AP'PENDIX, ■■• . '93 



m\ : 'M :: Cos.2 /. a ? + Sin 2 /. 6^ / Cos.s 7. <£ -f Sin.* 7. 5* which 



(Cos* /—Cos* 'I.— ' T \ r 

 s , ng 7 -^ 1 m J a general expression for the ratio 



m —Sin* f 



of the diameters- 



o', ,■ „ 



Now if 7#'=?6o82Q fathoms, m—60496 fathoms s and if 7 and I be 52 d. 26 



/Cos. 2 10 34 49— Cos. 2 52 2 20\#>§g Q v| T 

 © , „ 8 / ' 60496 I 



and 10 34 49 respectively, then 7— I - , iiW& ^ f - , .- 



\ Sin. 2 52 g 30— -- I. 3 —Sin. 2 10 34 4 

 \ 60496 i 



= rooao35? nearly, which call f^-, e being the ellipticity ■ .0030359. 



3. Having obtained the ratio of the diameters to each other, let the 

 length of a degree on such a spheroid be computed for latitude 116 23.5. 

 Then to get the formula from what is just demonstrated, we have 



, /Cos* HCos* 'L - | T v CosV-Co S n.r - IT _ 



t-t-=I - I-f ok" — — = ■ - — i— which reduced gives 



•\Sin« 't/f| JT_ Sin8 |/ i +e Sin 2 7.f - J T -Sin2« 



m' V m \\ \f Cos. 1 T7T+ ej 1 — SnlTZl 3 : t/ Cos. 2 7.(1 + ej a -—'- Sm"/71 3 



O f ft O r ' -/> ' - # 



and if ?»:= 60496 fathoms* and /, 7 be 10 34 49 and 11 6 23.5 res~ 



( Cos- 2 (10 34 49) .1.0030.361 — Sin. a 10 34 49 \| 

 , a r7~T I == 



Cos. 2 (11 6 83.5) . 1.0030361 —Sin. 2 11 6 23.5' / 



■■■■- ■ ■ - ' ' ' O , n 



60498 fathoms, for the meridional degree in latitude 11 6 23.5, on the 

 ellipsoid whose polar is to its equatorial diameter as 1 to 1.003036; 

 and this I call the degree in that latitude resulting from the arc Pvmnae 

 and Dodagoontah. But the degree in the same latitude, deduced from the 

 arcs Punnae and Paughur, Pwinae and Bomamndrum^ is 60465.5 

 nearly, which must therefore apply to a different ellipsoid. But the 

 mean between this and 60498 is 60486 j ; or, to avoid fractions, we may 

 take 60487 fathoms for the length of the degree in latitude 11 6 £4>or 

 me mean, length of the degree for the arc 5" 53 30, whose middle 'point 



Z 



