314 On the figure of the EARTH. 



the fun's zenkh diftance, and confequently equal to the 

 latitude of the place. It is evident that hodies near the 

 furface of the earth, are not attra£led in lines paffing 

 tlirough the earth's centre; hut in lines perpendicular to 

 the horizon ; for if it were otherwife a plummet would 

 hang in the diredion QI^C (paffing through the centre 

 of the eUipfis) and tlie latitude of the place would in that 

 cafe be equal to the angle /LQj but this angle never 

 would, except under the pclcs and at the equator, coincide 

 with the angle /LZ. It is plain, thex-efore, that the 

 difference of latitude cannot, v/ith any inftrument, be 

 meafured by the angles between lines meeting in the 

 earth's centre. 



But as the difference of latitude is meafured by the 

 angle formed between the perpendiculars to the two ho- 

 rizons, it follows that the nearer the curve of the meri- 

 dian approaches to a right line, the longer muft the part 

 of the arch be which iubtends any given angle. 



Befides it is evident, that were the earth a plane, and 

 of its adtual diameter, no fenfible difference v.'ould be 

 obfervcd in the fun's altitude on any part of its furf.ice, 

 and of courfe the nearer the earth approaches to a plane, 

 the Icfs will be the difference of altitudes obierved by 

 two perfons at any given diftancc, and coniequently the 

 degrees of latitude muff be longer as the earth is flatter. 



Independent of thefe circumftances, let ABDh be an 

 ellipfis of which AD and BE are the axes and C the 

 centre. Make CF equal to AC. Draw AF which pro- 

 duce to G. Blfedl AG in K. Draw KC which produce 

 to L and R. Through L draw MLO parallel to AG 

 and cutting AD and BE produced in O and H. Then 

 by conies will HLO be a tangent to the curve in the 

 point L. Through A draw Al perpendicular to AC and 

 confequently a tangent to the curve, and ET perpendi- 

 cular to LO. Now becaufe FC is equal to AC and 



FCA 



