The German measures with the heliometer gave apparently
concordant results, as follows:—
Transit of 1874: par.＝8·876″.
Transit of 1882: par.＝8·879″.
The combined result from both these methods is 8·857″, while the combination of all the contact observations made by all the parties gave the much smaller result, 8·794″. Had the internal contacts alone been used, which many astronomers would have considered the proper course, the result would have been 8·776″.
In 1877 Sir David Gill organized an expedition to the island of Ascension to observe the parallax of Mars with the heliometer. By measurements giving the position of Mars among the neighbouring stars in the morning and evening, the effect of parallax could be obtained as well as by observing from two different stations; in fact the rotation Planetary Parallaxes. of the earth carried the observer himself round a parallel of latitude, so that the comparison of his own morning and evening observations could be used as if they had been made at different stations. The result was 8·78″. The failure of the method based on transits of Venus led to an international effort carried out on the initiative of Sir David Gill to measure the parallax by observations on those minor planets which approach nearest the earth. The scheme of observations was organized on an extended scale. The three bodies chosen for observation were: Victoria (June 10 to Aug. 26, 1889); Iris (Oct. 12 to Dec. 10, 1888); and Sappho (Sept. 18 to Oct. 25, 1888). The distances of these bodies at the times of opposition were somewhat less than unity, though more than twice as great as that of Mars in 1877. The drawback of greater distance was, however, in Gill’s opinion, more than compensated by the accuracy with which the observations could be made. The instruments used were heliometers, the construction and use of which had been greatly improved, largely through the efforts of Gill himself. The planets in question appeared in the telescope as star-like objects which could be compared with the stars with much greater accuracy than a planetary disk like that of Mars, the apparent form of which was changed by its varying phase, due to the different directions of the sun’s illumination. These observations were worked up and discussed by Gill with great elaboration in the Annals of the Cape Observatory, vols. vi. and vii. The results were for the solar parallax π:—
| From Victoria, | π＝8·801″±0·006″. |
| From Sappho, | π＝8·798″±0·011″. |
| From Iris, | π＝8·812″±0·009″. |
The general mean result was 8·802″. From the meridian observations of the same planets made for the purpose of controlling the elements of motion of the planets Auwers found π＝8·806″.
In 1898 the remarkable minor planet Eros was discovered, which, on those rare occasions when in opposition near perihelion, would approach the earth to a distance of 0·16. On these occasions the actual parallax would be six times greater than that of the sun, and could therefore be measured with much greater precision than in the case of any other planet. Such an approach had occurred in 1892, but the planet was not then discovered. At the opposition of 1900–1901 the minimum distance was 0·32, much less than that of any other planet. Advantage was taken of the occasion to make photographic measures for parallax at various points of the earth on a very large scale. Owing to the difficulties inherent in determining the position of so faint an object among a great number of stars, the results have taken about ten years to work out. The photographic right ascensions gave the values 8·80″ + 0·007″ ± 0·0027″ (Hinks) and 8·80″ + 0·0067″ ± 0·0025″ (Perrine); the micrometric observations gave the value 8·806″±0·004 (Hinks).[1]
II. The velocity of light (q.v.) has been measured with all the precision necessary for the purpose. The latest result is 299,860 kilometres per second, with a probable error of perhaps 30 kilometres—that is, about the ten-thousandth part of the quantity itself. This degree of precision is far beyond any we can hope to reach in the solar parallax. The other element which enters into consideration is the time required for light to pass from the sun to the earth. Here no such precision can be attained. Both direct and indirect methods are available. The direct method consists in observing the times of some momentary or rapidly varying celestial phenomenon, as it appears when seen from opposite points of the earth’s orbit. The only phenomena of the sort available are eclipses of Jupiter’s satellites, especially of the first. Unfortunately these eclipses are not sudden but slowly changing phenomena, so that they cannot be observed without an error of at least several seconds, and not infrequently important fractions of a minute. As the entire time required for light to pass over the radius of the earth’s orbit is only about 500 seconds, this error is fatal to the method. The indirect method is based upon the observed constant of aberration or the displacement of the stars due to the earth’s motion. The minuteness of this displacement, about 20·50″, makes its precise determination an extremely difficult matter. The most careful determinations are affected by systematic errors arising from those diurnal and annual changes of temperature, the effect of which cannot be wholly eliminated in astronomical observation; and the recently discovered variation of latitude has introduced a new element of uncertainty into the determination. In consequence of it, the values formerly found were systematically too small by an amount which even now it is difficult to estimate with precision. Struve’s classic number, universally accepted during the second half of the 19th century, was 20·445″. Serious doubt was first cast upon its accuracy by the observations of Nyren with the same instrument during the years 1880–1882, but on a much larger number of stars. His result, from his observations alone, was 20·52″; and taking into account the other Pulkowa results, he concluded the most probable value to be 20·492″. In 1895 Chandler, from a general discussion of all the observations, derived the value of 20·50″. Since then, two elaborate series of observations made with the zenith telescope for the purpose of determining the variation of latitude and the constant of aberration have been carried on by Professor C. L. Doolittle at the Flower Observatory near Philadelphia, and Professor J. K. Rees and his assistants at the observatory of Columbia University, New York. Each of these works is self-consistent and seemingly trustworthy, but there is a difference between the two which it is difficult to account for. Rees’s result is 20·47″; Doolittle’s, from 20·46″ to 20·56″. This last value agrees very closely with a determination made by Gill at the Cape of Good Hope, and most other recent determinations give values exceeding 20·50″. On the whole it is probable that the value exceeds 20·50″; and so far as the results of direct observation are concerned may, for the present, be fixed at 20·52″. The corresponding value of the solar parallax is 8·782″. In addition to the doubt thrown on this result by the discrepancy between various determinations of the constant of aberration, it is sometimes doubted whether the latter constant necessarily expresses with entire precision the ratio of the velocity of the earth to the velocity of light. While the theory that it does seems highly probable, it cannot be regarded as absolutely certain.
III. The combined mass of the earth and moon admits of being determined by its effect in changing the position of the plane of the orbit of Venus. The motion of the node of this plane is found with great exactness from observations of the transits of Venus. So exact is the latter determination that, were there no weak point in the subsequent Mass of the Earth. parts of the process, this method would give far the most certain result for the solar parallax. Its weak point is that the apparent motion of the node depends partly upon the motion of the ecliptic, which cannot be determined with equal precision. The derivation of the distance of the sun by it is of such interest from its simplicity that we shall show the computation.
From the observed motion of the node of Venus, as shown by the
four transits of 1761, 1769, 1874 and 1882, is found
Mass of (earth+moon)＝Mass of sun332600.
- ↑ Mon. Not. R.A.S.(May 1909,) p. 544; ibid. (June 1910), p. 588·
