1871J Notices of Boohs. 531 



&c, these manuals by Mr. Armour are admirably adapted. This 

 member of the series is fully worthy of its predecessors, both in 

 the fulness of detail, and in the simplicity of the formulas 

 employed. Most of the questions are solved by simple arith- 

 metic and by logarithms ; in cases where trigonometrical rela- 

 tions have to be considered, as in the determinations of angular 

 force, everything is so clearly explained that no difficulty can be 

 said to exist. There can be no doubt that Mr. Armour's works 

 will be much appreciated. 



The Elements of Plane and Solid Geometry. By H. W. 

 Watson, M.A., Sometime Fellow of Trinity College, Cam- 

 bridge ; late Assistant Master of Harrow School. London : 

 Longmans, Green, and Co. 187 1. Small 8vo., 285 pp. 

 This little work is one of a series of text-books of science pub- 

 lished by Messrs. Longmans, and intended for the use of 

 artisans and of students in public and other schools. Mr. Watson 

 has with liberal views exposed himself to criticism in endea- 

 vouring to sift from the books of Euclid only the propositions 

 and so much of each demonstration as will be likely to benefit 

 those for whom he writes. It needs, however, only a glance at 

 his work to show that a new era has dawned upon elementary 

 geometrical science, when men of Mr. Watson's mathematical 

 standing acknowledge our elementary teaching to be at fault. 

 Euclid's prolixity — so puzzling to the young geometrician — has in 

 this work given way to an extended application of the principle 

 of superposition. It is true that Euclid himself recognises the 

 importance of this principle, but he employs it timidly, and, as in 

 Prop. 5, Book 1, often puts himself out of the way to avoid 

 its use where it would greatly assist the student, and would, 

 indeed, be the more correct method. Another innovation on 

 which Mr. Watson is to be complimented, is the arithmetical 

 treatment of ratio and proportion, thus rendering the 5th Book 

 of immense value in instruction. There is, under the present 

 system, hardly a boy of a lower form who, although having 

 passed through fractions, has an adequate idea of the properties 

 of ratio and proportion, while even in published scientific works 

 of an elementary character, the terms are often confounded. 

 The work certainly deserves the earnest attention of all who wish 

 to see geometry studied elementally on a truly logical method. 



A Treatise upon Terrestrial Magnetism. Edinburgh and 



London : William Blackwood and Sons. 187 1. 

 The writer of this work, which is unsigned, first considers 

 the present theories accounting for the phenomena of the 

 earth's magnetism, and then expounds a new hypothesis. Assu- 

 ming the earth an immense magnet, and inferring from his 

 VOL. VIII. (o.s.) — VOL. I. (n.s.) 3 z 



