Bibliogra/phy. 209 



the following extract from the preface of the work. " It is believed 

 that not a single error of importance will be found in these tables. But 

 for every essential mistake that may be discovered, a complete copy of 

 the whole, with the inaccuracy corrected, will be presented to the indi- 

 vidual from whom the communication has been received." It is added, 

 that the author has devoted nine years of assiduous labor and study to 

 the completion of the work, and has expended upon it already more 

 than two thousand pounds. 



As it is important that any errors which are detected in such a work 

 as the one before us, be immediately made public, we will here mention 

 two or three that have been observed in it on a cursory examination. 

 In the table of contents, the fifteenth table is said to be on page 603 

 instead of page 604. In the explanation of the tables, page 4, line 21, 

 for page 143 read page 153. Throughout the third table, in the col- 

 umn which gives the hundredths of seconds of time corresponding to 

 each second in a minute of space, '06® is made equivalent to 1", 

 •26^ to 4", 46^ to 7", &c. We are at a loss to see why 6 is here used 

 instead of 7. What good reason can there be for departing from the 

 common rule, which requires us to use for the last figure of a number, 

 that which will bring us nearest the truth ? As there is a uniform prac- 

 tice with regard to this case, in the several thousands of instances which 

 occur in the table referred to, we must conclude that the deviation from 

 the usual course was not unintentional ; but the reason for it should 

 have been somewhere stated for the satisfaction of the reader. 



8. The Principles of the Differential and Integral Calculus, and their 

 applications to Geometry. By Washington McCartney, Esq. — This- 

 work though designed for colleges and universities, is somewhat more 

 extensive than the common elementary treatises used in this country ; 

 and it may be doubted whether the author has not in this respect mis- 

 judged as to the wants of our higher literary institutions. The time 

 ordinarily allotted in them, to the study of the calculus is so short, that 

 no treatise can be thoroughly read by the student, which is not strictly 

 confined to the elements of the subject. 



But there are some peculiarities in the work before us, which may 

 give it an advantage over others in common use. Each distinct subject 

 of investigation is stated by the author in a formal proposition, that the 

 attention of the student may be fixed upon what is immediately before 

 him, and that the principles developed may be rendered more prominent 

 and be more easily remembered. It is a common error in treatises on 

 the calculus, to present the elements of the subject too abstractly, fur- 

 nishing so little of illustration to the student, that he is quite at a loss to 

 see the bearing or importance of much that he is required to learn. Ja 



Vol. XLViii, No. 1.— Oct.-Dec. 1844. 27 



