loS Notices respect i/iu New Hooka. 



ceptional children oi the above age could be brought to know much 

 more about Long division than that it is a process Leading to a certain 

 result. Nor docs this to any serious extent diminish the value ot the 

 intellectual training which u child goes through in the study of 

 arithmetic. That training is undergone hy means of particular ex- 

 amples. Thus, let the question proposed he this : — " A watch gains 

 uniformly 13 seconds a day. It is 2 minutes 10 seconds slow on a 

 certain day, hy how much will it he fast at the end of three weeks ?" 

 The reasoning by which a child arrives at the answer is quite inde- 

 pendent oi his knowledge of the ultimate reasons of the processes 

 of multiplication &c. that he employs. 



We suppose that in reality Mr. Fitch's opinion is not very differ- 1 

 out from ours; for we find that in the hook for children, of which he 

 is the joint author (the ' School Arithmetic'), no more is attempted 

 than the statement and illustration oi rules. The method oi the 

 book is this : — In each section a typical example is given and its so- 

 lution reasoned out step hy step; then follow a general rule, 

 another example worked out by the rule, and finally many examples 

 of the rule are given tor practice. Of the examples some are such as 

 can be worked mentally, others, involving larger numbers, are to be 

 worked on slate or paper. This classification of the examples seems 

 to us a very valuable feature of the book; and the work altogether 

 seems a very good school arithmetic. If we were to hint a fault, 

 it would be that, to secure cheapness; a paper and type are used 

 likely to prove hurtful to young eyes. 



The third work on the list (the ' Science of Arithmetic ') is one of 

 more pretensions. It aims at imparting a systematic acquaintance 

 with the principles as well as the rules oi arithmetic. The authors 

 have evidently bestowed much labour and thought upon the work, 

 and have produced a book from which a teacher of arithmetic would 

 doubtless learn much. The characteristic defect of the book is a 

 want of precision of statement, which sometimes contrasts quite 

 curiously with the air of laborious and systematic accuracy which 

 pervades the book : c. g. the authors mark out nineteen arithmetical 

 facts as axioms. Now, if we are justified in demanding precision in 

 any statement, it is in an axiom: yet here is one. Axiom XV. 

 p. 85 : — M If the dividend and divisor be either both increased or both 

 diminished the same number of times, the quotient remains un- 

 altered." What the authors intend is pretty plain ; but if they were 

 held to what they say, it would follow that the quotient of I '2 divided 

 by 6 might be the same as that of , c ) divided by 3. In short, num- 

 bers may be increased or diminished in other ways than by taking 

 equimultiples of both or dividing both by a common factor, which is 

 what they mean by increasing or diminishing the dividend and divisor 

 a certain number of times. This is by no means a solitary instance 

 of an inexactness which seriously diminishes the value of a book in 

 many respects well executed. 



