240 Mr J. Sang on a Systematic Method of 



1336 (+ 203) = + 271208 

 1774 (+ 1227) = + 2176698 



929 (+ 814) = + 756206 



725 (_ 637) = 461825 



0( 1017) = 

 1244 (_ 590) = _ 733960 



or to + 32041 12 _ 1 195785 

 1195785 



or to I 2008327 



therefore area = 10.04163 



But each of these products is also equal to the quarter square 

 of the sum of its factors, diminished by the quarter square of 

 the difference of its factors, and consequently twice the area of 

 the polygon will be simply equivalent to the algebraic sum of 

 these quarter squares ; hence the calculation may stand thus : 



| 2008327 . 

 and the area as before = 10.04163 



By throwing the corrections into the formula already given, 

 we can easily approximate to the error in area of any polygon 

 occasioned by the errors in measurement. For, in the same fi- 

 gure let the co-ordinates assumed for A, be A and , and let 

 the calculated co-ordinates be for the other points : 



B and b \ ( (B n) and (b m) 



C and c ( The corrected ) (C 2 n) and (c - 2m) 



13 and d > co-ordinates < (D 3 n) and (d 3 m) 



E and e I would be j (E 4) and (e 4m) 



A + 5 n and a + 5 m / v A and a 



In the first series, the whole error may be conceived to rest on 

 the point A, in the second, to be equally divided among all the 

 points. Let the area of the first be S, and the second s. We 

 have 



25 2S = ro(3A + 3B 2C 2D -2E) + n( 3a 3b 



