EXPLANATION OF CHARACTERS.

THE planetary characters, see page 28, are also used to represent the days of the week.

Thus, denotes Sunday, D-Monday,

Wednesday, 2,-Thursday,
Saturday,

-Tuesday, Q-Friday.

For the characters of the zodiacal constellations, see page 11.

Also, the ascending node of a planet, and 8 the descending node; A. M. (ante meridiem) put after any hour, signifies that the time is between midnight and noon; and P. M. (post meridiem) that the given time is between noon and midnight.

6 denotes

ASPECTS of the PLANETS

The aspect of a planet is its situation with respect to the Sun or to another planet. There are usually reckoned five aspects, viz. Conjunction, or planets having the same longitude. Sextile, the difference of longitude of the planets being 2 signs, or 60o.

Δ

Quartile, the difference of longitude of the planets being 3 signs, or 90°.

Trine, the difference of longitude being 4 signs,or 120”. Opposition, or planets situated in opposite longitudes, or differing 6 signs from each other.

ALGEBRAIC CHARACTERS.

Each of these characters, except the radical, is supposed to be placed between two quantities, to indicate whether the sum, difference, &c. of these quantities is to be taken.

The sign+, (plus) signifies, that the second quantity is to be added

-, (minus)

S

, or L

, or

to the first.

the second quantity is to be subtracted from the first.

the two quantities are to be multiplied.
the first to be divided by the second.
the diff. of the two quantities is to be
taken.

the first is greater than the second.
the first is less than the second.

It may be observed, that the less quantity is placed at the open
part of the character, and the greater at the close part.
the square root of the quant. within it.

When

xvi

EXPLANATION OF CHARACTERS.

When the sum or difference of two quantities is to be multiplied by a third; then these quantities, connected with their proper sign, are placed either within a parenthesis, or have a line, called a Vinculum, drawn above them. Thus, if the sum of a and b is to be multiplied by x, the product will be (a+b)xx, or a+bxx.

THE

THE

THEORY AND PRACTICE

OF FINDING THE

LONGITUDE AT SEA OR LAND.

BOOK I.

CONTAINING,

The Principles of the Aftronomical Methods of finding the LONGITUDE at SEA or LAND.

WITHOUT a previous knowledge of the figure and magnitude

of the Earth, the places of the heavenly bodies could not be accurately settled, from observations made on its surface; and therefore, computations made from observations of these bodies, could not be depended on for ascertaining the position of places on the Earth; hence, the necessity of knowing both the Figure and magnitude of the Earth is apparently obvious.

Of the FIGURE of the EARTH.

The opinions of the ancients concerning the figure of the Earth were various. It was supposed by many to be a plane indefinitely extended; some imagined it to be of a cylindric form, and a few suppos ed it spherical; but the discovery of its real figure was left to the illustrious

VOL. I.

B

trious Sir Isaac Newton. The following are a few of the arguments commonly used to prove, that the figure of the Earth is either spherical, or nearly so.

I..

The Earth has been circumnavigated by many persons, at different periods. The first who attempted this circumnavigation was Ferdinand Magellan, a Portuguese. He sailed from Seville, in Spain, August 10, 1519, in the ship called the Victory, accompanied by four other vessels. In April 1521, Magellan was killed, at the Island of Sebu or Zebu, one of the Philippines, in a skirmish with the natives; and one of his vessels arrived at St. Lucar, near Seville, Sept. 7, 1522. The next who circumnavigated the Earth was Sir Francis Drake. He sailed from Plymouth, December 13, 1577, with five vessels,† and arrived at the same place, Sept. 26, 1580. Since that time, the circumnavigation of the Earth has been performed by Sir Thomas Cavendish, Messrs. Cordes, Noort, Scharten, Heremites, Dampier, Woodes, Rogers, Schovten, Roggewein, Lord Anson, Byron, Carteret, Wallis, Bougainville, Cook, King, Clerk, Vancouver, and many others. These navigators, by sailing in a westerly direction, allowance being made for promontories, &c. arrived at the country they sailed from. Hence, the Earth must be either of a cylindric, or globular figure; but it cannot be in the form of a cylinder, because then the difference of longitude and meridian distance between any two places would be equal, which is contrary to observation; the figure of the Earth is, therefore, spherical.

II.

The upper parts only of distant ships are visible, when viewed with a telescope, the lower parts being hid by the interposed water, and more or less become visible, according to the distance. In making the land, the most elevated parts are first seen, and the lower parts become visible as the land is approached. The sun is observed sooner at rising, and later at setting, by a person at the mast-head of a ship, than by one on deck. These phenomena evidently arise from the spherical figure of the Earth; and, therefore, serve to prove the Earth to be of that figure.

III.

The continual appearance of the sun above the horizon, during the space of several months, in the neighbourhood of one pole, while at a place equally distant from the other pole, the sun is as long absent, is another proof that the Earth is spherical.

This island is also sometimes called Matan or Mactan; its metropolis is in latitude 10° 33' N and longitude 123 48" E.

The largest of these vessels was only 100 tons; the others were 8o, 50, 30 and 15 tons respectively,

IV.

IV.

LEMMATA.

1st, The distance of the nearest fixed star, when compared with the magnitude of the Earth, is so immense, that rays flowing therefrom, to any two points on the surface of the Earth, are physically parallel.

2d, If in a curve, the arches are proportional to the correspondent angles, that curve is a circle.

Now, if the Earth was an extended plane, the meridian zenith distance of any given fixed star would be the same in all places of the Earth, by lemma 1st; but it is found to be variable, and in such a manner, that the difference of the meridian altitudes of the same star is proportional to the intercepted arch of a meridian; hence, by lemma 2d, that meridian is circular: and since this is found to be the case in every part of the Earth, its figure is, therefore, spherical.

V.

LEMMA.

If the shadow of any body, when turned in every position with respect to the luminous body, be circular, when projected on a plane perpendicular to the line joining the centres of both, the body itself is a sphere.

Now, since a lunar eclipse arises from the passage of the moon through the shadow of the Earth; and as that portion of the Earth's shadow, which is projected on the lunar disk, is observed to be always circular, in every different position of the Earth-the figure of the Earth must, therefore, be that of a sphere.

VI.

If a lunar eclipse be observed at two places, differing in longitude, the time of the beginning, or end, will be observed to be later at the eastern than at the western place; and the difference of time will be found to be propotional to the difference of longitude. And if the eclipse be observed at two places in the same parallel of latitude, and also at two other places, under the same meridian as the former, but in a different parallel of latitude; then, although the same interval of time will be observed in each of the parallels, yet the meridian distances between the places will be different; and, upon calcalation, will be found to answer to a spherical figure, or nearly so. From observations of this kind the magnitude of the earth might also be determined.

VII.

The planets hitherto discovered are observed to be globular; but the Earth is also a planet, subject to the same laws, and revolving round the sun in the same manner as the other planets; therefore, by analogy, the Earth is globular.

Although it appears from the preceding proofs, that the Earth is of a spherical figure, yet it is not a perfect sphere, but an OBLate SPHE

B 2