from the measurement of an arc of the meridian > &c. 505 
A i ( 2 ) ( 1 ) , , ( 2 ) (i) s. Sin. 4 — Sin. 4 /* ^ 
Also m> = nr J + ( nr — nr ). rr? 77% * tnat 
1 V ' Sin. 4 / 2 * — Sin. 4 / 1 ' 
is m^=m^ 4- (w/°- — m^), by preserving the expres- 
sion m ^ which we will call d. Then we shall have 
m (l - ) = f- 0 
tyi> 2 ^— 4 * d 
( 1 ) Ci). Jsin.^-Sin, 4 / 1 )] 
/+)- m <* 
1 Sin. 4 / 2 )- 
. T fsin. 4 /^ — Sin. 4 / 1 )] 
+ i ls^-)ri-77 n|’ &c - 
to m <”'= m ( "+ d\ -••f 1 
T l Sin. 4 / 2 ) — Sin. 4 / 1 ^ J 
Here d is the only unknown quantity to be determined, since 
(0 
4- tf/ 0 4” m 
(3) 
m 
.^”)= A. the terrestrial measure 
of the arc of n complete degrees ; m being the measure of 
the first degree in latitude /° by observation. 
Then A 
(i) 
— nm> 
+ d 
(o + 
1 + 
Sin. 4 /(3)_sin. 4 / *) Sin. 4 /“)— Sin. 4 /° 
And d 
Sin. 4 / 2 )— Sin. 4 / 1 ) 
(A — - hw/ 1 )) . (Sin. 4 / 2 )— Sin. 4 /(0) 
(Sin. 4 / 2 )— Sin. 4 /0) +(Sin. 4 /3)_sin. 4 / '))+... . Sin. 4 / H L_ Sin. 4 / 
when d becomes a known quantity. AndsinceSin. 4 / 0 — Sin. 2 / 0 
is a constant and known quantity, if f - — — ? be called 
■ ! } 
Sin. 4 /l 2 ) — Sin. 4 /1 lJ 
Q, we shall have the order of contiguous degrees as follows : 
= m 4 - o 
nfi 2 ^ = in 4- d 
,(3) 
— m 4- Q {Sin. 2 / 3) — Sin. 2 / 0 } 
