Notices respecting New Books. 325 



member of (56) as a function of t f . The annexed table con- 

 tains sufficient to give an idea of the course of the function. 

 It is plotted in the figure. The second entry (t / = '05) requires 



the inclusion of 9 terms of the series. After t'='7 two terms 

 suffice; and after t'='2'0 the first term represents the series 

 to four places of decimals. 



By interpolation we find that the series attains the value *5 

 when 



^=•184. ...... (58) 



XXVI. Notices respecting New Books. 



An Elementary Course in the Integral Calculus. By Dr. D. A. 

 Murray, Cornell University. Longmans, 1898. Pp. x + 288. 



r^E. MUEEAY states his object to be to present " the subjeet- 

 -*^ matter, which is of an elementary character, in a simple 

 manner." This he has succeeded in doing, and the work is well- 

 arranged and the explanations given are exceedingly clear. In 

 Chapter I. he treats Integration as a process of summation, and in 

 Chapter II. as the inverse of differentiation. The author's object 

 herein is to give the student a clear idea of what the Integral Calculi s 

 is, and of the uses to which it may be applied. The first ten chapters 

 are devoted to a treatment of the matters handled in such works as 

 Williamson's, Edwards's, and other well-known treatises. Chap- 

 ter XL treats of approximate integration, and the application of 

 the Calculus to the measurement of areas. Here we have clear 

 statements and proofs of the trapezoidal rule, Simpson's one- 

 third rule, aud Duraud's rule. To this latter gentleman the 

 author is indebted for valuable suggestions of use to engineering 

 students. Prof. Durand has also put at Dr. Murray's disposal 

 his article on " Integral Curves " (in the • Sibley Journal of 



