302 FERGUSON'S LECTURES. 



LECT. the sun is in those degrees of the ecliptic, and they are 



s^-^-x^ the days required : for on them, and none else, the sun's 



declination is equal to the latitude of the given place : 



and consequently, he will then be vertical to it at 



noon. 



PROBLEM XIII. 



To fold all those places of the north frigid zone, where the 

 sun begins to shine constantly without setting, on any 

 given day, from the 2,1st of March to the 23d of 

 September. 



On these two days, the sun is in the equinoctial, and 

 enlightens the globe exactly from pole to pole : there- 

 fore, as the earth turns round its axis, which terminates 

 in the poles, every place upon it will go equally through 

 the light and the dark, and so make the day and night 

 equal to all places of the earth. But as the sun de- 

 clines from the equator, towards either pole, he will 

 shine just as many degrees round that pole, as are equal 

 to his declination from the equator ; so that no place 

 within that distance of the pole will then go through any 

 part of the dark, and consequently the sun will not set 

 to it. Now, as the sun's declination is northward, from 

 the 21st of March to the 23d of September, he must 

 constantly shine round the north pole all that time ; 

 and on the day that he is in the northern tropic, he 

 shines upon the whole north frigid zone ; so that no 

 place within the north polar circle goes through any 

 part of the dark on that day. Therefore, 



Having brought the sun's place for the given day to 

 the brazen meridian, and found his declination (by 

 Prob. IX.) count as many degrees on the meridian, from 

 the north pole, as are equal to the sun's declination 

 from the equator, and mark that degree from the pole 

 where the reckoning ends : then, turning the globe 

 round its axis, observe what places in the north frigid 



