PROBLEM VI.

TERRESTRIAL GLOBE.

Having the declination of a star, and the place to which it is appearing to pass vertically, to find all those places to which it is at that instant rising; and what portion of the time of each diurnal rotation of our earth, certain of these places severally spend in that star's beams.

Repeat the following:

Diurnal Arc, (def. 33); Planets, (def. 1); Hour Circle, (def. 25); Sidereal day, (def. 83); Learn remaining verses of "Rhymes on the Constellations," (Appendix.)

RULE 1. Elevate the pole to the latitude in which the star is vertical, or, which is the same thing, to the declination of the star; and bring the given place at which the star is vertical to the brass meridian. Then, the places along the western edge of the terminator will be those which are rising into that star's light.

2. Set the Index* of the hour circle to the time of the place at which the star is vertical, and give the globe its eastward rotation. It will be found that if the star be of the northern hemisphere, the southernmost place will first arrive at the eastern edge of the terminator; but that if the star be a southern one, that place most northern will first set out of its beams. Count the hours† elapsed, as each place arrives at the eastern edge of the terminator, and record them.

1. Each day, at the instant that Capella is vertical at Venice, I find that the cities of Mexico and Quito, St. Vin

*If the hour-circle be under the brass meridian, it is to be turned until the graduated edge of the brass meridian cuts the hour.

The hours must be counted, especially if the hour-circle have only one row of figures.

LATITUDE, DECLINATION, AND DIURNAL ARC.

79

cent, (near the bay of the Virgin, N. of California,) and the Isle of St. Francisco, (north of the Island of St. Catherina, east coast of South America,) are rising into its beams. Supposing it to be 10 o'clock at Venice, in how many hours, from that time, will these several places set out of Capella's beams?

Here, elevating the North Pole to 45°, (i. e. to the latitude of Venice), I bring Venice to the brass meridian, and set the hour circle to 10, the time given: All places now above the wooden circle, or terminator, have Capella above the horizon. Keeping the globe steady, I seek along the western edge of the terminator, and note down, the principal places rising into Capella's light, of which places, it is evident, that since Capella is a northern star, St. Francisco, the place most south, will first have passed through its beams. Next, turning the globe eastward, I find that when St. Francisco has arrived at the eastern edge of the terminator, to have Capella setting in the west, the index has traversed about 7 hours; but that Quito is not in this condition until about 12 hours have passed-Mexico, after somewhat more time-St. Vincent, California, after much more time, &c. These portions of time are to be given.

2. [June 20th, 12 at night], 7 of Draco, (Etanin) 51° N. D. is vertical at Blackheath: What places are at that instant rising into its rays; and of these places, what several portions of time do Chatham Isle (one of the Galapagos), Cuzco (Peru), the Island of St. Catherina, and the Island of Tristan de Conha, daily spend in those rays?

:

3. On 25th March, "Antares" (a of Scorpio) is vertical to Cape St. Mary (S. point of Madagascar), at 11 o'clock at night to what places is it rising; and of these places, how long will the following, severally, have it above their horizon? viz. Anglesea, St. Mary's (East I. of the Azores), and the south point of the Island of Chiloe (S. of Chili).

4. When 8 of Orion's Girdle is vertical to the Galapagos at a certain hour, (say 1 o'clock in the morning), it is rising to the following places :-Tanaga, (one of the Aleouskie Islands); Isle of St. Pierre, (11° N. lat.); the Feejee Islands; Cape E. New Zealand: How much of the sidereal day do they severally spend in its beams?

5. On 3rd May, 1840, the beautiful planet Jupiter will be in the zenith of any place 15° south when it is midnight at that place. What places will be rising into its beams when it is vertical just north-east of Otaheite; and of

these places, how long will the following severally continue in his light? viz. Cape Elizabeth, (the N. point of Saghalien,) Great Lekeyo, (Loo Choo Isles); N. E. point of Celebes, (adjoining the Sea of Celebes); and Sandy Point, or north-west Cape, (westernmost of New Holland).

6. When y of "Crux" is vertical to Cape Horn, 28th Sept. at noon, or on any other day at any other time, it is rising to the following places:- Savannah River; Bay of St. Magdalena, (S. W. of California); Christmas Isle, (a little north of the Equator); the principal of the Feejees; Erronan, or Erromango,* (south Island of the New Hebrides); Glass-House Bay, (New Holland); Nuyt's Islands, (S. coast of New Holland). What are the diurnal arcs of this star at these several places?

FROBLEM VII.

Remark. It is hoped that the pupil will now have perceived, that what is called the "rising" and "setting" of a heavenly body, and its daily westward course, are occasioned solely by the eastward revolution of our earth about its axis. The portion of time occupied by this apparently westward passage of a heavenly body, and which is called its "Diurnal Arc," varying in any certain latitude with the declination of the star; or, in the case of any certain star, with the latitude of the place; but being, invariably, 12 hours for every star to the inhabitants of the Equator, and twelve hours at every place if the star is in the Equinoctial. The apparent altitude of any heavenly body, or its elevation above the horizon of any place, at any certain time after its rising, is, in like manner, dependent upon latitude and declination; and, corresponding exactly with the elevation of that place in its light, may thus be found for any

It was by the inhabitants of this island, that the devoted Missionary, Williams, was killed, 22nd November, 1839.

LATITUDE, DECLINATION, AND ALTITUDE.

81

hour by the Terrestrial Globe, if the time of the star's rising, &c., be known.

TERRESTRIAL GLOBE.

Having the declination of a star, to find at what altitude the star appears to the inhabitants of a given place, after the lapse of a certain portion of time from its rising.

Repeat the following:

Complement, (N p. 2); Sensible Horizon, (def. 27); Rational Horizon, (def. 28); Zenith distance, (def. 40); Altitude, (def. 44); Repeat" Rhymes on the Constellations," (Appendix).

RULE.-Elevate the pole to the North or South declina tion of the star, to exhibit the latitudes of the surface which rise into its light: bring the given place to coincide with the western edge of the terminator, and set the index of the hour circle to any hour, as a mark. Next, turn the globe eastward until the index have passed over the portion of time given; and the elevation of the proposed place above the terminator, will be the altitude at which the star appears above the horizon. Find these degrees of elevation, by attaching the quadrant of altitude to the declination of the star in the zenith of the brass meridian, and making its graduated edge pass across the place.

Since the quadrant of altitude is thus attached to the zenith of the place where the star is vertical, its pivot may represent the star; and the number of degrees between this pivot and the given place, shows the zenith distance of the star.

1. At what altitude does Arcturus (Dec. 20, N.) appear above the horizon of London, an hour and a half after it has risen?

Here elevating the North pole 20°, I bring London to the western edge of the terminator; then, setting the hour-circle and turning the globe until the index has traversed 1 hour, I find by the quadrant that London is degrees above the terminator.

2. At what altitude does this star appear at Barbadoes 3 hours after rising, and 9 hours after rising?

At Cape Horn* 2 hours after rising?

At S. point of Iceland 9 hours after rising?

3. What is the altitude of Rigel, in the heel of Orion, (8 S.) 4 hours after rising at Blackheath; and what its altitude when it has been above the horizon 9 hours at that place?

4. When Sirius (a of Canis Major, 161 S.) has been above the horizon 12 hours at the several places following, at what altitudes will it appear: London-EdinburghJamaica, (Kingston)-Otaheite-Buenos Ayres-Cape of Good Hope?

5. At what elevation does a of Lyra, (38 N.) appear after it has been above the horizon of Madrid 3 hours, and 14 hours: Cape East, New Zealand, 2 hours, and 5 hours; Owhyhee, (N. point of) 5 hours; Pekin, 9 hours, and 14 hours?

PROBLEM VIII.

CELESTIAL GLOBE.

A certain star being in the zenith of a certain place, to find the amplitude of any stars rising or setting there; and the azimuth, at that instant, of any stars that may then be above the horizon.

Repeat the following:

Zenith, (def. 38); Nadir, (def. 39); Amplitude, (def. 46); Azimuth, (def. 45); Compass, (def. 36); Variation of the Compass, (def. 37).

RULE 1. Elevate the North or South Pole, according to the latitude of the place; or, which is the same thing, according to the declination of the star passing vertically.

* Cape Horn is the south point of an island.