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ON THE MEANS WHICH WILL BE AVAILABLE FOR CORRECTING THE MEASURE OF THE SUN'S DISTANCE IN THE NEXT TWENTY-FIVE YEARS.

By the Astronomer Royal. From the Monthly Notices of the Royal Astronomical Society.

At the meeting of the Society, on the 8th of April, the Astronomer Royal gave an oral statement" on the means which will be available for correcting the measure of the Sun's distance in the next twentyfive years; the substance of which is contained in the following abstract:

The members of the Society will not be surprised at our looking so far in advance as twenty five years. The special opportunity, which will then present itself, is the last which will occur for nearly a century and a half from the present time. Some years of preparation will be required to enable us to secure the full advantages which may then be within our reach. But, with all possible care, it will be found that the risk of total failure is not inconsiderable. The recognition. of this danger naturally leads us to examine whether there will not be some earlier opportunity, of a different kind, for arriving at the same determination. And it will appear (in the judgment of the Astronomer Royal) that circumstances will be favorable, in the course of a few years, for obtaining a very good measure by the use of a different principle; less accurate, undoubtedly, in each of its individual applications than the method upon which reliance has usually been placed, but admitting of almost indefinite repetition, demanding no co-operation of distant observers, and requiring only that, in each instance, the observations which are to be compared be made with the same instrument and by the same observer (or with observers only so far changed that any personal equation would correct itself.) But even this method requires appliances, which cannot be constructed at the moment of observation; and it is necessary to study well, some time before the operations shall actually commence, what equipment, instrumental and literary, is desirable for giving the best chance of success. It will appear that we are not beginning too soon to direct our attention to these matters in the present year.

The measure of the Sun's distance has always been considered the noblest problem in astronomy. One reason for this estimation is, that it must be commenced as a new step in measures. It is easy to measure a base-line a few miles long upon this Earth, and easy to make a few geodetic surveys, and easy to infer from them the dimensions of the Earth with great accuracy; and, taking these dimensions as a base common to every subsequent measure, it is easy to measure the distance of the Moon with trifling uncertainty. But the measure of the Moon's distance in no degree aids in the measure of the Sun's distance, which must be undertaken as a totally independent operation. A second reason is that, in whatever way we attack the problem, it will require all our care and all our ingenuity, as well as the application of almost all our knowledge of the antecedent facts of as

tronomy, to give the smallest chance of an accurate result. A third reason is, that upon this measure depends every measure in astronomy beyond the Moon; the distance and dimensions of the Sun and every planet and satellite and the distances of those stars whose parallaxes are approximately known.

The received measure of the Sun's distance depends on the transits of Venus of 1761 and 1769, but mainly on the latter. Very careful discussions of these will be found in the two books published by Encke, and in a memoir of great value by Don Joachim Ferrers, printed in our own memoirs. On examining these it will be found that, though there is very close accordance in the results obtained by the different investigators and from the different transits, yet all investigators have expressed their doubts upon those results. In the transit of 1761 the result depended almost entirely upon an accurate knowledge of the differences of longitude of very distant stations, which are undoubtedly subject to great uncertainty. In the transit of 1769 it happened that the result depended almost entirely upon the observations made by Father Hell at Wardhoe; and to these great suspicion has attached, many astronomers having, without hesitation, designated them as forgeries. It is evidently desirable to repeat the practical investigation when opportunity shall present itself.

It is desirable, for clearness, to begin with a reference to the simplest operation for measuring distance by parallax; as applied, for instance, to the Moon. In figure 1, let A and B be two observatories on the same meridian, and at A let the star C be observed to touch the moon's limb, and at B let the star D be observed to touch the limb. (It will readily be understood that it is not essential that the observatories should be on the same meridian, if, as is in fact true, the Moon's apparent change of place can be exactly computed; nor is it necessary that the star touch the limb, if its angular distance can be very exactly measured.) After communication of the observations, the observer at A can measure the angle CAD. This angle differs from AMB by the angle A D B; but such is the distance of the stars that the angle A D B is in every case unmeasurably small; and A M B, therefore, is to be taken as equal to CAD. Now, the dimensions of the Earth being known, the length and direction of the line A B will be known, and the directions of A M, B M, are known; and therefore the length of A M, B M, or of any other line drawn from M to any other part of the Earth is easily found. A small error in the angle at M-that is, in the angle CA D-will produce a great error in the result for A Mor BM. With this caution the problem is completely solved.

1 Parallax of Moon.

Fig 1.

Ο

The question naturally rises, cannot the same method be applied to the Sun? Practically it cannot, for the following reasons: First, if errors of equal amount were committed in determining the inclination of the two lines AM, BM, for the Sun and for the Moon, their effects on the results would be enormously unequal. Thus, if the error were 2", it would produce an error of one hundred miles in the Moon's distance; but it would produce an error of sixteen millions of miles in the Sun's distance. Secondly, no stars can be seen for observation in apparent contact with the Sun's limb. Thirdly, if for want of observable stars we rely upon the instrumental measure of the angular elevation of the Sun's limb, we introduce the risk of instrumental errors, and (far worse) of errors in the computation of atmospheric refraction at the most unfavorable of all times of observation; and these are sufficient completely to vitiate the method.

In consequence of these difficulties, astronomers have always sought to determine the distance of the Sun indirectly by determining the distance of a planet, either by referring the planet's apparent. place to stars or by referring it to the Sun. In order to make this indirect process available, it is necessary to rely upon the antecedent determination of the proportion of the distances of the different planets from the Sun.

M

Fig. 2.

of Planets

E

It is a historical fact that, in the time of Copernicus and Keppler, when astronomers did not know whether the Sun's distance from the Earth was nearer to ten millions or to a hundred millions of miles, the proportion of the distances of the different Proportions of Orbits planets was known almost as exactly as at present. The first and rudest means of obtaining these proportions may be understood from figure 2. Commence with the assumption that the planets move in circular orbits. At the Earth E the apparent angle SE V, between the Sun and Venus, reaches, but does not overpass, a certain value. At this time, then, the angle EVS is a right angle. Therefore, in the triangle EV S, two angles are known, (namely, at E and at V,) and therefore the proportions of the three sides can be found, and two of these sides are the distances of the Earth and Venus from the Sun. Again, conceive that from the Earth E' the planet Mars is seen in the direction E' M'. By an acquaintance with the movements of Mars, derived from the observations of many preceding years, it is known that his position, as seen from the Sun, is in the direction S M'. The angular difference between these two directions is the angle S M' E'. Also we know the angle SE' M', the apparent angular distance of Mars from the Sun. Hence (as in the instance of Venus) we know two angles of the triangle S E' M', and therefore we know the proportion of its three sides, two of which are the distances of the Earth and Mars from the Sun. These, at first, are very rude determinations; but they aid materially

in introducing more exact ones. It is found by degrees that some alteration must be made in the inferred mean distances of the planets. from the Sun; it is found by degrees that this will not suffice, and that the supposition of different degrees of ellipticity and in different directions must be introduced; and at length, by infinite repetitions of the process of trial and error, of which scarcely a trace remains, except in the results, proportions of very considerable accuracy are obtained. In all this there is not the smallest reference to any of the absolute distances.

In figure 3 is shown the first practical inference from this knowledge of proportion of distances, as applied to a transit of Venus. Let Venus V. be so exactly between the Sun and the Earth that she can be seen upon the face of the Sun. An observer at A sees her upon the point S, and an observer at B sees her upon the point S'. Suppose the relation between the points S and S' to be such as to admit of record (the mode of making this record will be considered shortly,) and suppose, by means of that record, the angle SA S' is measured. The angle which we desire to obtain, in order to measure the Sun's distance is A S' B. Now, the proportion of our measured angle S A S' to the desired angle A S' B, is sensibly the same as the proportion of SV to A V, or as 72: 28, very nearly. Thus it appears that we measure a large angle in order to infer from it a small one: and this is the circumstance which is the most favorable of all for obtaining an exact result. (If we tried. to use a transit of Mercury in the same way, it would be found that the measured angle at A is to the required angle at S' in the proportion of 4 to 6 nearly, that is, that we measure a small angle in order to infer from it a larger; hence the transits of Mercury are inapplicable to the measure of the Sun's distance.) It is further to be considered that, in this reference of the apparent place of Venus to the disk of the Sun, no use is made of stars, and nothing depends on the difficulty of computing refraction, inasmuch as Venus and the Sun are, at the time of the observation, subject to the same refraction.

This method then appears likely to be excellent, provided that we possess a practical pro

Parallax of Venus referred to the Sun

Fig. 3.

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cess for measuring the angle S A S'. The mode of finding this will be our next consideration.

Egress

Fig. 4.

Sun's Disk reversed

In figure 4 is represented by a black line the path which Venus will appear

to describe across the Sun's disk in the transit of 1882, (reversed in regard of right and left, for the convenience of subsequent investigations) as seen from the centre of the Earth. For the present let us lay aside the consideration of the Earth's rotation. An observer in the northern portion of the Earth will see Venus describe, not the Angress black line, but the fainter line below the black line and parallel to it. An

observer in the southern portion of the Earth will see Venus describe the fainter line above the black line. The path seen by the southern observer is longer than that seen by the northern observer, and therefore occupies a longer time. Consequently the mere observation of the duration of the transit at these two stations would give information on the lengths of the two chords, and therefore would give means of computing the amount of separation of the two chords: and this apparent separation corresponds to the angle S A S' in figure 3. We have therefore all the means of computing the angle A S' B, and of inferring from it the Sun's distance; although, as may be imagined, the intervening calculations are sufficiently complicated.

But this is on the supposition that the Earth has no motion of rotation. Let us introduce the consideration of rotation, and see how it modifies the result.

Let us place ourselves over a globe with its south pole elevated to represent the illuminated portion of the Earth on the day of transit. By bringing the meridian of 135° E. to the vertical, we shall see the portion of the Earth turned toward the Sun at the ingress of Venus on the Sun's disk; by bringing the meridian of 75° E. to the vertical, we see that portion turned toward the Sun at the egress. The reversed form given to the solar disk in the cut (fig. 4) enables us to refer lines on the globe and on the diagram to corresponding geometrical directions, when we imagine ourselves to be looking through the diagram upon the globe.*

Now, fixing our attention on a northern station, in the United States of America for instance, it will be seen that the translation of this place by the movement of rotation carries it to meet the motion of Venus. Consequently it tends to shorten the duration of the transit. But by virtue of the northerly position of that station, the duration of transit is already shortened. Consequently, by combination of these two effects, the duration of the transit at the northern station is very much shortened.

Now, can we select a southern station such that the same rotation

* On account of the unavoidable omission of the diagrams representing the illuminated portions of the Earth at the times of ingress and of egress of the two transits, a few pas sages have been omitted, and equivalent ones introduced, using the globe as a means of illustration.-J. H.

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