[ 3^6 ] 



Let the periphery of the circle be divided into forty parts, 

 or the quadrant into ten, and each of thefe again into ten 

 parts, in fuch a manner that the fines anfwering to the extre- 

 mity of e*ich divifion may be ,oi ,02 ,03 ,04 ,05 ,06, ,07 ,08 

 ,09 ,1,11, &c. radius being unity. Let alfo the periphery be 

 divided in the fame manner in a contrary dirccflion. The 

 principal divifions may be numbered i, 2, 3, 4, &c. but the 

 fub-divilions need not be numbered, left the numbers fliould 

 be confufed. If the magnitude of the inftrument admits it, 

 each of thefe fubdivifions may be again fubdivided by the eye 

 into 5. Every compafs ufed in i'urveying ought to be large 

 enough to admit this, otherwife the necefTary accuracy could 

 not be attained, whether it be divided by the old method or by 

 the one novr propofed. 



Hence it is evident that by infpecfllon we can have the fine 

 and cofine of the bearing pointed out by the needle to three 

 places of figures, and near the end of the quadrant even 

 to four, which will in every cafe give the area with as 

 much or greater accuracy 'as the method by the common 

 compafs. It may be objedled that the fubdivifions to be per- 

 formed or computed by the eye ought not to be equal ; but, 

 although they are not accurately, fo, yet they are fo nearly 

 equal, that no error will arife except for the fines of arches 

 near the end of the quadrant. Thefe fubdivifions, as they 

 include large arches, may be accurately fubdivided with great 

 eafe by the inftrument- maker ; or inftead of fubdividing thefe 

 a fmall table may be ufed for finding the fines of large or 

 cofines of fmall arches ; the tabular number to be entered 



with 



