a& Miscellanea Curiofa, 



d 0 its reciprocal -will be, 3437 5 74 < *77°7849* 

 9 i^6 &c. which multiplied into the afore- 

 faid 'Series, fhall give precifely the difference of 

 Meridional parts, between the two Latitudes, 

 to whofe half complements the aflumed Tan- 

 gents belong. Nor is it material from whe- 

 ther Pole you eftimate the Complements,whe- 

 ther the elevated or depreffed the Tangents 

 being to one another in the fame ratio as their 

 Complements, but inverted. . 



In the fame Difcourfe I alfo fhewed, that 

 the Series might be made to converge twice as 

 fwift, all the even powers being omitted : and 

 putting r for the fum of the two Tangents, the 

 fame Logarithm would be 



but the ratio of t to t, or of the fum of two. 

 Tangents to their difference, is the fame as 

 that of the /?w of the fum of the arches, to the 

 fme of their difference. Wherefore, if S be put 

 for the fme Complement of the Middle Lati- 

 tude and s for the fine of half the difference 

 of Latitudes, the fame Series will be 



wherein, as the differences of Latitude are 

 fmaller, fewer fteps will fuffice. And if the 

 Equator be put for the middle Latitude, and 

 confequently S=R 7 and s to the fine of the La- 

 titude, the Meridional parts reckoned from 

 the Equator will be 



