THE SOLAR ARC. 203 



tion has its limits; it stops at 23 27' 30" on either side of the 

 Equator ; this, too, is the maximum of the distance which the 

 imaginary axis of the photo-adumbrated sphere retires from 

 the axis of terrestrial rotation ; it is at the same time the value 

 of the obliquity of the ecliptic, or of the inclined plane which 

 the earth traverses in its annual movement of revolution. 



Fig. 42 , which represents the photo-adumbrated sphere 

 at the summer solstice, will enable the reader to comprehend 

 with the utmost facility the six months' day of the North Pole, 

 coinciding with the six months' night of the South Pole ; for 

 the triangle N C D indicates the amount by which the illu- 

 minated moiety increases in the northern hemisphere between 

 the spring equinox and the summer solstice, the amount being 

 equal to that by which the adumbrated moiety overspreads in 

 a contrary direction the South Pole in the southern hemi- 

 sphere. The superfluous quantity of the photo-adumbrated 

 sphere is nil at the apex of the two opposite triangles, or in 

 the equinoctial region. And then, in effect, both day and night 

 are always twelve hours long. Starting from the equinoctial 

 line, we see how easy it is to calculate for each locality the 

 variable dimensions of the arc which the sun, in its apparent 

 course, traces above the horizon. 



To see very distinctly the portion of the illuminated hemi- 

 sphere, which, passing beyond the North Pole, forms a lumin- 

 ous course on the darkened moiety of our globe, I have but to 

 place myself at midnight, on the 2ist of June, in the prolon- 

 gation of the terrestrial equator ; in the same way, to see the 



