. Love has had 

 to take on himself the whole of the work — and it must have proved 

 no light one. Following the excellent precedent of recent conti- 

 nental writers the author commences with an Introductory Historical 

 Sketch of pp. 34, founded, of course, on the late Dr. Todhunter's 

 History as edited and continued by Prof. K. Pearson. Herein 

 the course of the Mathematical Theories of Elasticity is briefly 

 traced from Hooke's enunciation of his famous law ' ut tensio sic 

 vis' in 1676 to those modern developments which JNavier and 

 Cauchy originated . 



A good deal of space in this, as in other recent works on special 

 branches of Mathematical Physics, is taken up — perhaps necessarily, 



