LATITUDE AND LONGITUDE. 91 



All this is further demonstrated by referring to the" 

 annexed figure. 



Suppose HSON is the rational horizon of any place 

 L, and pLa the terrestrial meridian, RQ the terrestrial 

 equator, consequently, the distance or arc LQ the 

 latitude of the place at L. 



Extending those lines to the heavens, we have PEA, 

 &c,, the celestial meridian, and imagining RQ prolon- 

 ged each way, EF will represent the celestial equator : 

 prolong likewise CL until it meet the concave surface 

 of the heavens in Z : then the arc ZE contained between 

 the zenith Z, and the celestial equator ET, is equal to 

 the arc LQ, that is to say, it is of the same number of 

 degrees as the latitude. It is thus we say the latitude 

 is equal to an arc of the celestial meridian contained 

 between the celestial equator and the zenith. 



Now if we conceive that HO is the line of intersec- 

 tion common to the planes of the horizon HNOS and 

 the meridian OPEHAT, it is clear that CZ is perpen- 

 dicular upon AO ; and since the axis AP is also per- 

 pendicular upon the line of intersection ET, common 

 to the planes of the meridian and equator; therefore, 

 the arcs OZ and PE are each 90 degrees. Take away 

 therefore the common arc PZ, and the remaining arc 

 PO is equal to the remaining arc ZE. But the arc 

 OP is the measure of the angle PCO, that is, the angle 

 of elevation of the pole P above the horizon. 



Therefore, the latitude ZE equals the height PO of 

 the pole P above the horizon, which arc PO measures 

 also the angle of inclination between the earth's axis 

 and the horizon. 



Therefore, to determine the latitude, we have only to 

 find the arc PO. 



Now it is not difficult to comprehend that in the 

 apparent revolution of the stars round the earth, many 

 are so situated as to be always in certain places visible, 

 that is, never set. Such is the case with the stars 

 about the pole, which appear to describe parallels 

 similar to VgW, such a star would be always present 

 above the horizon, and would be on the meridian twice 



