INCREASE OR DECREASE OF DAY.

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RULE.-If the given length of day be the longer, subtract the given difference to find the shorter day:

Bring the given place to the brazen meridian, set the index to 12, and turn the globe until the index have passed over so many hours as are equal to half the shorter day. Keep the globe from rotating, and elevate the north or south pole until the given place coincides with the eastern edge of the terminator: the elevation of the pole will show the declination on the shorter day. Continue the rotation of the globe for half the difference, i. e. until the index have completed half the length of the longer day; and the pole, elevated as before to accommodate the given place to the terminator, will show the declination on the longer day.

There are two days corresponding to each length; viz. one on each side of the summer solstice. If the days be increasing, take the interval between those two unequal days on which the sun is advancing towards the summer solstice; if the days be decreasing, take the interval in which he is declining from it in like manner.

1. What two days of the year are each 8 hours long at London; and in what time is the day increased by 24 hours?

Here, by bringing London to the meridian, setting the index, and turning the globe 4 hours, I find that, in order that London may coincide with the terminator, the south pole must be elevated 221°; answering to the 7th January, and 6th December. Turning the globe 1 hour more, I find that, to bring London to the terminator, it is necessary to have that pole elevated only 910, and this answers to 25th of February, and 17th October. As the place is north, and the days are increasing, I take the interval between 7th January and 25th February, and find it 49 days.

2. In what time will the day increase 2 hours more, when thus increased to 10 hours?

Here it will be found that the increase will be made in much less time, owing to the more rapid change of the sun's declination.

3. On what two days of the year is the sun above the horizon for 15 hours at Greenwich; and how many increasing days will elapse before he continues above the horizon one hour more?

4. What two days of the year are each 13 hours long at Petersburgh; and in what time, from the latter of these two days, will the day have decreased 4 hours?

5. What is the difference in the declination of the sun when he rises (a) at 7 o'clock at Stockholm, and when he rises at 3 o'clock there, and consequently gives 8 hours longer day; and how many days must elapse before this 18 hours' day again dwindles to the length of the former?

6. What two days of the year are each 16 hours long at the Cape of Good Hope?

7 On what two days does the sun set at half-past 8 at Edinburgh; and in how many shortening days will he set at half-past 7?

8 In what time from the latter date will the sun set, at Edinburgh, at half-past 6?

PROBLEM XVI.

TERRESTRIAL GLOBE.

To find the situations of the periæci, antæci, and antipodes of the inhabitants of any place; and to explain some of the various phenomena in those situations.

Learn definitions 77, 78, 79.

RULE. Make the poles of the globe coincide with the terminator, and bring the given place to the eastern edge; thus the graduations for amplitude will serve to point out latitude. If the given place be in north latitude, observe that latitude as shown in degrees of distance from the east towards the north, and the same number of degrees to the south of the east point will show the antoci; an equal number of degrees from the western point towards the north will show

(a) It will be recollected that the sun sets on any day so many hours after noon as he rises before noon.

ANTECI, PERICECI, AND ANTIPODES.

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the periœci; and the same number of degrees counted from the west toward the south will give the antipodes.

If the given place be in south latitude, for north read south, &c.

*

** If the hour-circle be so fixed as to prevent the poles' being placed in the terminator, the antoci may be seen by bringing the given town, &c. to the meridian, and observing the place also coinciding with the meridian, which corresponds in latitude of the opposite hemisphere. The index being now set to 12, let the globe be turned half way round, and the antipodes will be seen occupying the position of the antoci, and the periœci be substituted for the given place.

1. Required the antœci, periœci, and antipodes of the island of Burmuda.

Antœci a little north-west of Buenos Ayres, &c. &c.

2. Where are the antoci, periœci, and antipodes of the west of Newfoundland?

3 Where are the antoci of the Cape of Good Hope? 4. Where are the pericci of New York?

5. Where are the antipodes of Greenwich?

When our clocks are striking 6, and the summer sun is not yet set, our antæci and antipodes have him just so much depressed as we have him elevated; but whilst it is the darkness or twilight of winter evening to our antoci, it is the darkness or twilight of winter morning to our antipodes.

If the clocks are striking 6, and our winter sun has gone down, he is just so much elevated to our antæci and antipodes as he is depressed below our horizon; but he is a summer evening sun to our antæci, and a summer morning sun to our antipodes.

Our periæci, on the contrary, agree with us in season; but they are the antipodes of our antoci, and have opposite hours to theirs and our own. Hence, like our own antipodes, they are always as near to noon as we are to midnight; but at the two instants of 6 o'clock of every twenty-four

hours, their elevation or depression of the sun is equal to our own, except that their ascending sun is our descending one, and vice versa.

The night sky of our antoci and antipodes is totally different from ours, the stars which never rise to us never setting to them, and vice versá; that of our pericci corresponds with ours, except that it is presented to them twelve hours later, and the moon, consequently, has considerably changed her place amongst the stars.

To exhibit some of the Phænomena.

RULE. Find the antoci, perioci, and antipodes, by the rule just given, and mark each of them with a small dot of ink. Elevate the pole to the declination of the sun; bring the given place to the meridian, and set the index to 12; then turn the globe eastward until the index have passed over six hours. Affix the quadrant to the declination in the zenith, and it will be found by applying it to these situations (whether elevated or depressed) that they are circumstanced with regard to sun-light as just described.

6. What are the positions as to sun-light, respectively, of the antoci, pericci, and antipodes of the inhabitants of Greenwich, when it is 6 o'clock P. M. on the following days: 1st March, 25th May, 21st June, 21st December?

7. Supposing the moon to be full and therefore opposite to the sun, when it is 6 o'clock P. M. at Madrid on the 28th October; whether are the situations of Madrid and its antœci, periœci, and antipodes in moon-light or in sun-light; and, of those which have moon-light, which places have an ascending, and which a descending moon? (a)

(a) Here, the pole having been elevated to the declination of the sun, and the place of that luminary being thus represented by the degree of his declination on the uppermost point of the brazen meridian; the moon's place, on this occasion, is represented by the diametrically opposite point of it, and she is giving light to all below the terminator; those quitting sunlight entering into her light, &c., and any place having her at an elevation corresponding with its depression below the terminator. (See 8th question, p. 122.)

POLES OF THE EQUINOCTIAL AND ECLIPTIC, ETC.

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POLES OF THE EQUINOCTIAL-POLE STAR-FIXED STARSPOLES OF THE ECLIPTIC-CELESTIAL LATITUDE AND LONGITUDE.

There is one circumstance which may yet have been a stumbling-block to the enquiring minds of our young friends viz. the unvarying direction of the earth's axis to one particular point in the sky; and the consequent unvarying correspondence of the parallels of latitude on our earth with the parallels of declination in the sphere of stars around us, notwithstanding the earth's motion in her yearly orbit of nearly 600 millions of our miles. We would recommend a revisal of the familiar illustrations given in G and H, on p. 5, and request attention also to what follows.

the

As our tee-totum traverses the groove with its axis inclined, (as proposed on p. 108, and illustrated there and by the annexed figure,) it is evident that the upper point of peg must be directed to the different parts of a circle which may be traced on the ceiling, and which exactly corresponds to the table in size; but which is not immediately over the groove or orbit, being removed from a position immediately over it just so much as the axis is inclined, or 23° 28'.