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and so obtain the distance of the sun from the earth. In 1862, when Mars was in opposition, it came very near us, for it was in perihelion while the earth was in aphelion, so that its distance (as since ascertained) was only 126,300,000 - 93,000,000 = 33,300,000 miles. Observers at Greenwich and the Cape, and at various American and European observatories, calculated the distance of the planet from the north and south poles, as well as from several fixed stars, in precisely the manner just explained for obtaining the lunar parallax. The result of these observations fixed the solar parallax at 8.94".*
(2.) Calculation of solar parallax by observation of the transit of Venus.-In the figure, let A and B represent the positions of two observers stationed at
TRANSIT OF VENUS.
opposite sides of the earth. At the time of the transit, the one at A will see the planet Venus as a round black spot at V" on the sun's disk, while the one at B will see it at V'. The distance V'V" is the
* By the formula on page 302, we have
AS : AB :: Radius : Sin 8.94".
difference in the position of Venus as seen from the two stations on the earth. The distance AB is the diameter of the earth. The distance V'V" is as much greater than AB as VV" is greater than VA. The distance of Venus from the sun is known, by Prob. I., to be .72 that of the earth. The distance of Venus from the earth must be, then, 1.00 — 172 = .28. Hence, VV", the distance from the sun to Venus,= .72 : .28=2.5 times the length of AV, the distance of Venus from the earth. Therefore, V'V" is equal to 21 times AB, the earth's diameter, or 5 times the solar parallax. Knowing the hourly motion of Venus, it is only necessary for each observer to find when the planet's disk enters upon and leaves the sun's disk to determine the length of the path (chord) it traces. A comparison of the length and direction of these chords will give the length of V' V" in seconds of space.
The advantage of this method is, that as the distance V V" is two and a half times that of AB, an error in measuring that chord affects the solar parallax less than one-fifth.
Time of a transit of Venus.—This is an event of rare occurrence. It happens only at intervals of 8, 105}; 8, 1211, years, &c. Were the planet's orbit in the same plane as the ecliptic, a transit would take place during each synodic revolution; but as it is inclined about 31°, the transit can occur only when the earth is at or near one of the nodes at the same time with the planet, when in inferior conjunction. As the nodes
of Venus fall in that part of the earth's orbit which we pass in the beginning of June and December transits always occur in those months.
The transit of June 30, 1769, excited great interest King George III. fitted out an expedition to Tahiti, under the command of the celebrated navigator Capt. James Cook. In order to make the angle as great as possible, and so increase the length of the chords, or paths of the planet across the sun, astronomers were sent to all the most favorable points of observation—St. Petersburg, Pekin, Lapland, California, etc. The result of these calculations fixed the solar parallax at 8.58". This was considered accurate until lately, but has now ceased to have any value. The next transits will happen,
The first transit ever seen was witnessed by Horrox, a young amateur astronomer residing near Liverpool. His calculations fixed upon Sunday, Nov. 24, 1639 (O. S.)
He however commenced his watch of the sun on Saturday preceding. On the following day he resumed his observation at sunrise. The hour for church arriving, he repaired to service as usual. Returning to his labor immediately afterward, he says: “At this time an opening in the clouds, which rendered the sun distinctly visible, seemed as if Divine Providence encouraged my aspirations; when-oh
most gratifying spectacle! the object of so many earnest wishes—I perceived a new spot of perfectly round form that had just entered upon the left limb of the sun.”
The transits of Mercury are more frequent; but owing to the nearness of the planet to the sun, they are of little value in determining the solar parallax.
The difficulty of determining the solar parallax accurately will be seen, when one is told that the correction from the old value of 8.58" to the new one of 8.94", is a change in the angle equal to that which the breadth of a human hair would make when seen at a distance of 125 feet. Yet this reduces the estimated distance of the sun from 95,293,000 miles, to 91,430,000 miles.
4. TO FIND THE LONGITUDE OF A PLACE.—(1.) The solar method.—If the sailor can see the sun, he watches it closely with his sextant; and when it ceases to rise any higher in the heavens it is apparent noon. By adding or subtracting the equation of time (as given in his almanac), he obtains the true or mean noon. He then compares the local time thus obtained, with the Greenwich time as kept by the ship’s chronometer. The difference in time reduced to degrees, etc., gives the longitude.
(2.) The lunar method.—On account of the difficulty in obtaining a watch which will keep the exact Greenwich time through a long voyage, the moon is more generally relied upon than the chronometer.
The Nautical Almanac* is always published, for the benefit of sailors, three years in advance. It gives the distance of the moon from the principal fixed stars yhich lie along its path, at every hour in the night. The sailor has only to determine with his sextant the moon's distance from any fixed star, and then by referring to his almanac find the corresponding Greenwich time. By comparing this with the local time, and reducing the difference to degrees, etc., he obtains the longitude.
5. TO FIND THE LATITUDE OF A PLACE.—(1.) By means of the sextant find the elevation of the pole above the horizon, and this gives the latitude directly. (2.) In the same manner, determine the height of the sun above the horizon at noon. The sun's declination for that day (as laid down in the almanac), added to or subtracted from this gives the height of the equinoctial above the horizon. Subtract this from 90°, and the remainder is the latitude.
* It is pleasant to notice that the astronomer can predict with the utmost precision. He announces that on such a year, month, day, hour, and second, a celestial body will occupy a certain position in the heavens. At the time indicated we point our telescope to the place, and at the instant, true beyond the accuracy of any timepiece, the orb sweeps into view! A prediction of the Nautical Almanac is received with as much confidence as if it were a fact contained in a book of history. “On the trackless ocean, this book is the mariner's trusted friend and counsellor; daily and nightly its revelations bring safety to ships in all parts of the world. It is something more than a mere book. It is an ever. present manifestation of the order and harmony of the universe."