124. The EQUINOCTIAL POINTS are the first points of Aries and Libra. They are so called because, when the sun appears to be in either of them, the day and night are equal in every part of the globe.

125. The SOLSTITIAL POINTS are the first points of Cancer and Capricorn, and are so named because when the sun is near either of them, his meridian altitude continues the same for several days together.

PREPARATORY PROBLEM.

To cut a card so as to coincide with the convex surface of the globe, and the graduations on the brazen meridian.

With the semidiameter of the globe for a radius (that is, with a radius of 6 inches for a 12-inch globe, 9 inches for an 18-inch globe, and so on), and any point C as a centre, describe the arc A B of any convenient length. From C, through the points A and B, draw the lines C A D, C B E, and connect the points D and E with a plain or ornamental line; then, if the figure ABDE be cut smoothly out with any very sharp tool, the arc A B will fit the convex surface, and the sides A D, BE will become produced radii of the globe, corresponding exactly with the divisions marked on the brazen meridian. This card, for want of a better name, I have called an INDEX CARD.

The use of this card is to read off the brazen meridian correctly, as well as to preserve the globe from the injuries it frequently sustains from the pernicious custom of applying the point of a pair of compasses, &c. to its surface, particularly in working those problems that require a rotation of the globe on its axis, at the same time that a certain point of declination or latitude is preserved,

D

A

B

PROBLEMS PERFORMED BY THE TERRESTRIAL
GLOBE.

PROBLEM I. To find the latitude and longitude of any given place; also to find all those places that have the same longitude and the same latitude as the place given.*

* In applying the index card in this and other problems, place the flat side of the card against the graduated side of the brazen meridian, while the concave edge rests on the surface of the globe; then, if one of the extreme ends of the concave arc be brought exactly to touch the given place, the straight edge of the index card will cut the true latitude of that place on the brazen meridian, which will be read off as correctly and easily as if the graduated edge of the meridian itself extended to the very surface of the globe. Any degree, or even quarter of a degree of the equator, ecliptic, &c., intersected by the brazen meridian, may be read off with equal correctness and facility by a similar application of the index card,

Rule. Revolve the globe on its axis, till the given place comes under that part of the brazen meridian which is numbered from the equator towards the poles; the degree immediately over the place is the latitude sought, which is north or south, as the place is north or south of the equator; the degree of the equator, which is intersected by the brass meridian, is the longitude of the given place, which is east or west, as the place lies to the right or left of the meridian passing through London. All those places which lie immediately under the graduated edge of the meridian, from pole to pole, have the same longitude as the given place; and, if the globe be turned round on its axis, all places passing immediately under the observed latitude, have the same latitude as that place.

All places from 66° 28′ north, to 66° 28′ south longitude, having the same longitude, will have noon, or any other hour of the day, at the same time; but the length of their artificial day varies in different latitudes: all places in the same latitude have the same length of day and night; but the hour of the day varies with the difference of longitude.

Example 1. Required the latitude and longitude of Pekin; also what places have the same, or nearly the same longitude, and the same latitude, as that place.

Answer. The latitude of Pekin is about 40° N.; and the longitude, about 116° E.; the places having nearly the same longitude are, the island of Palawan, the eastern parts of Borneo and Java, Cape Chatham, in New Holland, &c. places having nearly the same latitude are, Constantinople, Cagliari, Minorca, Toledo, Philadelphia, &c.

The

2. What are the latitude and longitude of Quebec? also, what other places have the same, or nearly the same latitude and longitude?

3. Required the latitude and longitude of Cape Comorin; also, when it is noon at Cape Comorin, what other places

have noon likewise; and what places have the same length of day and night.

4. Required the latitude and longitude of the following places; and what other places have the same longitude and latitude as those places respectively.

Hobart Town,

Ispahan,

Mecca,

Nankin,
Palermo,
Rio Janiero,

Stockholm,
Washington,
York.

5. Find that point on the globe which has neither latitude nor longitude; all those places which have no latitude, and all those which have no longitude.

PROBLEM II. To find the difference of latitude and the difference of longitude between any two places.

Rule. Find the latitudes and longitudes of the given places (by Prob. I.); then, if the latitudes be both north, or both south, subtract the less from the greater, the remainder will be the difference of latitude; but if the latitudes be one north and the other south, add them together, and their sum will be the difference of latitude. Do the same with respect to the longitudes, taking their difference, if the longitudes of the two places be of the same name, or their sum, if one be east and the other west, for the true difference of longitude. If, however, in the latter case, the sum of the longitudes exceed 180°, take the sum from 360°, and the remainder will be the difference of longitude required.

Example 1. What is the difference of latitude and the difference of longitude between Mexico and Botany Bay?

Answer. Difference of latitude, 5310*; difference of longitude, 109°.

2. Required the difference of latitude and difference of longitude between the following places :

*The longitudes and latitudes, here and throughout the problems, are given to the nearest quarter of a degree, which is as near as can be read off common globes.

Amsterdam and Rome,
London and Cape Horn,
Alexandria and Cadiz,
St. Helena and North Cape,
Mount Heckla and Mount
Vesuvius,

Rio Janiero and Cape Fare

well,

Straits of Magellan and Bhe-
ring's Straits,
Calcutta and Naples.

PROBLEM III. The longitude and latitude of any place being given, to find that place.

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Rule. Find the given longitude on the equator, and bring it to the brazen meridian, then under the given latitude will be found the place required.

Example 1. What place is that whose longitude is about 17° W.; and latitude, 321° N. ?

Answer. Madeira Isle.

2. What places have the following longitudes and latitudes * ?

PROBLEM IV.

To find the distance on a great circle between any two places.

Rule. Lay the graduated edge of the quadrant of altitude over both places, the degrees on the quadrant comprehended between the two places multiplied by 60, will give their distance in geographical miles, or if multiplied by 69.1, will give the distance in English miles.t

Example 1. Required the distance between the Lizard Point and the island of Bermudas.

Answer. About 47° = 2820 geographical, or 3248 English miles.

The longitudes are given, in this and some other problems, before the latitudes, for the greater convenience of the pupil. A degree of the equator contains about 69.07 English miles: 69 is an expression near enough to the truth for common purposes.