There were thus three powerful methods which converged upon a value close to 8.80 seconds. But to set against them was a method which we have not yet noticed.

The perturbations in the motions of other planets produced by the earth depend upon the mass of the earth, and from them that mass can be determined. There is further a well-known relation between the mass of the earth, the value of the gravitation constant, the length of the year, and the distance of the sun, from which the latter may therefore be derived when we know the others. Professor Newcomb had thus determined the parallax in two different ways, and had found two results agreeing closely among themselves, with mean 8·76 seconds, but differing widely from the others. No explanation of this divergence could be found. But the evidence was 3 to 1 in favor of 8.80 seconds, and 880 seconds was adopted in 1896 as the value to be used in all the almanacs from the beginning of this century.

It might well have been thought that the question would have been allowed to rest there for a while. At the end of a century of labor four principal results had emerged, and there was a majority of 3 to 1 in favor of 8.80 seconds. But there is a phenomenon, known in politics as the swing of the pendulum or the flowing tide, by whose operation a majority hardly won begins immediately to melt away. A like phenomenon appears to affect the solar parallax. We have seen how its adopted value has swung from 8.57 to 8.95 seconds, and back again to 8.85 and 8.80 seconds. Scarcely had the resolution of the Paris Conference been taken than the majority in favor of 8·80 seconds began to melt away. The beginning of the century had been chosen as an auspicious moment in which to make a change, without considering that there were at the end of the preceding century many investigations just then drawing to a close. The value of the aberration constant corresponding to 8.80 seconds is 20 478 seconds. Almost every determination of that constant published since 1896-and there are many-had come out above 2050 seconds, many of these a long way above. Further investigation of the parallactic inequality of the moon had not only altered the observed value of the inequality, but had modified the theoretical relation by which the parallax is deduced therefrom. The evidence for 8:80 seconds was giving way badly; and before the 1901 Almanac came into use we had this revised table propounded by one of the chief instigators of the adoption of 8.80 seconds. The majority was now 3 to 1 in favor of a value at least as low as 8.77 seconds.

I suppose that there will always be two opinions upon the question: Is the adopted value of the solar parallax to depend upon direct observation or are the indirect determinations through the constant of aberration, the parallactic inequality, and the mass of the earth to be allowed a weight in some proportion to their numbers? I take it that those of us who have determined the parallax by direct observations may not unnaturally look upon these indirect methods as interesting confirmations of our result if they agree with it, while if they differ there must be something wrong with them. But in the absence of a direct determination of overwhelming weight there must always be a feeling of uneasiness when one sees three or more results conspiring to deny the truth of one. And however that may be, it is certainly true that about the year 1898 there was a very general suspicion abroad that the value 880 seconds was too large.

At this moment there came a curious stroke of fortune. Doctor Witt, of the Urania Sternwarte, Berlin, was engaged in a photo

FIG. 1.-Eros campaign 1900-01. Distribution of Observatories.

graphic search for a minor planet which had long been lost. He failed, but found instead a minor planet for which one would willingly barter the remaining five hundred odd; a minor planet indeed, but moving in a most remarkable orbit, lying for the most part within that of Mars, very eccentric, considerably inclined to the elliptic, and approaching the earth on favorable occasions within about 15,000,000 miles. It was immediately recognized that here was a new opportunity for determining the solar parallax and that the determination must be made at once or left alone for thirty years, for a comparatively favorable opposition was due in 1900 and no more good ones till 1930 and 1937. At the meeting of the permanent committee which directs the making of the astrographic chart and catalogue of the whole sky it was resolved to invite a great cooperation of observatories to make a combined onslaught on the problem. The suggestion was readily taken up, with an alacrity, indeed, which might almost have suggested that the observatories concerned had nothing to do and were glad of a job, an imputation which is immedi

ately rejected when one finds that some of the most energetic participants were precisely those observatories that had their hands most full with the astrographic chart (fig. 1). By a cruel stroke of fate Sir David Gill at the Cape was compelled to remain a spectator of the work, for the planet came so far north that it was practically unobservable in the Southern Hemisphere, while in England we had the unique spectacle of a planet north of the zenith.

Figure 2, borrowed from Professor Wilson's articles in Popular Astronomy, shows very clearly the circumstances. Corresponding

FIG. 2.-Relative positions of Eros and Earth from Oct. 1, 1900, to Feb. 28, 1901.

EROS

positions of the earth and the planet are joined, and if we follow out in imagination the directions that these lines must have, remembering that the orbit of the planet is inclined 10° to that of the earth, we see that the planet described a loop at opposition, as all exterior planets do, but that the loop was of very unusual proportions (fig. 3).

To discuss in any detail the circumstances of the apparition and the way in which they can be utilized for a determination of the parallax would take too long. But we may get a good idea of a

fairly typical case by transplanting ourselves in imagination to the planet Eros on the evening of the 2d of December, 1900, armed with an imaginary telescope ridiculously out of proportion to the real size of the planet, which is probably not more than 20 miles in diameter (fig. 4). The earth is past inferior conjunction with the sun, and appears as a crescent. The North Pole of the earth is tilted toward us, and by the aid of this projection of the meridians and parallels of latitude we can with great ease trace the path of each observatory as it is carried round by the rotation of the earth and can measure from the scales the angular distance at any moment of an observatory from the center, or the distance between two observatories, which angular distances as seen from the planet are the precise equivalents of the parallactic diplacements of the planet as seen from the earth.

In the programme of observations there was one novel and promising feature the application of photography. With the exception of the transit of Venus observations, in which its success was not striking, photography had not been previously applied in a determination of the solar parallax, for the very good reason that in 1889, at the time of the opposition of Victoria, there was practically only one telescope in existence which was capable of taking photographs for exact measurement, that pioneer photographic equatorial made by the Brothers Henry at Paris. The fact that there were in 1900 eighteen photographic telescopes engaged in observing Eros shows how rapidly the equipment of astronomy has grown in the last few years. We were so fortunate at Cambridge as to have our new

photographic equatorial just completed and made to work. (I may remark parenthetically that it took longer to make the machine work than to build it, for when one embarks upon a large experiment and sets up an instrument, the first of its kind, built upon improved lines, one sets out upon a sea of troubles.)

The great advantage of the photographic method in such an undertaking must be sufficiently well known by you. It is, of course, this, that one is rendered very much more independent of continued fine weather. A photograph of the planet and the surrounding stars could be made in two or three minutes of actual exposure. Given an hour's break in the clouds, one could accumulate far more valuable

FIG. 4.-Meridians and parallels of latitude of the Earth as seen from Eros, Dec. 2, 1900 (negative). The blackened portion represents the bright crescent of the Earth, the planet being more than a month past opposition.

material than could be obtained in a whole night's visual observation, for the photograph once secured could be measured at leisure, by day or on cloudy nights.

Throughout Europe the skies of that winter were far from clear. I had the pleasure at Cambridge of sitting up from dusk till dawn for nearly three months on end and during that time had not half a dozen nights clear right through. Had I been making visual observations I should have done little; as things turned out I was able to get some five hundred exposures. The programme was to get four exposures per hour throughout the night, making a number of exposures on each plate, and moving the plate a little between each exposure.