1 38 Notices respecting New Boohs. 



paid attention to the method have derived their first knowledge of 

 its principles. It is one of the losses which University College, 

 London, has most to lament in Clifford's death, that with him 

 has apparently died the effort to establish the elements of Qua- 

 ternions in its Mathematical programme. Strangely enough, in 

 France, too, the most flourishing School of Quaternions is not to be 

 found in Paris, but in the provincial Faculty of Bordeaux. Apart 

 from the interest of their authorship, it might be a question 

 whether Clifford would have wished these Lecture Notes to have 

 been published among his own papers. Whatever there is novel 

 in the treatment is probably incorporated in his ' Dynamic ; ' and a 

 cursory examination of a page or two indicates the necessity of a 

 revision of the Notes by some one conversant with the subject. 

 Thus at p. 502, " a point of no velocity " is an error for " no 

 acceleration" and the whole paragraph is a corollary to one in the 

 following page ; wherein, again, a reference to " equation (2) " 

 should be a reference to another equation not numbered, just 

 above. Such errata as for are either typographical or con- 

 sequences of the hurry of note-taking. 



Of much more general interest will be the unfinished " Algebraic 

 Introduction to Elliptic Functions," in which, though Prof. Smith 

 finds that it " contains no new results and perhaps no original 

 methods of investigation," the most recent contributions to the 

 subject by Eosenhain, Ivonigsberger, Schrdter, Gropel, Cayley, and 

 Smith had been incorporated. This " Introduction " was probably 

 drawn up with immediate reference to his intended course of lectures 

 in University College. The third most considerable paper in the 

 Appendix, " On Power Coordinates in general,'' should certainly 

 have been preceded by the Notes on the Theory of Powers 

 which follow it. The remarks (p. 555) with which the Editor 

 has introduced these ' Notes ' are very unfortunate : if " they are, 

 in places, apparently inaccurate" and "it is not easy to see how 

 the equations in (1) and (4) are got, nor how the other equation 

 in (1) contains a linear relation between the powers of a point 

 with respect to a &c," — of course cela depend ; but if Mr. Tucker 

 had referred his difficulties in this case, as he did in others, to any 

 of the many mathematicians who would gladly have cleared them 

 up, it wouid have been pointed out to him that the results are 

 perfectly accurate to a factor pres (as it might have been expected 

 any such work of Clifford's would be), and that the last equation 

 in (1) has the significance assigned to it. In the last equation but 

 one of (4) as printed there is certainly an erratum of the sign ( — ) 

 for ( x ) ; but this would probably not be found in the MS. 



Of great interest is the collection of Problems and Solutions 

 from the ' Educational Times ; ' and it appears that there is still 

 a goodly number of Questions proposed by Clifford remaining 

 unanswered, the solutions of some of which would perhaps be 

 found, in substance at least, among the Papers and Fragments now 

 for the first time published. 



