370 Astronomical and Nautical Collections. 



enthusiast, whose imprudence seems almost to have impaired his 

 reason, might perhaps serve in some slight degree, if they served 

 for any thing, to make it probable that the method which he so 

 clamorously professed to have improved, was in itself of some 

 value : but as even this does not yet appear to be u?iiversally ad- 

 mitted, it may not be superfluous to give one or two additional 

 instances of its application. 



The general equation, as investigated in the sixth number of 



these Collections, is ps— vr + ( — i_ — — ) r^ + ( _z — + 



\27)ips 2 / \6mps 



6mp-s^ J \ 247nps 2Amp^s^ 24mpV \ mps 



^"' V^ + ...; fbeing = ^,r= 4andr= -^l and 

 12mpV / dz dr dr 



vf& may take for — .001294, and for p, .0002835, so that 



7n mp 



r: 4.5644, and _i— = 16100. 



mp- 



A. The first hypothesis of Kramp has been abandoned by Bessel 

 on account of its intricacy, and it has lately been declared even by 

 Mr. Ivory " too complicated for calculation." We have here 



z = 6""'""'"'-'+"', 0- being — m.[x — 1), and d<7 — mdx = 2, 



z 



and since— = — —, — — — — : butd2=:zd( — - — e" + 

 dr ps dr psz \ e « 



t^) = ztdtr (1 - —e") = - 21^ (1 - -1 e") = - tdy (1 - 



E 2 £ 



-^ e"), and ^ =: — — , or initially = — — , which must be = 



£ £ — e" £ — 1 



5 J 1 J . I o 5 1 jj> — 25£e"'d(7' 



— , ands — — , and m general ^~ , whence a^=: 



4 5 Se"— 1 (5e"— 1)« 



and ^ = r = "^^^^"^" . and lastly^ = T = T ( — + 

 dr {5t"'—iypsz dr \ vdr 



d^_^di_ d(5e--i y_dz_\ . ^,^^^^^ .^.^.^„y ^, ^ ::25^^ 



e"dr ^dr (5e"— )-c?'" zdr/ 64 ps 



