A place being given at which a certain star is culminating vertically, to find those places where certain other stars are vertical at that instant.

Learn the Note just preceding Problem IX. Learn Poles of Celestial Sphere, (def. 12); Repeat Quadrant of Altitude, (def. 48).

RULE 1. Bring the given place to the brazen meridian, and elevate the pole to its latitude: this will bring the given place uppermost, and cause the wooden circle of the globe truly to represent the rational horizon of the place.

2. Bring the star which is vertical at the given place to the brazen meridian, and elevate the pole to its declination : this will bring the star to the zenith.

3. Screw the quadrant of altitude to the zenith, and, making the graduated edge of it coincide with the other star, note down its zenith distance, and its azimuth, or "bearing" from the north or south of the horizon.

4. Apply the quadrant, in like manner, to the Terrestrial Globe, (screwing it to the brass meridian over the given place), and the place corresponding in degrees of distance and apparent bearing will be the place required.


1. When of Draco ("Etanin"), is vertical to the inhabitants of London, where is a of Lyra ("Vega") vertical?

2. Where are the stars in the head of Delphinus then nearly vertical?

Here, having arranged the globes by Sections 1 and 2 of the Rule, I find by Sections 3 and 4, that the azimuth and zenith distance of a of Delphinus, agree with the distance and apparent bearing of that narrow part of the Red Sea which is W. of Sana.


3. Where is Spica" (a of Virgo), then vertical?

4. When "Cor Caroli" (in the Dogs of Boötes) is vertical to the Observatory at Pekin, where is "Regulus" (a of Leo Major) culminating vertically?

5. When "Cor Caroli" is just south of the zenith of Madrid, where are Regulus and "Deneb" (8 of Leo) vertical?

6. At Madrid, on the 20th April, at 11 o'clock, I observed that "Cor Caroli" was culminating in my zenith : over whose heads was "Castor," (a of Gemini), then brightly shining in my north-west?

7. At sea, 8th March, half past 7, p. m. (in lat. 16° S.) at a time when the inhabitants of the Marquesas saw Canis Major due south of them, I observed the mast pointing directly to "Sirius," (a in Canis Major): near what islands, and how situated, was the remarkable southern constellation Crux," at that time?

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8. At the same instant where were the stars in the head of "Aries" vertical?

9. Where, then, the stars in the head of the " Lynx,” (then culminating low in my north,) vertical?


10. Where, at that instant, was Vega" (a of Lyra) in the zenith, although not above my horizon?

11. Where was the Pole Star at that instant; that is, how situated with respect to the Polar point?



A place being given, to find what other places lie in the same plane with that place and with both of the Poles of our Earth, and consequently with its whole axis.

Repeat the following:

Axis of the Earth, (def. 9); Plane of the Meridian, (def. 19); Meridians, (def. 22); Longitude of a Place, (def. 23); Plane, (G, on page 9).



RULE. If there be a meridian line drawn on the globe,* passing through the place, note down the places lying likewise on it for the answer; but, if not, make the poles coincide with the wooden circle, and bring the given place to the graduated edge of the brazen meridian; then, all places coinciding with the brazen meridian will be the places required.

Note.-Those coinciding with the under semi-circle of the brazen meridian, although in the same plane, may, in this instance, be left unnoticed.

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the Island of Chiloe,

and with the whole axis of the earth?

2. When γ of Virgo is vertical to that part of the east coast of Africa which is on the Equator, what places have that star exactly north of them, and what places have it exactly south?

3. When any place passes northward or southward of Aldebaran, (in Taurus), on the night of Christmas day, it is 10 o'clock; what places have, all of them, 10 o'clock when that star is vertical at the Island of Guadaloupe?

4. Some hours after this occurs, in consequence of the eastward rotation of our globe, this star will appear in the zenith of the inhabitants of the Ladrones: where will it then be 10 o'clock, as well as at those islands?

5. When it is 3 o'clock in the morning, or any other particular time of day, at Cape Horn, where is it the same time of day?

6. When the sun is on the meridian of St. Helena, and

*It would be well if the pupil were always to conceive of the "meridians" drawn on the Terrestrial Globe, as circular disks of paper, each of them passing through the solid body of the Globe, and each crossing all the others in the whole length of the axis; their edges peeping out at the circumference of the Globe and appearing as lines, only because of having been rubbed down to coincide smoothly with its surface.

it is, consequently, noon at that island, at what other particular places is it also noon


7. When, on any day, three hours have elapsed since St. Helena had the sun on the meridian; and it is, therefore, 3 in the afternoon there; to what other places also is it 3 in the afternoon?

8. Seven hours before that place or Gibraltar had the sun on the meridian, or mid-day; and when, consequently, it was 5 o'clock in the morning at those garrisons, to what other places was it 5 o'clock in the morning?

9. On a certain night the moon was exactly full when culminating in the zenith of the western point of Jamaica : to what places did she cast shadows duly northward, and to what places did she cast them duly southward, at that instant; and since it must have been midnight at these places and Jamaica, in what parts of the world was the sun culminating at the same time?


Remark.—The imaginary plane passing through London, Havre, &c., and the whole axis of our globe; and which, if continued, will cut through the middle of the Aleouskie Islands, the easternmost of the Fejees, and a point very near the East Cape" of New Zealand, is a standard plane of British Geographers; viz. that from which they reckon eastward and westward.

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When London is brought to coincide with the brass meridian, the graduated surface of its whole circle represents an extension of this plane-(See next Examples). It will be evident to the intelligent pupil, that if, after so placing London, we move the surface of the Globe either eastward or westward, the plane, or rather semi-plane, in which London is situated, and which so passes along the axis, will be inclined, at a certain angle, to one exactly similar, pointed out in like manner by the brass meridian as now coinciding with it. This inclination of the meridian plane



of any place to that of London, (our first meridian), is called the longitude of that place. The angle, or inclination of the two planes, might be measured on any of the parallels of of latitude; but, for convenience sake, its degrees are reckoned on the Equator, which is graduated for this purpose.

When, by the rotation of our earth, the plane of the meridian of any place is brought to coincide with the sun, it is mid-day or 12 at noon to that place. Hence the clocks, or sun-dials, of all places having the same meridian plane, will correspond at 12; and, therefore, at any other hour.

But, since all these semi-planes are moving eastward, those places which belong to that half-surface of our earth which is east of our London meridian, and which, consequently, precede us in receiving the noon-day sun, will have their clocks faster than ours; whilst those on the western half-surface, and which, consequently, we ourselves precede, will have their time-keepers, or their sun-dials, slower than ours, in proportion as they are situated westward.

Hence, a correct time-keeper, transferred from the place in which it has been correctly set, will give the longitude of the place at which it is consulted, by showing the contrast of its time; and consequently, the degrees of inclination* to the east or west of its own meridian.


15° of longitude one twenty-fourth of the circumference. one hour.



2 times 15..30


four minutes of time.

four seconds of time.

6 times 15.. 90

10 times 15..150

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* We use this term because, as the pupil will see a little farther on, the length of a degree of longitude varies with the latitude.

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