INTRODUCTION. 19 



particular hour at the time given, by moving the globe till the in- 

 dex points at the hour desired, and observing the places that are 

 then under the brazen meridian. 



Prob. 17. The Day and Hour being given, to find by the Globe 

 that particular Place of the Earth to which the sun is vertical at 

 that Time. 



The sun's place in the ecliptic (a) being found, 

 and brought to the brazen meridian, make a mark (a) Prob. 6. 

 above the same; then (6) find those places of the (6) Prob. 16. 

 earth in whose meridian the sun is at that instant, 

 and bring them to the brazen meridian ; which done, observe that 

 part of the ,earth which falls exactly under the aforesaid mark in 

 the brazen meridian; for that is the particular place to which the 

 sun is vertical at that time. 



Prob. 18. The Day and Hour at any Place being given, to find 

 all those Places where the Sun is then rising, or setting, or in the 

 Meridian ; consequently all those Places which are enlightened at 

 - that Time, and those which have Twilight, or dark JVight. 



This problem cannot be solved by any globe fitted up in the com- 

 mon way, with the hour-circle fixed upon the brass meridian, un- 

 less the sun be on or near either of the tropics on the given day. 

 But by a globe fitted up with the hour-circle on its surface below 

 the meridian, it may be solved for any day in the year, according to 

 the following method. 



Having found the place to which the sun is vertical at the given 

 hour, if the place be in the northern hemisphere, elevate the north 

 pole as many degrees above the horizon as are equal to the latitude 

 of that place : if the place be in the southern hemisphere, elevate 

 the south pole accordingly, and bring the said place to the brazen 

 meridian. Then, all those places which are in the western semi- 

 circle of the horizon, have the sun rising to them at that time, and 

 those in the eastern semicircle have it setting : to those under the 

 upper semicircle of the brass meridian it is noon ; and to those un- 

 der the lower semicircle it is midnight. All those places which 

 are above the horizon are enlightened by the sun, and have the sun 

 just as many degrees above them as they themselves are above 

 the horizon ; and this height may be known, by fixing the quadrant 

 of altitude on the brazen meridian over the place to which the sun 

 is vertical ; and then laying it over any other place, observing what 

 number of degrees on the quadrant are intercepted between the 

 said place and the horizon. In all those places that are 18 degrees 

 below the western semicircle of the horizon, the morning twilight 

 is just beginning; in all those places that are 18 degrees below 

 the eastern semicircle of the horizon, the evening twilight is end- 

 ing ; and all those places that are lower than 18 degrees, have dark 

 night. 



If any place be brought to the upper semicircle of the brazen 

 meridian, and the hour index be set to the upper figure of XII, or 

 noon, and then the globe be turned round eastward on its axis ; when 

 the place comes to the western semicircle of the horizon, the index 

 will show the time of the sun's rising at that place j and when th© 



