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XXX. Notices respecting New Books. 



Modern Arithmetic, a Treatise adapted for School Work and Private 

 Study. By the Rev. John Hunter, M.A. Pp. 246. London : 

 Longmans and Co. 



PERHAPS the chief difficulty of drawing up a good practical book 

 on arithmetic arises from the fact that the order in which the parts 

 of the subject have to be taught is not that in which they would be 

 systematically arranged. For purposes of systematic arrangement 

 the parts of the subject would follow each other thus : — First, the 

 rules of addition, &c. for integers, vulgar and decimal fractions ; next, 

 the same rules and subsidiary processes for concrete or mixed num- 

 bers ; and, lastly, the application of the rules to questions of com- 

 mercial arithmetic. A book so arranged may be very proper for boys 

 or young men already instructed, who merely wish to revise and ex- 

 tend their knowledge of the subject, but is quite unfit as a manual 

 even for intelligent boys. If the reader doubt this, let him imagine 

 an arrangement by which a boy is taught to "find the sum of 0*125, 

 4*163, and 9*457 correct to five places of decimals," before he has 

 been taught to " find the value of 11 lbs. of beef at lO^d. a pound." 

 Yet this is the order adopted in perhaps the majority of modern books 

 upon arithmetic, and certainly in some written with conspicuous 

 ability. And it must be allowed that a completely satisfactory alter- 

 native arrangement is not easily suggested — though there can be 

 little doubt that the right order for teaching is to divide the subject 

 into two courses, so as to introduce the learner to concrete numbers as 

 soon as possible. This is in fact what Mr. Hunter has done in the 

 treatise before us. His first course consists of the four rules for 

 integers, one or two processes in vulgar fractions in anticipation of 

 the distinct treatment of that subject in the second course, mixed 

 numbers, miscellaneous examples, and rule of three. The arrange- 

 ment, though causing a want of symmetry in the book, is doubtless 

 substantially right ; but we think it might be improved in detail ; 

 e. g. such examples as "multiply £76 19s. S^d. by 5f" (p. 49) 

 should hardly be introduced before the formal treatment of vulgar 

 fractions. 



The remainder of the work takes in the whole of the subjects ge- 

 nerally contained in the best modern treatises, and seems to us, so 

 far as we have examined it, to be very well done. On the whole, we 

 can cordially recommend it to any one in want of a good practical 

 treatise on arithmetic, illustrated by a large number of well- chosen 

 examples. 



Easy Introduction to Conic Sections. By the Rev. John Hunter, 

 M.A. London: Longmans, Green, and Co. 1866. Pp.87. 

 This work consists of a selection of the most elementary proposi- 

 tions in coordinate geometry, illustrated by a considerable number of 

 very elementary examples. How limited is the selection will be 

 gathered from the fact that, in the case of each conic section, nothing 



