2 10 Bihliogra'phy. 



the treatise of Mr, McCartney, however, geometrical illustrations are 

 introduced at the outset, and are given w^ith great fullness throughout the 

 work. Indeed they constitute much the largest portion of it ; as they 

 should do, according to the view which the author takes of the Differen- 

 tial Calculus, when he states that " its object is to determine the proper- 

 ties and relations of lines, and the properties and relations of surfaces, 

 and the relations of lines to sui-faces." Though this may not be deem- 

 ed a just view of the calculus, it will be admitted that the applications 

 of the science to geometry, furnish the best illustrations that can be 

 given of its principles. The work of Mr. McCartney, so far as we 

 have examined it, appears to be well executed, and we would com- 

 mend it to the attention of mathematical teachers, as furnishing a better 

 view of the applications of the calculus to geometry, than any other 

 work published in this country, with which we are acquainted. 



9. Elements of Geometry ; on the basis of Dr. Brewster''s Legendre : 

 to which is added a Book on Proportion ; loith notes and illustrations : 

 adapted to the improved methods of instruction in schools and acade- 

 mies. By James B. Thomson, A. M., Editor of the Abridgment of 

 Day's Algebra. New Haven : Durrie & Peck — Philad. : Smith & Peck, 

 1844. 12mo, pp. 237. — This volume is one of the series of Day and 

 Thomson's Elementary Course of Mathematics for Schools and Acad- 

 emies, of which the Algebra is already published, and has been receiv- 

 ed with well-merited approbation. The present work is derived from 

 a treatise of the highest reputation, and retains the spirit and character 

 of its original, while at the same time it is well accommodated to the 

 wants of younger students. Mr. Thomson has performed his task with 

 judgment and skill, and we can safely recommend the work as the best 

 within our knowledge for the class of scholars for which it is intended. 



10. New York Geological Survey. — The very interesting reports 

 which have already appeared from the different gentlemen in whose 

 hands the several sections of the State were placed, have already been 

 noticed in our former volumes, and we are now in course of presenting 

 a full analysis of their results by an able hand, of w^hich several por- 

 tions have already appeared. But one most important and indispensa- 

 ble portion of this great work still remains incomplete — a portion which 

 the scientific world will esteem as far the most valuable of all, and on 

 the thorough execution of which the final reputation of the survey will 

 largely rest. We refer of course to the Paleontology, of which, al- 

 though there have been many interesting details, no systematic and 

 comprehensive view has yet been furnished. This portion of the 

 work was originally intrusted to a gentleman of high reputation and 



