■$$ APPENDIX. 



I — i (Rad.) then m'-i to :: TT^l s ■: /Cos. 2 7. (i + e>* + Sih.*7"l 3 , and m 



»n V^Oos.i 7. (i 4. e )2 +• Sin. 2 7, 1 60437 ^Cos. 2 (U 6 84). 1.00324251 2 + Sin. a 1°1 6 24 



1 



'.T+el 3 "' 1.0032423 \ 3 ■ . .' 



60^65 £*thoins s the measure of the meridional degree at the equator. 



7. IjET. rd .and- r d be the measures of 

 two degrees of longitude in the latitudes 

 ©f / and" 7, then r / and R'l will repre- 

 sent the radii of curvature of d and d 

 respectively. But R l is expressed by 



rr m 



a 2 . Cos.t-'I 



2 y Cos. 2 7. o 2 + Sin. 2 '/. 6 2 



fl2 



Hence 



2 -j/^2 -}- tang. 2 7. 6 2 

 a 2 



.... 



and for the same reason r I 



d or 



2 j/ fl 2 I tang.2 i. -b.i 2|/ii 2 -|-tang. 2 f. 6 2 " ^\/a^-\- tang. 2 7. £2 



i/a'+taiig.* 7. 6 2 J yV + laug. 2 /.>*" '.'.'■ d \ 'd that is l/r+~P|. * -Hang. 2 7 



2 i/T+7-1 *jtang7T • ' d : 7i. And when ^ is at the equator, and therefore 

 tang* 2 t~=? : oj then -/r+ii 2 +tang-. a T : i -f e : : d : W; and therefore 

 -'*/== — .^(i + f)_ — a general formula. Let / = 10, d — 60858 fathoms, 



, „ , , , 60858(1.003342) ton/irk 



as jn article 5, and 1+* as before ; then d = -^^====^===59940 



From this formula a table of degrees of longitude on this spheroid, may 

 be computed, from the equator to the pole. 



-/ 



8 Let p be the degree perpendicular to the meridian in latitude /, 



! and p' that in latitude l\ Therjp, these being as their respective verticals or 

 radii of curvature, we have & :p° "-.'• - — * — = • >. 



x ■■* 2 j/Cos. 2 i. «*-t-Sin.*. (.*» -* vCos.-ar. a 2 -f Sin. 2 7. 6*-, 



that IS p ' p' ': rfCmJT. a 2 + Sin.* f. 6 2 ; V'Cos. 2 /. « 2 + Sin. 2 /. b 2 I that 



JsJ> _: p' : '. a/Cos.*7. (H-e) 2 + Sin. 2 7" " ^Cos. 2 /. (f+^+'Sin. 2 / ; and when 



/» is at the equator, and therefore Sin. 2 I=o 3 and Cos .^ /-= i (Rad.) 



then p; :p' -. -r Vgos. 2 '7. (1 +#*'"+ '■&!>.•* 7 * 2 + e» Hence /^; 



p (i+O 



/Cos. 2 a (I+e) 2 + Sifl -' 2 ' i 



