Page images
PDF
EPUB

EFFECT OF POSITION OF MOON'S PATH.

317

EFFECT OF VARIOUS POSITIONS OF THE MOON'S PATH UPON HER RISING, ETC.

H Like that of every other heavenly body, the moon's stay above the horizon of any place depends upon the relation which her declination bears to its latitude.

We have learned (see quest. 6, 8, 12, p. 163) that at the North Pole, or in a Parallel Sphere, her continuance, like that of the sun, or of the rest of the planets, is for half her time at once, because an exact half of her course is north of the equinoctial, which there coincides with the horizon.

But the period of the moon's continuance above the horizon of all other places in the regions about the Pole, will be lengthened or shortened by the position of her node; for, as we have just seen, this affects the extent of her declination; and she cannot continue twenty-four hours without setting if her declination is less than the co-latitude. (See note preceding the Rule on p. 136.) When the moon's ascending node is in Aries, her declination (as we have seen from 7 of Prob. C) will become as much as 2830, and she may then continue more than the twenty-four hours even in as low a latitude as 6110*: whereas, if her ascending node be, on the contrary, in Libra, her declination cannot become more than 1840, and then many places even in the Frigid Zone will be without her continuous light; for this declination answers to the co-latitude of 7130, and it will be recollected that the polar circle is the parallel of 66°.

There are peculiarities in the moon's rising in our lower latitudes, which are occasioned by her rapid change of declination, and these are increased or diminished by the position of her node: but the pupil who has gone over Problem C, will be in no danger of being misled, if, for the sake of illustration, the ecliptic itself be taken as representing the average position of the moon's orbitual path.

At the equator, or in a Right Sphere, every degree of the eastward motion of the moon amongst the stars produces

* Little higher than the latitude of Petersburgh.

its full effect of delaying the time of her next rising; for there the ecliptic (her average path) has but little inclination towards the horizon: she rises there, as she culminates every where, about fifty minutes later each succeeding day (i. e. with an average increase of about 13° of Right Ascension). But to any place of considerable latitude, those signs of the ecliptic which are called the Spring signs of the hemisphere, rise with great obliquity, whilst the opposite, or autumnal ones, have, at their rising, more nearly the position which they have in the Right Sphere. The consequence is that, although in one part of the month the daily difference of the times of the moon's rising is considerable, in the other part of the month this difference is far less for the daily delay of her rising which would result from her eastward motion, becomes, in a great measure, counteracted, when her course is lying through the Spring signs, by the hastening effect of her increasing declination. In a high latitude, under certain circumstances, she may (as seen in quest. 11. p. 162) rise for several nights even with the same degree of the equinoctial; and, if we elevate the pole to the latitude of the polar circle, we shall find that there, the whole of the six signs that tend towards the elevated pole rise at the same instant.

THE HARVEST MOON.

↳ The moon at full, that is, in opposition to the sun and therefore rising at his setting, can, of course, be in the Spring signs of our hemisphere only when the sun is situ ated in the Autumn ones, or during our harvest months, and then the hastening of her times of rising, just referred to, which in other months is unobserved because it takes place either in the daylight or during our time of rest, becomes conspicuous. Night after night, for several risings before and after her opposition or time of being full, she is ready with the aid of her light, to enable the husbandman to avail himself of favorable weather for gathering in the harvest; and this especially in the precarious climate of a high latitude, like our own.

[blocks in formation]

M As this phenomenon of the Harvest Moon is produced by her increasing declination, her diurnal arc is increased (Prob. VI. Sect. 1) and this increase (as may be observed by looking for her in the succeeding forenoons) is made up by the delay of her setting-for the signs in which, as we have seen, she is then situated, and which have the least difference of oblique ascension, are those which have the greatest difference in their oblique descensions; and thus, on these occasions, after having hastened to supply us in the evening, she seems, as it were, to loiter, and let her lamp dwindle away in the next day's sky.

PROBLEM F.

CELESTIAL GLOBE.

Given, the moon full on the 23rd September, to find the times of her rising for several preceding and following evenings.

First, taking the Ecliptic as representing the average position of her path.

RULE.-Stick very small patches of moistened paper upon the first point of Aries, and at three intervals of 13° each on the parts of the Ecliptic immediately preceding and following (viz. at 21° -4° and 17° of -14° and 27° of and 10° 8). Elevate the North Pole to the given latitude; bring 1° to the east of the horizon, and set the index to 6.* Then, each of the other patches being brought to the horizon, the time of the moon's rising on the preceding and following days will be shewn (very nearly) by the hour circle; or † the differences of the moon's oblique

Because the sun is in 1°, setting in the west, and this is the hour of his setting on this day.

The pupil will find this latter method, of marking the oblique ascension, the more exact and satisfactory.

ascensions on these days may be noted and turned into time.

Secondly, The effect of the position of her node being taken into consideration.

Arrange a white cord or thread to the given node (as in Prob. C), and mark it with dots, from a soft pencil, at intervals of 13o, measured off by the quadrant of altitude from 1°. Then the index of the hour circle, or the differences of oblique ascension of these several marks when brought to the horizon, will point out the increased or lessened advantage resulting from the position of the moon's

orbit.

Ex. 1. Required, the times of the moon's rising in lat. 51° N. on the 20th, 21st, 22nd, and on the 24th, 25th, and 26th days of September, in a certain year in which she was full* exactly at sunset of the 23rd of that month, and consequently rose at six o'clock :-the longitude of her node being supposed to be such as to cause her path to have an average inclination to our horizon.

Ex. 2. Required the times of the moon's rising, on those days, in latitude 56° of the same longitude.

Ex. 3. Required the times of her setting in latitude 56° on these occasions.

Ex. 4. Find what would have been the several times of the moon's rising on these occasions in latitude 514° N., if her 8 had been 1° r.

Ex. 5. And what would then have been the times of her rising if our latitude had been 56° instead of 511° ?

Ex. 6. What, if the latitude had been 60° N.?

Ex. 7. Find what would have been the several times of the moon's rising, on the evenings mentioned, in the latitudes of 510 and 600 N., if her & had been 1o ~.

* We have taken the precise time of sunset of the 23rd Septem ber; but the illustration is a fair one; for the pupil will readily allow that the circumstances would not have been very different if the moon, instead of being full at 1° r, had been full a week before, or a week after; that is, when the sun's place was 23° my or 8, her longitude must have been 23° or 8o T.

and

EFFECT OF MOON'S PARAllax.

321

PROBLEM G.

TERRESTRIAL GLOBE.

Given, the moon in the zenith of a certain place at the instant of her occultation of a star, &c., to find her appearance with regard to that star from certain other places.

[The parallax of the moon, &c., is explained in pp. 18, 19, and it is there also mentioned that, seen in the zenith, she is in her true or geocentric position (def. 99). Her greatest or horizontal parallax varies (as may be seen by tracing down the column on the right hand of p. 48) from more than 61' to less than 54'. This is owing to the excentricity of her orbit, and to her being thus alternately nearer to us and more distant from us.

We

The moon's various parallax for the various altitudes at which she may be under observation, is given in books of navigation, &c. insert an extract below the rule, but give the zenith distance, or complement of her altitude, instead of the altitude itself, as more convenient for the present purpose.]

First, the bearing of the zenith in which the moon was situated being given.

RULE.-Elevate the pole for the latitude in which the moon is vertical, or (which is the same thing) for the declination of the star or of the moon's geocentric place. Bring the place where the moon was vertical, to the brazen meridian, and affix the quadrant over it in the zenith :- -the nut of the quadrant may thus represent the moon.

Find, now, the distance of the other proposed place, by bringing the graduated edge of the quadrant to it, and counting the intervening degrees; and they will shew the zenith-distance of the star at this place at the proposed instant. Against the number of degrees most nearly according with the zenith-distance, in the table given below, the parallax of the moon will be found :-If the moon's bearing was north of the place of observation, her parallactic displacement was northward; if her bearing was south, her displacement was southward; if east, it was eastward; if south-east, it was south-eastward, &c. &c. :-the

« PreviousContinue »