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Problem Xlii. Tojind the moon's declination for Jor ami given day or hour.
The place in her orbit being found by Prob. xli, bring it to the brazen meridian ; then the arc of the meridian contained between it and the equinoctial will be the declination sought.
Problem Xliii. Tojind the moons greatest and least meridian altitudes in any given latitude, that of London, for example.
It is evident, this can happen only when the ascending node of the moon is in the vernal equinox; for then her greatest meridian altitude will be 5 deg. greater than that of the sun, and therefore about 67 deg.; also, her least meridian altitude will be 5 deg. less than that of the sun, and therefore only 1O deg.; there will therefore be 57 deg. difference in the meridian altitude of the moon; whereas that of the sun is about 47 deg.
N.B. When the same ascending node is in the autumnal equinox, then will her meridian altitude differ by only 37 deg.; but this phenomenon can separately happen but once in the revolution of a node, or once in the space of 19 years: and it will be a pleasant entertainment to place the silken line to cross the ecliptic in the equinoctial points alternately; for then the reason will more evidently appear, why you observe the moon sometimes with
in 23 deg. of our zenith, and at other times not more than 1O deg. above the horizon, when she is full south.
Problem Xliv. To illustrate, by the globe, the phenomena of the harvest moon.
About the time of the, autumnal equinox, when the moon is at or near the full, she is observed to rise almost at the same time for several nights together: and this phenomenon is called the harvest moon.
This circumstance, with which farmers were better acquainted than astronomers, till within these few years, they gratefully ascribed to the goodness of God, not doubting that he had ordered it on purpose to give them an immediate supply of moonlight after sun-set, for their greater convenience in reaping the fruits of the earth.
In this instance of the harvest moon, as in many others discoverable by astronomy, the wisdom and beneficence of the Deity is conspicuous, who really so ordered the course of the moon, as to bestow more or less light on all parts of the earth, as their several circumstances and seasons render it more or less serviceable.*
About the equator, where there is no variety of seasons, moon-light is not necessary for gathering in the produce of the ground, and there the moon rises about 50 minutes later every day or night than on the former. At considerable distances from the equator, where the weather and seasons are more uncertain, the autumnal full-moon rises at sun-set from the first to the third quarter. At the poles, where the sun is for half a year absent, the winter moons shine constantly without setting, from the first to the third quarter.
* Ferguson's Astronomy.
But this observation is still further confirmed, wben we consider that this appearance is only peculiar with respect to the full-moon, from which only the farmer can derive any advantage; for, in every other month, as well as the three autumnal ones, the moon, for several days together, will vary the time of its rising very little; but then in the autumnal months this happens about the time when the moon is at the full: in the vernal months, about the time of new-moon; in the winter months, about the time of the first quarter ; and in the summer months, about the time of the last quarter.
These phenomena depend upon the different angles made by the horizon, and different parts of the moon's orbit, and that the moon can be full but once or twice in a year, in those parts of her orbit which rise with the least angles.
The moon's motion is so nearly in the ecliptic, that we may consider her at present as moving iri it.
The different parts of the ecliptic, on account of its obliquity to the earth's axis, make very different angles with the horizon as they rise or set. Those parts, or signs, which rise with the smallest angles, set with the greatest, and vice versa. In equal times, whenever this angle is least, a greater portion of the ecliptic rises than when the angle is larger.
This may be seen by elevating the globe to any considerable latitude, and then turning it round its axis in the horizon.
When the moon, therefore, is in those signs which rise or set with the smallest angles, she will rise or set with the least difference of time; and with the greatest difference in those signs which rise or set with the greatest angles.
Thus, in the latitude of London, at the time of the vernal equinox, when the sun is setting in the western part of the horizon, the ecliptic then makes an angle of 6 2 degrees with the horizon; but when the sun is in the autumnal equinox, and setting in the same western part of the horizon, the ecliptic makes an angle but of 15 degrees with the horizon; all which is evident by a bare inspection of the globe only.
Again, according to the greater or less inclination of the ecliptic to the horizon, so a greater or less degree of motion of the globe about its axis will be necessary to cause the same arc of the ecliptic to pass through the horizon; and consequently the time of its passage will be greater or less in the same proportion; but this will be best ilhustrated by an example.
Therefore, suppose the sun in the vernal equinox, rectify the globe for the latitude of London, and the place of the sun; then bring the vernal equinox, or sun's place, to the western edge of the horizon, and the hour index will point precisely to VI; at which time we will also suppose the moon to be in the autumnal equinox, aud consequently at full and rising exactly at the time of sun-set.
But on the following day, the sun, being advanced scarcely one degree in the ecliptic, will set again very nearly at the same time as before; but the moon will, at a mean rate, in the space of one day pass over 13 deg. in her orbit; and therefore, when the sun sets in the evening after the equinox, the moon will be below the horizon, and the globe must be turned about till 83 degrees of Libra come
up to the edge of the horizon, and then the index will point to 7 h. 6' min. the time of the moon's rising, which is an hour and quarter after sun-set for dark night. The next day following there will be two hours and an half, and so on successively, with an increase of one hour and a quarter dark night each evening respectively, at this season of the year; all owing to the very great angle which the ecliptic makes with the horizon at the time of the moon's rising.
On the other hand, suppose the sun in the autumnal equinox, or beginning of Libra,and the moon opposite to it in the vernal equinox, then the globe, rectified as before, being turned about till the sun's