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into a redilineal outline, by fliort balance, or (as they are vul- 

 garly called) give and take lines, drawn by the affiftance of a 

 tranfparent ruler, with a thin fiducial edge : The polygonal fpace 

 A muft then be reduced to a triangle by an operation familiar 

 to furveyors, and its area found, by the ufual mode of multi- 

 plying half its altitude into its bafe : By a fimilar procefs, find 

 the area of the polygonal fpace B, which added to that of A, 

 will give the area of the quadrilateral ; and if this nearly co- 

 incides with the fum, which refults from multiplying its mean 

 extent in longitude by 60, there has been no material error in 

 the operation : The fum of the areas thus found will be fre- 

 quently very different from the true area of the quadrilateral, 

 Ihewn by the table, and the error muft be corrected by dividing 

 the difference between the true and meafured areas proportionally 

 between the fpaces A and B, thus, 



Let the quadrilateral abed be fituate between the 50th and 

 51ft parallels of latitude, and its true area of courfe 2287 fquare 

 miles : But, in confequence of the inevitable deviation from 

 truth, in the projedion of the map, this area produces by men- 

 furation only 22+7 fquare miles ; the fpace A 1032, and the fpace 

 B 1 2 1 5 : To find the true areas of A and B, 



as 2247 the meafured area of the quadrilateral. 

 1032 the meafured area of A. 

 2287 the true area of the quadrilateral. 

 1050 the true area of A. 



as 



