[ 126 ] 



XVIII. On Mr. Herapath's Demonstration of the Binomial 

 Tluorem. 



[We have received a communication occasioned by the letter of a Cor- 

 respondent in our last Number, respecting Mr.WARD's objection to Mr. 

 HtRAPAxn's demonstration of the Binomial Theorem ; from which we 

 give the following extract. — Edit.] 



« A GENTLEMAN who, in your last (p. 50), signs him- 

 -^*- self ' ACor respondent,' appears to be highly offended at 

 Mr.Wai-d, for having (vol. Ixv. p. 4.32) noticed and supplied a 

 defect in Mr. Herapath's demonstration of the Binomial The- 

 orem. — Now, sir, in justice to Mr. Waj-d, I assert that the 

 part of the demonstration which he has supplied is the most 

 important part (in the demonstration for integral exponents), 

 and that chiefly from which the proof can be fairly inferred." 

 " Further, since a product implies the multiplication of tim 

 or more factors, that quantity ought not to be denominated a 

 product which contains but one factor : hence, in strict pro- 

 priety, q must be greater than Q ; and hence, even in this re- 

 spect, your correspondent has no reason to accuse Mr. W. of 

 being too hasty. " I am, sir, &c. 



Wisbeach, Aug. 2d, 1825- Y + Z." 



XIX. Notices respecting New Books. 



Zoological Researches in Java and the neighbouri^ig Islands. 

 By Thomas Horsfield, M.D. F.L. & G.S. London, 1821 

 — 182i. 4to. 



[Continued from p. 63.] 



nnO the birds described in the concluding three numbers of this 

 -* work, we shall add those considered in the numbers for- 

 merly noticed in the Philosophical Magazine, for they include 

 several interesting new genera, of which the names only were 

 given upon that occasion ; and no analysis of the work has 

 yet appeared in any other publication. We shall enumerate 

 the whole, in the order they take according to Mr. Vigors's 

 development of the Quinary Distribution, in this department 

 of nature. It will likewise be useful to refer to some recent 

 memoirs by that naturalist, showing in detail the existence of 

 the same principle in some of the subordinate subdivisions of 

 the class. 



Commencuig then with the Raptores, we find three species 

 of one of the normal iamiWes, (ihe Falconida:,) described in 

 this work ; viz. Falco Ichthrjcetus, F. ccerulescens, and F. Lim- 

 nttetus. 



F. Ichfhya-fKs. F. fuscus, ccra caerulea, pedibus flavescen- 



tibus. 



