season; and light takes about sixteen minutes to traverse that distance. In the middle of November the eclipses of Algol are taking place eight minutes earlier than the average. In May, could we observe the star so near the sun, they would be found eight minutes behind their time; and a practised observer could, on a long series of observations, determine that inequality, with a total range of sixteen minutes, well within two minutes-that is to say, with an accuracy of about 10 per cent. We have then only to combine this quantity with the known velocity of light and we have a measure of the sun's distance. A mere curiosity in itself, it will serve to introduce us to some indirect ways of determining the distance of the sun which have, both practically and historically, a peculiar interest and importance.

At the present time we are in the thick of a new determination of the distance of the sun on a scale of operations greater than has been known before. More than fifty observatories of the Northern Hemisphere are engaged more or less deeply on the work, which has occupied a great many of us closely for the last four years and will give plenty of trouble to some of us for several years to come. Before we enter upon the consideration of the new method and the new opportunities we might well pause to answer the question, which is by no means superfluous, How does it come about that, at the end of the nineteenth century, which had seen attempts almost innumerable to measure the distance of the sun, the result was still so much in doubt that it was worth while to concentrate quite a large proportion of the total astronomical energy of the world upon a new attempt? I believe that we shall find some explanation of this fact if we examine the history of the various values of the solar parallax that were used in the Nautical Almanac during the nineteenth century.

A determination of the distance of the sun by direct observation of the sun itself is impracticable; the sun is too difficult an object to observe with any great accuracy; its distance is too great, and our base is too small for any method of direct trigonometrical survey to be possible. But we can in effect diminish its distance by substituting for it one of the planets, which can be more accurately observed, for when the distance of any one planet from the earth is known, the dimensions of other orbits follow by the application of Kepler's third law. And at the same time we can, as we shall see, secure the inestimable advantage that the measures to be made are relative and not absolute.

Let me digress for a moment to insist upon the importance of this distinction. If you wished to find the difference in latitude and longitude between your Institute and the trigonometrical point at Darland, you might determine the latitude and longitude of each and take the differences, or you might triangulate from one to the other.

One is an absolute method, the other a relative, and it is scarcely necessary to emphasize the difference in accuracy between the two. We shall see that, various as are the kinds of measurement which may be made to contribute to a knowledge of the solar parallax, they are all of them relative measurements. For example, one may observe the displacement of the planet Mars among the stars, as seen from a northern and a southern station-say Greenwich and the Cape-or one may observe the displacement of the place of Venus in transit across the sun from stations suitably chosen. In each case we are measuring the displacement as viewed from different stations of a near object with respect to one farther off, the displacement of Mars among the stars or of Venus against the sun. We have secured the advantages that the parallactic displacement to be measured is greater than that of the sun itself; that the objects to be observed, Mars or Venus, are better adapted for observation, and that the measures are relative.

In the middle of the eighteenth century Lacaille made observations of Mars at the Cape of Good Hope, which were compared with others made at various observatories in Europe, and he deduced a parallax of about ten seconds. In the same century there occurred the two famous transits of Venus of 1761 and 1769, which were very extensively observed, among others by Captain Cook on his celebrated expedition for that purpose to the South Seas. Many and various were the results obtained by different discussions of the observations, lying between eight and one-half and nine and one-half seconds, but decidedly less than the parallax found from Mars, and we find that at the beginning of the nineteenth century the Nautical Almanac adopted a value in round numbers, nine seconds, as the best that could be made of them.

Values of the solar parallax used in the Nautical Almanac during the nineteenth century.

1801-1833

1834-1869

Encke, from transits of Venus, 1761 and 1769.

1870-1881

Leverrier, from parallactic inequality of moon (1858). 1882-1900

Newcomb, from general mean of many methods (1867).

π

9"

8.5776"

8.95"

8.848"

In 1824 the German astronomer Encke submitted to a very searching examination the collected results of the transit of 1769 and deduced the result 85776 seconds, which, with its imposing train of decimals intact, was incorporated in our Nautical Almanac for 1834, survived until 1869, and was responsible for the statement, which many of us can remember in the schoolbooks, that the distance of the sun is 95,000,000 miles.

Meanwhile the attack upon the problem had been maintained in several different ways, and particularly by an indirect method that has many points of interest.

In the lunar theory there occurs, among the short-period perturbations to which the motion of the moon is subject, an inequality in a period of a month which depends upon the fact that the disturbing action of the sun is greater on that half of the moon's orbit which lies toward the sun than upon the other half. The result of this is that the moon is more than two minutes behind at first quarter and two minutes ahead at last quarter of the place which she would occupy were there no perturbation. It is clear that the magnitude of the effect must depend upon the ratio of the distances of the sun and moon from the earth; and since the effect is large, an oscillation either way of about one hundred and twenty-five seconds, this should give a strong determination of the solar parallax, provided that the moon can be observed with the required accuracy and that the theoretical relation between the perturbation and the solar parallax is firmly established. In 1858 Leverrier found in this way a value of 8.95 seconds; several other determinations supported this large value, and practically all the determinations made since 1830, however much they might disagree among themselves, agreed at any rate in one thing, that Encke's value was much too small. We find, therefore, that in the Nautical Almanac for 1870, published in 1866, Leverrier's value, 895 seconds, is adopted, and the official distance of the sun changed at one swoop from 95,000,000 to 91,000,000 miles.

But now preparations were in full swing for the observations of the transit of Venus of 1874 and 1882, which for many years had been eagerly awaited in the full expectation and belief that then, with all the manifold improvements in the arts of observation, in the invention of the heliometer and the application of photography to celestial measurement, the question of the solar parallax would be definitely settled. We can not do more than glance at the most beautiful and most complicated geometrical problems involved in the consideration of all the circumstances of a transit of Venus. But these two diagrams will show some of the circumstances of the very important phenomena, the times of internal contact at ingress and egress, the times when Venus is just completely on the sun and just about to begin to go off. Great preparations were made for observing these times of ingress and egress, and the results would undoubtedly have been successful had it not been for the cruel way in which the geometrical sharpness of the phenomenon is ruined by the lighting Showing the passage of the earth through the cones enveloping the sun and (Not reproduced.—EDR.)

Venus.

SM 1905-11

up of the atmosphere of Venus; there was no instant when tangency was perceptible, and, to be frank, the transit of Venus as a means of determining the distance of the sun was a failure. The photographic and heliometer observations had for various reasons met with no better success than the observations of contacts; there was no consistency about the results.

But just as the preparations for the transits were beginning in 1867 Prof. Simon Newcomb had published an elaborate discussion of the solar parallax based upon several different methods. With some of these we are already familiar, and I will call attention to one only, the last, which we have not as yet discussed.

_seconds 8-833 ._do____ 8-809 ._do_. 8.832

Newcomb, "Lunar equation of the earth
Powalky, "Transit of Venus, 1769 ".
Foucault's "Velocity of light," and Struve's "Aberration const."___do____ 8·860

Weighted mean__

_seconds__ 8:848

It is an effect of aberration that every star describes yearly in the sky an ellipse of which the semimajor axis is about 205 seconds, and this number is called the constant of aberration. It is the ratio of the velocity of the earth in its orbit to the velocity of light. When the constant is known and the velocity of light is known, the velocity of the earth in its orbit is known; and since the time of describing that orbit is also known, the size of the orbit and the distance of the earth from the sun follow immediately.

In 1876 it appeared then that there was strong evidence against the value 8.95 seconds; and without waiting for the results of the transit of Venus expeditions, the Nautical Almanac adopted for the while the value 8 848 seconds found by Newcomb from this galaxy of results which looked so accordant; and that value was first used in the Almanac for 1882, the year of the second transit.

But meanwhile Sir David Gill, who had observed the transit of 1874 at Mauritius and had made up his mind very definitely that no good would come out of the transit of 1882, had borrowed Lord Lindsay's heliometer and established himself on the island of Ascension to observe with the heliometer the opposition in 1877 of the planet Mars. Every night the observing station in Mars Bay was carried some six or seven thousand miles by the rotation of the earth and the planet thereby displaced among the stars by some forty seconds. The heliometer is by far the most refined instrument for the

visual measurement of distance from star to star; the observations extended over months instead of hours; they could be pursued without any of the disquieting feelings that a temporary breakdown would ruin everything; and they were brought to a successful end in a parallax of 8.78 seconds. But one doubt was cast upon the result. Was it possible that the red color of Mars had influenced the measures systematically? It could not be denied that the effect of the dispersion of the air, which gave the planet a blue fringe above that might be lost in the blue sky, and a red fringe below that would be indistinguishable from the red planet itself, might have produced some effect; and Sir David Gill resolved to try again, utilizing this time three minor planets farther away than Mars, with less parallax therefore but with disks so small that they were indistinguishable from stars.

In 1888 and 1889 five observatories, the Cape in the Southern Hemisphere, and Yale, Göttingen, Leipzig, and the Radcliffe Observatory at Oxford in the Northern Hemisphere, combined to observe the planets Victoria, Iris, and Sappho with the heliometer. The labor was immense. The observations proved to be so accurate that they demanded the use in a great part of the work of eight figure logarithms. When only a few years ago the whole work was published in two enormous volumes of Annals of the Cape Observatory, it might well have been thought that here was the last word of observation for many years. Yet we are are now attacking the problem with more energy than ever.

About ten years ago the end of the century was in sight, and there was a general impression abroad that it was time to set one's house in order and to make a good start on the 1st of January, 1901. The directors of the four nautical almanacs (the British, French, German, and American) resolved to meet in Paris in 1896, and with the help of certain distinguished advisers to agree upon a uniform set of constants to be adopted in all the Almanacs from the year 1901. Among these constants was the solar parallax. We may summarize the information which was at the disposal of the conference thus:

Solar parallax from

Gill's heliometer, minor planets
Constant of aberration of light__

Parallactic inequality of moon

Mass of earth from motion of node of Venus alone..

Mass of earth from secular variation of four inner planets_

Seconds.

8.802

8.799

8.791

8.762

8.759

Gill's heliometer measures of minor planets gave 8 802 seconds, and no other direct observational result could be compared with this; the transits of Venus were discredited even though some of the final results had not, and have not even now, been published. The most recent determinations of the constant of the aberration of light gave 8-799 seconds, the parallactic inequality of the moon, 8.794 seconds.