An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

TIME. 43
approach the tropic, as the angle made between the ecliptic
and the meridian constantly increases, until, when we reach
the tropic, the meridian is at right angles to both circles, and
the longitude and right ascension each equals 90~, and they
are of course equal to each other. Beyond this, from the
tropic to the other equinox, the arc of the ecliptic intercepted
between the meridian and the autumnal equinox being greater
than the corresponding arc of the equinoctial, of course its
supplement, which measures the longitude, is less than the
supplement of the corresponding arc of the equator which
measures the right ascension. At the autumnal equinox again,
the right ascension and longitude become equal. In a similar
manner we might show that the daily increments of longitude
and right ascension are unequal.
In order to illustrate the foregoing points, let - (Fig. 12)
Fig. 12.
aP
represent the equator, r T the ecliptic, and PSE, PS'E',
two meridians meeting the sun in S and S'. Then in the
triangle TES, the are of longitude TS, is greater than TE, the
corresponding arc of right ascension; but towards the tropic
the difference between the two arcs evidently grows less and
less, until at T the arcs become equal, being each 90~. But,
beyond the tropic, since E' —, TS'-, are equal to each other,
each being equal to 1800, and since S' —is greater than E'm,
therefore TS' must be less than YE'.