Trigonometrical Survey. 
45i 
rem above) = c, a . c, H . c, h -f 5, H . s, b * . • s, d a + 2 s% * 
£■ d a .'tya — 't, a — 't, a . c, H . c, h — s, H . s, h x cosec. a 
= t',a — 't, a x £ c, H — h -j- £ c, H -f- £ — cosec. a 
x r, H — £ — H -\- h (because t',a = £'t,£a — £ t,£a\ 
and cosec. a — £ 't £ a -\- £ t, £ a) = £t\ £ a 
x 1 — £ c, H 
-A 
x H 
c, H -J- b — £ 't, £ a x 1 — c, H 
— £t,£a x 1 — c, H -f /> = £ 't, £ a x vs, H — h — £ t, 
x vs, H -j- h — 't, £ a . s\ £ H — h — t, £ a . s\ £ H -f- h. 
Put n — 't,£a. s\ £ (H — b) — t,£a. s % , £ (H b), 
We shall have 
s, d a + 2 s z ,£ d a .'t,a = n\ 
and s, d a = n — 2 s z ,£ d a .t', a. 
But s, d a = 2 s, £ d a . c, £ d a 
s, d a n — 2 s l ,\da .'t,a 
s,£da, 
2 c, i d a 
2 c, \ d a 
and s,d a = n — 2 s z ,£ d a . t', a = n — 2?, a 
d a .‘t, 
because 
= 7 + 
n— zs^y^da.ta 
2 c,\d a 
vi 1 s r ,\d a . 
2 c, \ d a 
\n . s 2 , \ da . t 1 , a + \ s*, ^ d a . ‘f 1 , a 
— n . s z ,£ da .'t,a 
4 x I — i d a 
n . s*,£d a . 't } a 
-f s*,£da.'f,a)=n — £n z . t', a — £ n z . 't, a . s% ’£ d a 
+ 2 n . 'f , a . s 1 , £ d a -f- 2 n 'f, a . s 4 , £ d a — 2 't\ a . s 4 -f £ d a, 
by substituting for s,£ d a its near value n , 
= n — |m s t r , a — + £n 3 f, a -j- £ n 5 'f, a — £n* 't\ a , 
where the last term but one containing the 5th power of n may 
be rejected, as it has been omitted by M. de Lambre. 
As d a is always very small, the arc da in parts of the 
radius, unity, = s, d a in parts of the same radius, therefore 
MDCCXCVII. 3 N 
