﻿Notices respecting New Booh, 305 



being made, as with us, the starting-point, the hundredth part of it 

 is called a grade &c." (p. 218). We are, of course, aware that what 

 is called the French division of the circle is given in most English 

 text-books, but had always thought it appeared in them mainly on 

 grounds of conservatism, or because examiners sometimes ask for an 

 account of it. The history of the matter is thus stated (and, we 

 believe, correctly) by the late Dean Peacock : — " The French, simul- 

 taneously with the establishment of their systeme metrique decimate, 

 proposed to divide the quadrant into 100 degrees, the centesimal 

 degree into 100 minutes, and the centesimal minute into 100 seconds, 

 and so on ; and this division was adopted in the Mecanique C&este of 

 Laplace and other contemporary scientific works. The change, how- 

 ever, from the nonagesimal to the centesimal degree was attended 

 with no advantage sufficient to compensate for the great sacrifice of 

 tables and records which its adoption rendered necessary, and its 

 use was speedily abandoned, even in France " (Treatise on Algebra, 

 vol. ii. p. 146, note). 



Algebraical Exercises and Problems ; with Elliptical Solutions. By 

 Hugh McColl. Pp.100. Longmans and Co. 1870. 

 This may be fairly called a remarkable book : in the well- worked 

 field of elementary algebra the author has hit on some things which 

 (so far as our knowledge goes) are new. The value of the novelties is, 

 to be sure, a different question. In the first place the " elliptical 

 solution " is a novelty. We shall best give a notion of what is meant 

 by an elliptical solution by producing a specimen. The question is 

 this : — " A plays at chess with B, winning 3 games out of 4 ; and 

 afterwards with C, winning 2 games out of 3; at the end of 21 

 games he has won 15. How many did he play with each ?" (p. 34). 

 And this is the elliptical solution : — " He played oc games, suppose, 

 with B, out of which he won .... games ; and he played .... 

 games with C, out of which he won .... games. And since we are 

 told that he won altogether .... games, we have the equation 



from which we get #=12" (p. 69). The elliptical solutions give 

 just the kind of information which a teacher commonly gives vivd 

 voce to the learner who has not yet acquired the art of expressing 

 questions in an algebraical form, and there can be no doubt as to 

 their value. 



The second novelty is this : — A considerable number of examples 



are set in a form such as the following. "If 1 — _ ounces cost 



1+2- 



1 — ■— - 2 shillings, what is the price per ounce ? What would 



( 1 + x) 



x+ - ounces cost at the same rate ? " (p. 27). This is, of course, 



x 



equivalent to the exercise commonly written thus : — Simplify 



KX-^W-w} 



