20 INTRODUCTION. 



same place comes to the eastern semicircle of the horizon, the 

 index will show the time of the sun's setting-. 



To those places which do not go under the horizon, the sun sets 

 not on that day : and to those which do not come above it, the sun 

 does not rise. 



Prob. 19. The Month and Day being given, with the Place of the 

 Moon in the Zodiac, and her true Latitude, to find the exact 

 Hour when she will rise and set, together with her Southing, or 

 Coming to the Meridian of the Place. 



The moon's place in the Zodiac may be found by an ordinary 

 almanack ; and her latitude, which is her distance from the ecliptic, 

 by applying the semicircle of position to her place in the zodiac. 

 For the solution of the problem, elevate the pole (a) , v p „ 



according to the latitude of the given place ; and the ^ ' 

 sun's place in the eclipdc at the time being (6) found, ,,v p fi 



and marked, as also the moon's place at the same time, ^ ^ 

 bring the sun's place to the brazen meridian, and set the index of 

 the horary circle at noon ; then turn the globe till the moon's place 

 successively meet with the eastern and western side of the horizon, 

 as also the brazen meridian ; and the index will point at those 

 various times the particular hours of her rising, setting, and south- 

 ing. 



GEOGRAPHICAL OBSERVATIONS. 



1. The latitude of any place is equal to the elevation of the pole 

 above the horizon of that place, and the elevation of the equator 

 is equal to the complement of the latitude, that is, to what the lati- 

 tude wants of 90 degrees. 



2. Those places which lie on the equator have no latitude, it 

 being there that the latitude begins; and those places which lie on 

 the first meridian have no longitude, it being there that the longitude 

 begins. Consequently, that particular place of the earth where the 

 first meridian intersects the equator has neither longitude nor 

 latitude. 



3. All places of the earth equally enjoy the benefit of the sun, in 

 respect of time, and are equally deprived of it. 



4. All places upon the equator have their days and nights equally 

 long, that is, 12 hours each at all times of the yeav. For although 

 the sun declines alternately from the equator towards the north and 

 towards the south, yet as the horizon of the equator cuts all the 

 parallels of latitude and declination in halves, the sun must always 

 continue above the horizon for one half a diurnal revolution about 

 the earth, and for the other half below it. 



5. In all places of the earth between the equator and poles, the 

 days and nights are equally long, viz. 12 hours each, when the sun is 

 in the equinoctial : for, in all the elevations of the pole short of 90 

 degrees (which is the greatest) one half of the equator or equinoc- 

 tial will be above the horizon, and the other half below it. 



6. The days and nights are never of an equal length at any place 

 between the equator and polar circles, but when the sun enters the 

 signs *f Aries and =g= Libra. For in every other part of the ecliptic, 

 the circle of the sun's daily motion is divided into two unequal parts 

 by the horizon. 



