Notices respecting New Books, 67 



Suppose the chucks disconnected and the chuck-table Y fixed ; 

 then b)^ placing Q on a determinate point of Y, we thereby place 

 P in the position to trace out (on the moving chuck-table X) a 

 curve of determinate form. For instance, the bicyclic chuck X 

 being adjusted in any given manner, it is easy to draw on the 

 fixed chuck-table Y a locus which is such that, Q being placed 

 at any point thereof, the curve traced out by P shall be cuspidal 

 (the locus in question is, with a difference of position only, the 

 locus of P such that the curve traced out by P shall be cus- 

 pidal) j and this being so, as Q is placed on the one or the other 

 side of the locus, the curve' traced out by P will have or will not 

 have a node. The locus is of a high order — in the case in which 

 I have drawn it, a closed self-intersecting curve met by various 

 lines in four real points. Moving Q along any such line, the 

 curve traced out by P is successively A, C, N, C, A, C, N, C, A 

 (A without a node, C cuspidal, N nodal). Similarly, if Q be 

 moved along a line which meets the locus in only two real points, 

 then the forms are A, C, N, C, A; and if the line does not meet 

 the locus, then the form is A throughout. We thus by means 

 of the locus obtain a curve of the required form. 



Again, supposing the chucks disconnected, and Q attached to 

 Y : keeping Y fixed and moving X we obtain on chuck-table X 

 a curve; moving Y through a small interval and again fixing it, 

 we obtain a second curve, and so on; that is, we obtain on 

 chuck-table X a series of curves each due to the construction of 

 X, but in an arrangement due to the construction of Y. 



VII. Notices respecting New Books. 

 An Introductory Algebra, containing the chief rules in the first part of 

 Colenso's Elements of Algebra simplified; with additional illustra- 

 tions, and followed by a large Appendix of new examples arranged 

 in the order of the rules. By the Right Rev. J. W. Colenso, 

 D.D., Lord Bishop of Natal, and the Rev. J. Hunter, M.A.,for- 

 .merly Vice-Principal of the National Society's Training College, 

 Battersea. London: Longmans, Green, and Co. 1872. 18mo. 

 Pp. 242. 

 npHE title-page, which we have given at full length, sufficiently 

 -*- describes the work. It contains the usual course of Elementary 

 Algebra, including, however, indeterminate equations of the first 

 order connecting two unknown quantities, and excluding the Bino- 

 mial Theorem. All elementary books on Algebra with which we 

 are acquainted place the solution of simple equations early in the 

 course ; the present authors go a step further in this direction than 

 most of their predecessors ; for no sooner has the learner been taken 

 through addition and subtraction than they set him to work easy 

 equations of the first degree of one unknown quantity, then to ex- 

 press numerical relations in algebraical language ; and thus they lead 



F2 



