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20° 28° 36° 44° 50° 56° 64° 72° 80°

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20° 28° 36° 44° 50° 56° 64° 72° 80°

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On the cause of the Sun and Moon's apparent Diameter varying.

The cause of the semi-diameter of both sun and moon varying are as follows:

The orbit of the earth is an ellipse, and in whose foci is the sun; therefore in a year, or one revolution of the earth, it will be at its least and greatest distance from the sun.

The moon's semi-diameter varies considerably during its monthly revolution round the earth. The semi-diameter of the sun is set down in page third, of the month of the Nautical Almanac, is the greatest when nearest the earth, that is, when he is in his perihelion, and least when farthest from it, or in his aphelion. The moon's semi-diameter is effected by reason of her orbit being an ellipse, being greatest when she is in her perigee, or when nearest the earth; and least when in her apogee, or farthest from the earth. See plate V. fig. 1 and 2.

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The moon has also an apparent augmentation as she approaches the zenith. In the Epitome of Navigation, called augmentation of the moon's semi-diameter, when she is in the zenith, she is a semi-diameter of the earth nearer the spectator, than when she is in the horizon. Let the arch H Z, plate VI. fig. 3. represent the track in which the moon rises from the horizon to the zenith; this arch being at an equal distance from the earth's centre E. A spectator placed at S, on the surface, will have the moon a semi-diameter of the earth nearer to him than when she is in the horizon, which will be perceived by measur ing the distance from S to H, being a semi diameter of the earth greater than the distance from S to Z.

I shall now proceed to treat of the semi-diameters of the sun and moon, as used with the observed distances of the sun and moon, or of the moon and a star.

As the edges of the sun and moon cannot be made a fixed point for the determination of their apparent distance, on account of the augmentation, or increase and decrease of diameter; therefore the centres are considered to be brought in contact, by allowing the semi-diameters. The side of the moon nearest the sun being always enlightened by him, therefore the nearest limbs of the sun and moon are always taken in measuring the distance, and consequently, the semi-diameters of sun and moon are always additive.

This will be better illustrated by the figures 1 and 2, Plate VI.

Fig. 1. Fig. 2.

O

As the diameters of the sun and moon are not always the same, allowance has been made; and the semi-diameter of the moon, for noon and midnight, is given in the Nautical Almanac, page 7. By figures 1 and 2, it is plain that the centres of the sun and moon are not in contact by a semi-diameter of each; the semi-diameters therefore being added, they are reduced to their true centres.

The star, however, is sometimes on the defined side, and sometimes on the broken side; the moon's semi-diameter therefore is sometimes additive, and sometimes subtractive. Fig. 3, represents the nearest

limbs of the star and moon in contact; here the moon's semi-diameter is additive. The star being small no semi-diameter is allowed on it.

Fig. 4, shows the star taken from the broken side of the moon, and brought in contact

with the round or de

fined side. There the distance is

Fig. 3.

Fig. 4.

semi-diameter of the moon

too much, which of course must be subtracted.

Of the Index Error.

THE rules for adjusting the sextant are laid down in every Epitome of Navigation, I shall only add a few observations on the method of obtaining the index error with as much facility as possible, as, during my long practice at sea, I have had occasion to notice several young men, who thought they had learned the theory of lunar observations, but have nevertheless called on me to explain to them the method of getting the index error. I have, therefore, endeavoured, by the following method, to make it as plain as possible.

Set the index of the sextant at 0; screw in the telescope, and turn down the screens, to take off the glare of the sun; look at the sun through the telescope, and move the index forward until the edges of the direct and reflected images of the sun be in contact; then read off the miles and seconds. Move the index back until the contrary edges of the sun come in contact, and

read off the miles and seconds: half the difference of the two readings will be the index error.

If the sun's diameter should measure more on the arch than on the extra arch, it shows that the arch measures too much; the half difference therefore must be subtracted from the distance; but if the sun's diameter on the arch measures less than on the extra arch, the arch measures too little, and the half difference must be added to the observed distance.

If both the diameters should be taken on either the arch or the extra arch, the half sum will be the index error, and is additive, or subtractive accordingly.

We will suppose the index brought toward you, until the nonius on the index passes the first twenty miles on the extra arch, rather more than midway between twenty and forty; then observe on the arch where the miles cut; suppose at eight, and falling in between twenty and forty, I subtract eight from forty, leaving thirty-two miles on the extra arch; now, admitting that I have measured the diameter on the arch, and have found it to be 31' 30", the difference is 30", and half is 15", the index error, to be added to the observed distance, as the arch measures less than the extra arch. If the O on the index had fallen in between forty and sixty, the miles where they cut on the arch would be subtracted from sixty, &c. In place of subtracting eight from forty, if the index is marked up to twenty, you may begin at twenty and count to the right hand; by the time you have counted twelve, you will find them cut: add twelve to twenty, and you have the same result. Should they cut at any number, more or less, you must act accordingly.

Sextants are differently graduated: if each degree is cut into three, or into divisions of twenty miles on the arch, and each mile on the index into four, or fifteen seconds to each mile; because the degrees on the arch are each cut into three, or divisions of twenty miles, the index counts as high as twenty miles, and no higher. But suppose a sextant graduated thus; the degrees on the arch, cut into four, or divisions of fifteen miles each, the index marked up to fifteen, and cutting to fifteen; now, if the nonius on the index cuts somewhere between thirty and forty-five on the extra arch, beginning to count from fifteen toward the right hand on the arch, supposing it cuts at 13' or 2' from the fifteen to the right, you may either add 2' to the 30" or subtract thirteen from forty-five, the result will be the same; thirty-two to be used as before.

Some sextants have each degree divided into five, of twelve miles each, some into six of ten miles each, and the indices are regulated accordingly; the beginner must therefore be guided by the preceding precepts.

By the following figures I have endeavoured to represent the

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