Divisions of Time. 7 



upon the equator. Suppose the plane of the 

 meridian to pass from the situation M M into 

 the situation N N, in going through the arc A B, 

 one degree of the equator, it will go through 

 the arc C more than one degree of the ecliptic. 

 For in the triangle ABC, the angle at B is a 

 right angle, and the hypothenuse A C is conse- 

 quently the longest side. 



At the solstices, the obliquity of the ecliptic 

 has a contrary effect, and contributes to lengthen 

 the solar days. Thus, (in fig. 3) T T is part of 

 the tropic of Capricorn, C D part of the ecliptic, 

 coincident with the tropic for some distance on 

 each side of the solstitial point, viz. from A to B, 

 and therefore meridians which are perpendicular 

 to the tropic may be considered so far as perpen- 

 dicular to the ecliptic. A meridian, then, in 

 going from A to B will go through as large an 

 arc in the tropic as in the ecliptic ; but the tropic 

 not being so great a circle, any arc, as a b, taken 

 in both these circles will measure more minutes 

 than in the ecliptic, and that in proportion as 

 the ecliptic exceeds the tropic in dimensions. 

 The circumference of the ecliptic is to that of 

 the tropic as 60 to 55, and therefore the arc a b 

 of 55 minutes on the ecliptic, will be 60 in the 

 tropic. As every meridian, therefore, passes in 

 the same time through similar arcs in the celes- 

 tial equator, and all circles parallel to the equa- 

 tor, and such are the tropics, at the solstices 

 every arc of the ecliptic passed through by any 



