32 



ASTRONOMICAL and 



fides miift be twice added if a northings but \£d.fouthwg^ twks 



JubtraBcd fro^jtlie ultimate calculatral diflance of the preced- 

 ing fide J xhtfirfl obtains the mean calculatral diflance^ and the 



fccond the ultimate calculatral dijlance <£ that fide. Multiply 



t\it mean calculatral dtjlaiue of "each fide by its hafe. Then take 

 the d'lff'erence of the Eajl and Wejl produ(5ls or areas, half of 

 '^\-hich will he the required area of the field. 



1 



-h^ 



EXAMPLE. 



V... S» a* 



S. 69 43 W. ai \% 



E. Areas. 

 191.6100 



aia.04z6 



403.66Z6 

 309,6496 



94.0130 



Area is 



47-0065 



"W. Areas. 



I - ^ 



198.1000 



75.6286 



35-9iio 



309.6496 



i i ^i 'i 



J 4 



■t -^ 



'^ 



^V- 



^5-5* 



3J-5^ 



10.0c 



No. Ill 



A general fclution of the problem to find the 



\ 



folygon^ having the Jfdi 



and angles given 



of an irregular 



Let the feveral fides of the polygon A B, B C, C D, D E, E A 

 (Plate I. %. 1 1,) be confidered as hypothenufes of right angled 

 aiangles, of which the perpendiculars B F, C G, D H EI are 

 paraUel to the prime fide A B, or the fide with which 'the oper- 



ation 



