2. Bring the given star* to the brass meridian, and it will now be in the zenith; and the innermost circle of figures on the wooden horizon, will show the degrees of amplitude from the east or west at which any star is found at its rising or setting in that latitude.

3. For the azimuth, attach the quadrant to the meridian so that the bevelled edge of its nut may coincide with the zenith and the star; then the graduated edge, made to pass through any proposed star, will cut the horizon at its azimuth or bearing from the north or south, as shown by the second circle of figures.

1. At Cape Comorin (S. of Hindostan), on a certain night, when a of Aquila (" Altair" 8° north dec.) is in the zenith, what is the amplitude, or distance from the east, of a of Aries, then just rising; and what the azimuth, or bearing from the south of "Fomalhaut" (a of the Southern Fish), which had risen more than two hours before?

Here, elevating the N. Pole 8°, and bringing Altair to the brazen meridian, and consequently to the zenith, I find that a of Aries is rising 2240 N. of E.; and by affixing the quadrant to the zenith, I find that its graduated edge cuts Fomalhaut in azimuth - S. towards E. as shown by the marking on the horizon.

2. What also, at that instant, was the azimuth or bearing from the north, of Arcturus, then within three quarters of an hour of its setting?

3. At Blackheath, (lat. 510) I observed y of Draco ("Etanin") vertical: What was the amplitude of 8 (in the west shoulder of Virgo,) then just setting; and what, at that instant, was the azimuth of the following stars :

"Antares," (a of Scorpio) s. towards W.
'Arcturus," (a of Boötes)

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B of Ursa Major, (one of "the Pointers") N. towards W.
Schedir," (a of Cassiopeia) N. towards E.
Markab," (a of Pegasus) S. towards E.

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The pupil must remember that the rotation of the Terrestrial Globe, representing the rotation of our earth, and being eastward, that of the Celestial Globe, a representation of reversed motion apparent only in consequence of the earth's rotation, must be invariably westward.

4. At sea, near the Marquesas (lat. 10 S.), when the brilliant star, a of Virgo, was passing in my zenith, I observed that "Canopus," (a of Argo Navis) and "Pollux," (8 of Gemini) were both setting: what are their several amplitudes there; and what, also, is that of (a of Lyra), “Vega," which then had just risen between north and east?

5. At the Cape of Good Hope, (lat. 34 S.) on the evening of the same date, but some hours before, my friend likewise had watched the rising of a of Lyra and the setting of Canopus and Pollux, in order to ascertain the variation of the compass there: what were their amplitudes at his station?

6. And what amplitudes have those stars at Buenos Ayres and what azimuth, when a of Lyra is rising, have any stars of the 1st magnitude which are above the horizon at that place?


Remark. It has been explained (def. 36), that the Mariner's Compass is a representation of the sensible horizon, and that its 32 points are graduations in degrees of this horizon: what is called the " bearing" of one place from another, is its situation with regard to the horizon of the latter place as indicated by these compass points.

But since the horizon is a plane (D p. 1), and the earth's surface convex, the true bearing of any place situated considerably beyond my horizon is not shown by the compass, unless the place be on the same meridian semicircle: i. e. unless it lie due North, or due South; for the same reason that the leaf of this book, or any sheet of paper, cannot be made to coincide with the convex surface of the globe.

Suppose an individual to travel duly west from London, following the pointing of his compass card, (corrected for



variation): as he constantly changed his horizon he would as constantly keep the same angle, or bearing, with every meridian he crossed, and thus truly trace out our parallel of latitude. For a certain distance he would be apparently, as well as really, west of me; but, prosecuting his way half round that parallel, he would arrive at the Fox Islands (on the opposite meridian), and to point out his station, I must direct my finger duly north. Hence, any distant place having apparent position toward our west, must lie considerably south of his station, or of our parallel. Galapagos themselves, (situated on the Equator), have due west for their apparent bearing.


On some globes, but few, the true bearing of places is traced by means of rhumb-lines; a kind of spiral curves,* which accommodate themselves to the sensible horizons of the various places through which they pass by making equal angles with their meridians, like the course of a traveller continually guided by his compass.

Note. Since the earth is but a point when considered with the celestial sphere, and our sensible horizon therefore corresponding with the rational one in the sky, (See B, p. 10), the compass, which describes bearings on the one circle, serves to describe them on the other; and the azimuth or bearing of any star in the sphere, (being reckoned on the rational horizon), coincides, at any instant, with the apparent bearing of the place in the zenith of which it is shining.— (See the next two Problems).


A place being given, with the Angle of Position or apparent bearing of another place of given distance, to find that place.

Read the foregoing remarks. Repeat the following:

Angle of Position, (def. 47); Meridians, (def. 22); Markings of the Horizon, &c. (def. 31); Cardinal Points, (def. 35).

RULE. Bring the given place to the brass meridian, and elevate the pole to its latitude; then will the given place be uppermost, and the wooden circle represent its rational

* Called in Mathematical language, Loxodromic.


horizon. Affix the quadrant of altitude to the zenith of the place, and bring its graduated edge to cut the horizon in that point of the compass given as the bearing. If the distance be given in English or Geographical miles, bring them into degrees, and find their complement (N p. 2): Under this complement on the quadrant will be the required place.

1. What city is that which lies E. S. E. from Edinburgh, and is distant from it 25° ?

Elevating the pole to the latitude of Edinburgh, and bringing that city to the meridian, I screw the quadrant over it, and make the graduated edge cut E. S. E. on the horizon; then, at 25° distance, or under 65°, its complement on the quadrant, I find Constantinople.

2. What place is that which is distant 45° from Cape Town, and considerably westward of it, in pointing towards which, I must direct my finger 96° from the true south of my horizon?

3. What remarkable Cape is that distant from Cape Town exactly 604, and in pointing towards which, my right hand must make with my left 40°, when the latter is directed southward in the plane of my meridian?

4. The North Magnetic Pole is stated, by Captain Ross, to be in 701 of north latitude: give (nearly) the longitude of this spot by the bearing of 2441 W. which is the variation of the compass from our Greenwich meridian ?

5. What city is that which is situated 5140 English miles from London, and which lies within 15° of the equator, but which has an "angle of position" of 90°, or apparently bears due E. of London ?

Conversely-6. Cherson (at the mouth of the Dnieper) lay under the edge of the quadrant when the last answer was found; and it may have been inferredthat the Indian city sought must have the apparent bearing of 90° from Cherson also.—Find that bearing from Cherson?

7. What is the distance and apparent bearing of Jamaica from London?

8. If, in Madrid, a person direct his right arm along the plane of the meridian towards the north, and his left towards Philadelphia, how many degrees of the horizon will there be between these pointings of his hands?





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 Y 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.

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