Notices respecting New Books. 51 



being unity. For not detailing in minutiae this very obvious 

 and easy consequence, Mr. Ward pronounces Mr. Herapath's 

 demonstration to be " no proof." Let us see the amount of 

 this charge. Employing Mr. H.'s notation, namely, 



1, 2 , 3 , 4 , . . . . g 



' 7i' n' n' ^n 



for the binomial coefficients, the quotients (B) are equivalent to 



2 3 4- 9 



n » " n 



^~~' "2^ ' IT' • • • • (j_ 1, 



" " ^ n 



Now it is evident that there are here q — l terms, and that 

 the product of them all is q , which is the ^^th coefficient, as 



Mr. H. says, p. 323. This is Mr. Ward's difficulty ; for not mi- 

 nuting which he finds fault with a demonstration much sur- 

 passing in simplicity, brevit}', and completeness any other that 

 has been given of the binomial theorem. 



Had Mr. H. prefixed 1 to the quotients (B), and said that 

 the yth coefficient is the product of q of them, it might have 

 been considered by some an improvement. 



It is evident that in Mr. H.'s proof q may be 2, 3, 4, 



or any whole number greater than 1, which shows that Mr. 

 Ward has likewise been too hasty in his observation, that it 

 must be " any whole number greater than 2." 



A Correspondent. 



VIII. Notices respecting New Books. 

 Zoological Researches in Java and the neighbouring Islands. 

 By Thomas Horsfield, M.D.F.L. & G.S. Nos.VI.toVIII. 

 London, 1823, 1824. 4to. 



FROM the aspect which the study and pursuit of zoology 

 now wears in this country, it would seem as if our natura- 

 lists, sensible of the neglect which this important and beauti- 

 ful department of the investigation of nature has hitherto ex- 

 perienced from us, were determined, by rapid and extensive 

 advances, to overtake and compete with on equal terms, if 

 not in their turn to excel, our zealous continental neighbours. 

 Those indefatigable inquirers have too long given us the law 

 in many branches of this science ; but the results of their re- 

 searches, s})lendid as they are, are now becoming the founda- 

 tions for a superstructure of unequalled grandeur and exquisite 

 proportions, raising by our own countrymen, which will pre- 

 sent the science of animated nature in a form far more attrac- 

 tive, and far more useful to mankind, than could have been 

 hoped for, a few years back, by its most sanguine votaries. — 

 We allude of course, first, to the extensive collection of facts 



(i 2 respecting 



