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The above are calculated from the mean place of the star as given in Loomis's "Practical Astronomy."

425. Fifth Method. By equal altitudes of a star.

If a theodolite or a transit with a vertical arc is at hand, the meridian may be run very accurately by observing a star when at equal altitudes before and after passing the meridian.

For this purpose select a star situated near the equator, and, having levelled the instrument with great care, take the altitude of the star about two or three hours before it passes the meridian, and notice carefully the horizontal reading. When the star is about as far to the west of the meridian, set the telescope to the same elevation, and follow the star by the horizontal motion until its altitude is the same as before, and again notice the reading.

Then if the zero is not between the two observed readings, take half their sum, and turn the telescope until the vernier is at that number of degrees and minutes: the telescope will then be in the meridian. If the vernier has passed the zero, add 360 to the less reading before taking the sum.

Thus, if the first reading were 150° 37' 30", and the 431° 2' 30" second 280° 25', the half sum

2

would be the reading for the meridian.

= 215° 31′ 15′′

Instead of taking the readings, a stake may be set up at any distance—say ten chains-in each observed course: then bisect the line joining the stakes, and run a line from the instrument to the point of bisection.

The mean of a few observations taken in this manner will determine the meridian with considerable precision.

SECTION II.

LATITUDE.

THE latitude of a place may be determined in various modes.

426. First Method.—By a meridian altitude of the Pole Star.

The altitude of the pole is equal to the latitude of the place. Take the altitude of Polaris when on the meridian, and from the result subtract the refraction taken from the following table. Increase or diminish the remainder by the polar distance of the star according as the lower or upper transit was observed: the result will be the latitude.

427. Refraction to be taken from the apparent latitude.

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428. Second Method.-Take the altitude of the star six hours before or after its meridian passage. The result, corrected for refraction, will be the latitude.

429. Third Method. By a meridian altitude of the sun.

Take the meridian altitude of the upper or the lower limb of the sun, and correct for refraction. The result,

increased or diminished by the semidiameter of the sun according as the lower or the upper limb was observed, will be the altitude of the sun's centre. (The apparent semidiameter of the sun is given in the American Almanac for every day of the year.)

To the altitude of the sun's centre, add his declination (taken from the same almanac) if south, but subtract it if north the result subtracted from 90° will give the latitude. Instead of the sun, a bright star, the declination of which is small, may be observed.

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430. If the exact direction of the meridian is not known, the telescope must be fixed on the body some time before it is south. As the sun or star approaches the meridian its altitude increases, and it will therefore rise above the horizontal wire. Move the telescope in altitude and azimuth so as to follow the body until it ceases to leave the wire. The reading will then give the observed meridian altitude. The altitude alters very slowly for some minutes before and after its meridian passage, thus affording ample time to direct the telescope accurately towards the object.

431. Fourth Method. By an observation of a star in the prime vertical.

Any great circle passing through the zenith is called a vertical circle. All such circles are perpendicular to the horizon.

That vertical circle which is perpendicular to the meridian is called the prime vertical: it cuts the horizon in the east and west points.

Level the plates of the transit or theodolite carefully, and direct the telescope to the east or west, so that it may move in the prime vertical or nearly so. Then, having selected some bright star which passes the meridian a little south of the zenith, (the declination of such a star is rather less than the latitude of the place,) observe the time of its crossing the vertical wire of the telescope before passing the meridian, and again, when in the west, after its meridian passage. Let

these times be called T and T'. Let the interval between T and T' be called x, which must be reduced to sidereal time by adding to the solar time 3 minutes 56.55 seconds for 24 hours, or 9.85 seconds per hour; also, let L be the latitude of the place, and D be the declination of the star. R. tan. D

Then

tan. L =

cos.x

Thus, for example, the transit of a Lyra over the prime vertical was observed July 1, 1855, at 10 h. 43 m. 4 sec., and again at 13 h. 3 m. 48 sec., mean solar time. Required the latitude, the apparent right ascension of the star (as given in the American Almanac) being 18 h. 32 m. 4 sec., and the declination 38° 39′ 0.4".

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Here the interval is 2 h. 20 m. 44 sec., solar time.

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432. Half the sum of the observed times is the time of meridian passage in mean solar time. If this is reduced to sidereal time and increased by the sidereal time of mean noon at the given place, the result should be equal to the right ascension of the star.

In the example before us the times of observation are

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Sidereal time, mean noon, at Greenwich 6 h. 35 m. 54 sec.

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8"

Error in position of the instrument

A slight error in the position of the instrument will make no appreciable error in the result. Hence, this method affords perhaps the best means of determining the latitude.

SECTION III.

TO FIND THE TIME OF DAY.

433. First Method.-IF a good meridian line has been run, the transit or theodolite may be placed in that line, and, being well levelled, the telescope, if adjusted by being directed to the meridian mark, will, when elevated, move in the meridian.

Observe the time that the western limb of the sun comes to the vertical wire, and also when the eastern limb leaves it. The mean between these will be the time that the centre of the sun is on the meridian, or apparent noon. Increase or diminish the observed time of the passage of the centre by the equation of time according as the sun is too slow or too fast, and the result will be the time of mean noon as given by the watch. The difference between this and twelve hours will be the error of the watch.

434. Second Method.-Calculate the time that a fixed star having but little declination will pass the meridian as directed for Polaris, Art. 415. Then the difference between the observed and the calculated time will be the error of the watch.

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