92 LATITUDE AND LONGITUDE. 



in 24 hours at the points V and W. Let us now ima- 

 gine an observer placed at L, (at the moment when such 

 a star comes to the meridian at V, that is, the moment 

 it ceases to rise, and begins to descend,) can measure 

 with an adequate instrument the angle VCO or the arc 

 VO, and likewise when it again comes to the meridian 

 at the point W, that is, at the moment when it ceases 

 to descend and begins again to rise. He measures 

 with the same instrument the angle WCO or the arc 

 WO ; then it is clear that the pole P being equally 

 distant from every point of the parallel, we have half 

 the sum of the two altitudes equal to the latitude, or 

 half the sum of the two arcs VO -f WO = PO =ZE 

 or LQ, that is, in degrees and parts of a degree, which 

 is thus farther demonstrated : 



Since VO is the greater elevation, and WO is the 

 less elevation, then is VW the difference of those 

 elevations ; PW half the difference, and PW -f WO 

 = PO, that is, half the difference of the elevations -f 

 the less elevation = PO = EZ = the latitude. 

 Now since PW + WO=PO, 



therefore 2 PW -f 2 WO =2 PO 



that is VW 4- 2 WO = 2 PO 



or (VW -f WO) + WO = 2 PO 



