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or increased, distance from the celestial pole ; its extremepositions being attained on the days of the solstices ; uponone of which (in December) its distance from the north poleof the heavens is (as we have previously mentioned) 113)°,while upon the other (in June) * its distance is only 06£°. Itsdiurnal path upon the day of the December solstice is thereforerepresented by the curve dec; and upon the day of the Junesolstice by'the curve jun.
If, instead of the poles being supposed to be in the horizon,as in the above figure, the north pole be supposed to beelevated to a moderate extent above it, and the south poleto be equally depressed below it, as would be the case fora place situated between the equator and the Tropic of Cancer(for which the elevation of the pole, being equal to the latitudeof the place, would be less than 23^°), it is not difficult tounderstand that a somewhat similar figure would apply. TheSun’s path would not be quite vertical, as in Fig. LIII.;but it would pass through the zenith, so that the Sunwould be vertically overhead at noon, on two days in eachyear, when its angular distance from the north pole would beequal to the distance of that pole from z. Indeed, for anysuch place this latter distance must be between 66^° and 90°;and the Sun’s north polar distance diminishing from 90° atthe equinox to 66^° on the day of the June solstice, it is anecessity of the case, that on some day before that solstice, andat an etyual interval after it, the two must be equal to oneanother; from which it would result, that the Sun would passthrough z at noon. In the interval between these two datesit is also evident, since the Sun’s angular distance from thenorth pole would be less than that of z, that it would cross themeridian (e'zu in the above figure) to the right of z, or onthe opposite side of it to that upon which it would passduring the rest of the year. It may in like manner be seenthat a similar effect, relatively to the south pole, would occurfor places situated between the equator and the Tropic ofCapricorn, by supposing the south pole to be elevated above
* The respective dates at present are June 21st or 22nd, and December21st or 22nd.