214 A^otices respecting Netv Books. 



of course, no one can take objection ; and the less so, as in this in- 

 stance they have been faithfully executed. The researches of other 

 mathematicians on the subject have been carefully collected, and 

 not unfrequently considerably improved ; besides which the author 

 has added mucli of his own, and treated the subject throughout with 

 great ability and elegance. Nevertheless it is worthy of considera- 

 tion, whether, by expanding the second chapter on ' Elementary Prin- 

 ciples,' and by entering more fully into those details of which we have 

 before spoken, the sphere of the book's usefulness could not be con- 

 siderably increassd. 



The Elements of Plane Practical Geometry, with Illustrative Applica- 

 tions. By E. W. Dallas, F.R.S.E. London : John W. Parker 

 and Son, West Strand. 1855. 



The author's object in writing this work was " not so much to 

 educate mathematicians as to provide the ordinary w'orkman with an 

 intelligent reason for many of those problems of geometry that occur 

 in the operations in which he is daily employed, and a knowledge of 

 the principles of which must tend to correctness and excellence of 

 execution." It is a difficult task to avoid embarrassing such a class 

 of readers with too much theory, and at the same time to preserve 

 the necessaiy mathematical precision and sequence. This task the 

 author has accomplished with praiseworthy skill ; for although a 

 mathematician would certainly detect imperfections, they are of such 

 a nature as not to diminish the value of the book to tliose for whose 

 perusal it was written. 



The number of theorems in the first part is as small as the ' work- 

 man ' can desire, and they are demonstrated concisely and clearly. 

 The practical problems in the second part are, for the most part, 

 well chosen and skilfully solved. Amongst them the mathematical 

 student will recognize many ' deducibles ' whose solutions have cost 

 him much labour, and he will certainly find it instructive to compare 

 his own solutions with those hei'e given. He must not forget, how- 

 ever, that in his case the principal value of these problems is to be 

 found in solving them, rather than in knowing their solutions. 



The • observations and ajjplications ' appended to many of these 

 problems are not so skilfully chosen as we could desire ; they are 

 intended to " afford some indication to the reader of the very general 

 application of geometry," but thej' do so very inadequately, and it 

 it is quite possible that their perusal may be a source of some dis- 

 appointment to the ardent student. Many of them he will certainly 

 find interesting, others superfluous, because he would undoubtedly 

 have made them for himself; others, again, he may find trivial, and 

 a few, siich as the remark about diverging rays in the sky (p. 65), 

 are of doubtful accuracy. Nevertheless the work will be a welcome 

 one to those for whom it was intended ; and the fact that it was 

 undertaken at the suggestion of the Honourable the Board of Trus- 

 tees for the Encouragement of Manufactures, &c. in Scotland, is a 

 good guarantee that such a work was needed. 



