at the meridian, which is thirty degrees west of the meridian of Greenwich; and make noon at all places that are on that meridian, and a new day will commence at all those places on it, when it is two o'clock in the afternoon at Greenwich. The same reasoning will hold good for places which are still further west; and it is therefore evident, that the difference of longitude between any two places, bears the same proportion to the difference between the times at these two places, that fifteen degrees bear to an hour of time; consequently, if the difference between the times at two places be turned into degrees, minutes, &c. at the rate of fifteen degrees to an hour, one degree to four minutes, and one mile to four seconds, a half mile to two seconds, and a quarter of a mile to one second, it will be the difference of longitude between those two places: and it is further manifest, that if the time at the meridian of Greenwich be greater than the time at ship or place, the ship or place is to the westward of Greenwich; but if the time at ship or place be greater than the time at Greenwich, the ship or place is to the eastward of Greenwich; because the sun must have been on the meridian of the ship or place earlier than at Greenwich, and it was noon there before it was noon at Greenwich; and of course the day at ship or place commenced first, as the earth revolves from west to east, as has been already mentioned; this gives the sun an apparent motion from east to west. Hence it appears, that to find the longitude of any place, from another given one, as Greenwich, we must find the time of the day at each place: take the difference between these two times, and turn it into degrees and minutes, by allowing fifteen degrees for every hour, one degree for every four minutes; and one mile for every four seconds of time. The time at ship may be found from an observation of the sun's altitude, in the day time, or from au altitude of a known fixed star in the night, by rules which are given in the Epitomes of Navigation. For finding the time at the first meridian when at sea, many methods have been proposed; but two only have been found to perform it with reasonable accuracy; one is by observing the distance of the moon from the sun or fixed star, and the other is by means of a time-keeper.

The angular distance between the moon and sun, or moon and star, alters at about an average of twelve degrees in the twenty-four hours. It is manifest that the distance of the moon from the sun or star, cannot, under any other meridian, at noon, or any other time, there immediately deduced from observation, be the same as at noon; or the same time deduced from observation at Greenwich.

Suppose any distance of the moon from the sun or star, at any hour, under the meridian of Greenwich, say at noon; when it is noon in longitude ninety degrees west, it will be six hours.

3

Of the principle on which the Longitude is obtained. past noon at Greenwich; and the moon will have moved three degrees either further from, or nearer to the sun or star, accord. ing as the angular distance is increasing or decreasing; therefore, supposing the moon's daily motion to be just twelve degrees, it will be by proportion as twelve degrees motion of the moon is to twenty-four hours, so is three degrees to six hours; the difference of time between the two meridians, which, turned into degrees, make ninety west longitude; but when it was noon ninety degrees in east longitude, it wanted six hours of noon at Greenwich. The moon's distance from the sun, and such stars as are given in the Nautical Almanac, are in that work calculated as near the truth as possible, by the best tables, to every three hours, for the meridian of Greenwich; and by proportions, the distance may be found to any minute; consequently, if their distance under any other meridian is exactly determined, the longitude of the place may be found nearly. The greatest obstacle of this method of determining the longitude at sea, is, the difficulty of clearing the observed distance from the effect parallax and refraction; by these are many methods for clearing the observed distance from the effects of parallax and refraction. That which is given in this work is short and easy; it is of my own invention, and I have made use of it, in manuscript, during many years, at sea.

Formerly the longitude was reckoned from the island of Faro, the most westward of the Canary Islands; because it was the most westwardly land that was known when that practice was adopted; and the longitude was reckoned wholly eastward up to three hundred and sixty degrees. The Dutch, and Germans, and some others, still reckon their longitude in this manner from the meridian of the Peake of Teneriffe.

'The Spaniards, in sailing westwardly by Cape Horn, when they discovered the Philippine Islands, lost the greater part of twenty-four hours. In consequence of this, some of the inhabitants of Manilla, in the island of Laconia, keep Monday, believing it to be Sunday, to this day.

The following figure is a representation of the earth, on which are marked off the degrees and miles corresponding to the hours and minutes.

On it is also represented a ship sailing round the globe on the equator or any parallel of latitude; as every parallel is equally divided into three hundred and sixty degrees, which is the circumference of the earth.

Starting eastward from the meridian of Greenwich, and sailing one hundred and eighty degrees (no land being supposed to intercept her course) she has performed one half the circumference of the globe, and finds herself again on the meridian of Greenwich. Passing that meridian, she changes her longitude

from east to west; and the longitude is continually decreasing, until she again arrives at the meridian of Greenwich, or her starting point.

In sailing eastward, therefore, and performing the circumference of the earth, it is evident that for every fifteen degrees she sails, the sun will appear to her on the meridian one hour sooner than at Greenwich; consequently the ship as represented at one hundred and eighty degrees, has gained twelve hours, or it will be noon with her when it is midnight at Greenwich. It follows of course, that, having gone completely around the globe; in other words, arrived at Greenwich; she has gained one day; so that if she arrived on Sunday, it would be Monday by ship

account.

The contrary takes place when sailing westward; as represented (Plate I. fig. 1. and 2.) In performing three hundred and sixty degrees she loses one day; or, arriving on Sunday, it will be Saturday by ship account.

If two ships start from the meridian of Greenwich, and one sail east, the other west, until they both meet on the meridian of Greenwich, having both sailed completely round the globe; they will differ two days in their account.

On the Revolution of the Moon round the Earth.

THE moon makes her revolution round the earth in twentynine days, twelve hours, forty-four minutes, and three seconds;* that is from new moon to new moon; and in that three hundred and sixty degrees being performed, it will average about twelve degrees in twenty-four hours, about half a degree per hour, or two miles in four minutes, which four minutes agrees with one degree of longitude, and two seconds of distance will make one mile of longitude.

As the moon revolves round the earth, and follows the earth round the sun, at the new moon she is between the sun and the earth; the side, therefore, next us is in total darkness; except the light reflected on her from the earth, which we cannot perceive. As she becomes more enlightened, the angle she

* The sun advances almost one degree in the ecliptic in twenty-four hours the same way the moon moves, therefore the moon, by advancing thirteen degrees and one-sixth in that time, goes little more than twelve degrees from the sun in twenty-four hours. Were it not for this correspondent motion, the moon would make her revolution round the earth in about twenty-seven days and eight honrs, as her revolution in her orbit is made from a fixed star to the same star again in twenty-seven days and eight hours,

makes with the sun will be the observed distance, which you get on the sextant in measuring the distance. As she advances eastwardly, the surface towards the earth becomes enlightened; and when she is ninety degrees east of the sun, which will be about seven and a quarter days, she will come to the meridian about six o'clock in the evening, having the appearance of a bright semi-circle. As she advances still to the eastward, she becomes more enlightened, and, in about fourteen days and a half, she will be on the meridian at midnight; being diametrically opposite to the sun, and will appear a complete circle, or it is said to be full moon. The earth is now between the sun and moon, and that half of her surface which is constantly turned towards the earth, is wholly illuminated by the direct rays of the sun; whilst that half which is never seen from the earth is involved in complete darkness.

The reason why one side is constantly turned towards the earth is because she revolves on her own axis in the same time that she performs her revolution round the earth.

The moon, continuing her progress eastwardly, becomes deficient in her western edge; and about seven days and eight hours from the full she is again ninety degrees from the sun, and appears a semi-circle, with the convex side to the sun. Moving still eastwardly, the deficiency of her western edge becomes still greater; and then her convex or round side is turned to the east, and her horns towards the west; and in fourteen days and a half from the full moon she has again overtaken the sun. This period being twenty-nine days and a half, or a little more, the convex or well defined side is always turned towards the sun, and the horns of the moon will appear to the east or left hand of the spectator. This happens in north latitude from the new to the full moon; and the convex edge will appear to the east, from the full moon to the new, and her irregular side to the west or right hand. In south latitude the contrary takes place. By paying attention to the above, you will know what side of the moon to bring the star in contact with; as when she is nearly full it appears dubious which is her defined edge: but this, however, is a sure criterion.

The moon is subject to a small variation called the libration of the moon; so that she sometimes turns a little more of her one side or face toward the earth, and sometimes a little more of the other.

On Parallax.

AS beginners will require an explanation of the parallax, I have endeavoured to elucidate its meaning as much as possible, by plate II. figure 1.

It is necessary to premise that astronomers take their calculations from the centre of the earth; so that it is evident that the parallax must be allowed on those calculations where it is required. Then

Suppose a spectator at the centre of the earth, will see the moon in her true place, whilst to a spectator on the surface she will always appear lower. The moon appearing among the stars, although she is nearer by an immense distance; the spectator on the surface will see her at A (plate II. fig. 1.) whilst the one supposed at the centre will see her at B. (plate II. No. 1.) The difference between A and B, No. 1, is the moon's parallax in altitude, and the difference between A and B, No. 2, is her horizontal parallax.

The moon's parallax is greater when she is in the horizon, and decreases until she reaches the zenith, where she has no parallax, and then the spectator on the surface will see her in a direct line with the one at the centre.

As the parallax always makes the objects appear lower, and the refraction makes them appear higher than they really are, it follows that to obtain the true altitude of the moon, the refrac