ASTRONOMICAL and 



11% EFG=i26°^, FGH=9o°^, GH A=i24'' 56' ; ana 



the fides AB-io, B C=4, C D-9, D E-8, E F=7, F G-3, 



G H^i, H A=io.o4 ; required the area. 



* 



The magnetical needle is - found to vary feveral minutes 

 from a true traverfe. Tliis is occafioned by fridtion. Where 

 a great accuracy therefore is required in taking the furvey of 

 a field, this general rule for finding the polygonal area may be 

 very advantageoufly applied. For this end take the menfura- 



+ 



tion of the including angles of the field, independent of the 

 needle, which may be done with great exa6lnefs with a good 

 inflrument. Then having meafured the fides with care and 



exacflnels, we have the angles and fides of an irregular polygon 

 given to find the area. If the bearings of the feveral fides are 

 defired, they may in the following manner be made to arife 

 from the calculation itfelf. Interpolate the polygon, at the 

 prime angle, with an indefinitely fhort fide, being a meridian 

 line, had by celeflial obfervations, or the magnetical needle. 

 Take the angles, which this fide makes with the adjoining 

 fides of the polygon, and note them down with the refl. This 

 infinitefUmal fide is to be confidered as the prime fide, and 

 may be exprefled by O. Having obtained the angle of com- 

 mutation for the fecond fide^ inflead §f the defignating letters 

 A, B, introduce the initial letters of the cardinal points proper 

 to that fide ; diftinguifhing thofe that fland in the room of B 

 by a dafh over the top. The angles of commutation will now 



become the points of compafs, and exprefs the true bearing of 

 each fide. 



EXAMPLE 



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