INTRODUCTION. 21 



7. The nearer any place is to the equator, the less is the dif- 

 ference between the length of the days* and nights in that place ; 

 and the more remote, the contrary : the circles which the sun des- 

 cribes in the heavens every 24 hours being cut more nearly equal 

 in the former case, and more unequal in the latter. 



8. In all places lying upon any given parallel of latitude, however 

 long or short the day and night, be at any one of those places at any 

 time of the yeai*, it is then oi the same length at all the rest ; for in 

 turning the globe round its axis (when rectified according to the 

 sun's declination) all those places will keep equally long above and 

 below the horizon. 



9. The sun is vertical twice a-year to every place between the 

 tropics ; to those under the tropics, once a-ycar, but never any 

 where else. For there can be no place between the tropics, but 

 that there will be two points in the ecliptic whose declination from 

 the equator is equal to the latitude of that place ; and there is but 

 one point of the ecliptic which has a declination equal to the latitude 

 of places on the tropic which that point of the ecliptic touches ; 

 and as the sun never goes without the tropics, he can never be 

 vertical to any place that lies without them. 



10. In all places lying exactly under the polar circles, the sun, 

 when he is in the nearer tropic, continues 24 hours above the 

 horizon without setting, because no part of that tropic is below 

 their horizon. And when the sun is in the farther tropic, he is 

 for the same length of time without rising, because no part of that 

 tropic is below their horizon. But at all other times of the year, 

 he rises and sets there as in other places ; because all the circles 

 that can be drawn parallel to the equator, between the tropics, are 

 more or less cut by the horizon, as they are farther from, or nearer 

 to, that tropic which is all above the horizon ; and when the sun is 

 not in either of the tropics, his diurnal course must be in one or 

 other of those circles. 



1 1. To all places in the northern hemisphere, from the equator to 

 the polar circle, the longest clay and shortest night is when the sun 

 is in the northern tropic; and the shortest day and longest night is 

 when the sun is in the southern tropic ; because no circle of the 

 sun's daily motion is so much above the horizon, and so little below 

 it, as the northern tropic ; and none so little above it, and so much 

 below it, as the southern. In the southern hemisphere, the con- 

 trary takes place. 



12. In all places between the polar circles and poles, the sun 

 appears for some number of days (or rather diurnal revolutions) 

 without setting, and at the opposite time of the year without rising } 

 because some part of the ecliptic never sets in the former case, and 

 as mush of the opposite part never rises in the latter. And the 

 nearer unto, or the more remote from, the pole, these places are, 

 the longer or shorter is the sun's continuing presence or absence. 



13. If a ship set out from any port, and sail round the earth 

 eastward to the same port again, let her perform her voyage in 

 what time she will, the people in that ship, in reckoning their time, 

 will gain one complete day at their return, or count one day more 

 than those who reside at the same port ; because, by going con- 

 trary to the sun's diurnal motion, and being forwarder every even- 

 ing than they were in the morning, their horizon will get so much 

 the sooner above the setting sun, than if they had remained for a 



