76 rilArrJCAL exercises in (JKOGRAPllY 



stage is readied, better values of the sun's declination may be taken 

 from tiie Nautical Almanac for the current year, accessible in the 

 larger ihiIjHc libraries. If it is not accessible there, ask the librarian 

 to get it. 'J'he teacher of mathematics should be able to explain how 

 to use it in finding the sun's declination on any date. 



The Yedv. — The time and direction of sunrise and sunset should be 

 tabulated and diagramed. The correlation of the day's length, the 

 direction of the sun at rising and setting, and the changes in midday 

 altitude are most instructive. Each quantity affords occasion for 

 prediction and verification of its future values. All the changes in 

 these quantities are run in a period of 365 days, and in the same 

 period tiie star grouj) first seen in the east shortlj' after sunset is again 

 seen there at the same hour. Now let the scholars try to explain this 

 return to a previous condition, suggesting to them that a line may be 

 imagined starting at the sun, passing through the earth, and extend- 

 ing to the distant stars. This line has been found to sweep through 

 the sky, pointing to one star group after another, and to return to the 

 original group in the same period as that in which the noon altitude 

 and its correlated quantities run through their variations. Then the 

 earth must go around the sun once in 365 days. The time unit, 

 called a year, has long been familiar to the scholars ; they have prob- 

 ably heard or read that the earth goes around the sun in a year, but 

 those words are now fuller of meaning than the)'' were ever before.* 

 The sensible constancy of the sun's diameter apparent (determined 

 by letting a ray of sunlight pass through a pin-hole in one sheet of 

 paper and fall upon another sheet at a fixed distance from the pin- 

 hole) should serve to give a good idea of the form of the curve or 

 orbit tbat the earth runs around. 



Inclined AUilade of Axh to Orbit. — The facts regarding noon altitude 

 and the correlated quantities can all be explained if it be suggested 

 tliat the axis on which the earth has been found to turn does not 

 stand vertical to the ])lane of the orbit in wliich it has l)een found to 

 revolve. Here again a globe is of value as a mental aid and an aid 

 in visualizing the necessary geometrical relations. So are the dia- 



* In order to give a l>etter (ietcnnination of the length of the year tliiin t;:in lie obtained 

 merely by general inspection of the eastern constellations after sunset, the following plan may 

 be adopted : Observations in September and October will show that the stars occupy more and 

 more western positions at a given hour on successive evenings. Let the more skillful scholars 

 make record of tin- position of some recognizable star with respect to a roof or chimney at a 

 certain hour on a certain evening, then ask them to discover when the star will again be in 

 that position at that hour. It will be well to have records of this sort made on several ditl'er 

 ent evenings, so as to lessen the possible trouble frmii cloudy evenings in the fi>llt)\ving year. 



