Wrights Mathematical Papers. 77 
From the sum of the products in the column N W, SE, subtract 
the product in the column NE, SW, and divide the remainder by 
2 according to the rule, and we obtain, 
DEAl+ HAig — GHar-+FGrm=ACFGH. 
Demonstration. 
lk x km=2DEAI. 
(2m¥ — Fn)nG=2FGrm. 
(2rG-+-0H)Go=2GH¢r. 
(2gH —Hp)pA=2H Aig. 
Hence, subtracting 2GH qr, and dividing by 2, we have, 
DEAl+ HAiqg—GHgr+FGrm=EDIAIAHGF mn. 
For EF m substitute its equal CD/, and for BC& substitute its equal 
ABz, and we have, DEAI4+-HAzg — GHgr-+- FGrm=ACFGH. 
No. Ii.—The propositions contained in this paper are obvious, 
and may, pernaps, be found in many treatises on surveying. I have 
chosen, notwithstanding, to send it for insertion in the Journal of - 
Science, for the purpose of bringing the methods contained in the 
first and third papers, side by side, that their connexion and relation 
may readily be seen. 
A method of finding the contained angles of a field, having the 
courses and sides given. 
The courses of the two sides, that form the angle, when compared 
together, admit of the four following variations. viz. 
Var. 1. Unlike, like; when letters are a or a and a or 7 
The contained angle is the sum of the points of compass. 
Var. 2. Unlike, unlike; when they are a or Re and Bi or Me 
The contained angle is the difference of the points of 
compass. 
| Dip 
Var. 3. Like, unlike; when they are a or Si and yr OF 7 
The angle is their sum subtracted from 180°. 
Var. 4. Like, like; when they are Ms or =r and i or be 
The angle is their difference subtracted from 180°. 
The following rule may be of use to the surveyor, in ascertaining 
the accuracy with which the courses have been taken. 
