MATHEMATICAL PAPERS. 27 



RULE. 



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Make a dtvifion in. the field book of two colunans ; in the 

 firfl of wliich note down the courfes and fides of the field, as 

 they occur. Find the bafes and perpendiculars of the feveral 

 fides, which may be expeditioufly done by the help of a table^ 

 place the bafes in the firfl column underneath the fides, and 

 the perpendiculars in the fecond column, prefixing xh.tjig?i 

 to thofe that are foutblngs. 'Let the caJculatrix be confidered 



p 



as bifeBing xh^jirji fide ; then the mean calculattal dtjiance of 

 xh^jirjljtde is equal to ; and its perpendicular is equal to its 

 ultimate calculatral dtjiance. When they are both northings^ or 

 both fouthings ^ take xh^fum of the ultimate calculatral dijlance of 

 the firft fide, and the perpcjidicular of the fecond \ and it will 

 be the mean calculatral dijlance of the fecond fide. Again, take 



w 



the Jum of the aforefaid perpendicular and tuean calculatral dij- 



r 



iance ; and it will be the ultimate ealculatral dijlance of the 

 fecond fide. But when they are, one a northing and the other 

 a foutblngs take their difference inflead of fum. Here let it be 

 obferved, that the mean and ultimate calculatral diftance is of 

 the fame name with the number added to, or fubtraded 

 from 5 and when it is a fouthing, it muft be defignated by 

 prefixing the fign — to it. In like manner proceed with each 

 of the remaining fides. Multiply the mean calculatral diftance 

 of each fide by its baje. Then bring the feveral produds, 

 whofe fadors are northings and eaflings, or fouthings and 



."weftings, into one fum : likewife bring the produt^s, whofe 



fadors 



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