side of a large room.
Lastly, I would urge this general argument against a theory which seems to me to have even less to recommend it to acceptance than the faith in astrology.8 If it requires, as we are so strongly assured, the most costly observations, the employment of the heaviest guns (and “great guns” are generally expensive), twenty or thirty years of time, and the closest scrutiny and research, to prove that sun-spots affect terrestrial relations in a definite manner, effects so extremely difficult to demonstrate cannot possibly be important enough to be worth predicting.
NEW WAYS OF MEASURING THE SUN’S DISTANCE.
It is strange that the problem of determining the sun’s distance, which for many ages was regarded as altogether insoluble, and which even during later years had seemed fairly solvable in but one or two ways, should be found, on closer investigation, to admit of many methods of solution. If astronomers should only be as fortunate hereafter in dealing with the problem of determining the distances of the stars, as they have been with the question of the sun’s distance, we may hope for knowledge respecting the structure of the universe such as even the Herschels despaired of our ever gaining. Yet this problem of determining star-distances does not seem more intractable, now, than the problem of measuring the sun’s distance appeared only two centuries ago. If we rightly view the many methods devised for dealing with the easier task, we must admit that the more difficult—which, by the way, is in reality infinitely the more interesting—cannot be regarded as so utterly hopeless as, with our present methods and appliances, it appears to be. True, we know only the distances of two or three stars, approximately, and have means of forming a vague opinion about the distances of only a dozen others, or thereabouts, while at distances now immeasurable lie six thousand stars visible to the eye, and twenty millions within range of the telescope. Yet, in Galileo’s time, men might have argued similarly against all hope of measuring the proportions of the solar system. “We know only,” they might have urged, “the distance of the moon, our immediate neighbour,—beyond her, at distances so great that hers, so far as we can judge, is by comparison almost as nothing, lie the Sun and Mercury, Venus and Mars; further away yet lie Jupiter and Saturn, and possibly other planets, not visible to the naked eye, but within range of that wonderful instrument, the telescope, which our Galileo and others are using so successfully. What hope can there be, when the exact measurement of the moon’s distance has so fully taxed our powers of celestial measurement, that we can ever obtain exact information respecting the distances of the sun and planets? By what method is a problem so stupendous to be attacked?” Yet, within a few years of that time, Kepler had formed already a rough estimate of the distance of the sun; in 1639, young Horrocks pointed to a method which has since been successfully applied. Before the end of the seventeenth century Cassini and Flamsteed had approached the solution of the problem more nearly, while Hailey had definitely formulated the method which bears his name. Long before the end of the eighteenth century it was certainly known that the sun’s distance lies between 85 millions of miles and 98 millions (Kepler, Cassini, and Flamsteed had been unable to indicate any superior limit). And lastly, in our own time, half a score of methods, each subdivisible into several forms, have been applied to the solution of this fundamental problem of observational astronomy.
I propose now to sketch some new and very promising methods, which have been applied already with a degree of success arguing well for the prospects of future applications of the methods under more favourable conditions.
In the first place, let us very briefly consider the methods which had been before employed, in order that the proper position of the new methods may be more clearly recognized.
The plan obviously suggested at the outset for the solution of the problem was simply to deal with it as a problem of surveying. It was in such a manner that the moon’s distance had been found, and the only difficulty in applying the method to the sun or to any planet consisted in the delicacy of the observations required. The earth being the only surveying-ground available to astronomers in dealing with this problem (in dealing with the problem of the stars’ distances they have a very much wider field of operations), it was necessary that a base-line should be measured on this globe of ours,—large enough compared with our small selves, but utterly insignificant compared with the dimensions of the solar system. The diameter of the earth being less than 8000 miles, the longest line which the observers could take for base scarcely exceeded 6000 miles; since observations of the same celestial object at opposite ends of a diameter necessarily imply that the object is in the horizon of both the observing stations (for precisely the same reason that two cords stretched from the ends of any diameter of a ball to a distant point touch the ball at those ends). But the sun’s distance being some 92 millions of miles, a base of 6000 miles amounts to less than the 15,000th part of the distance to be measured. Conceive a surveyor endeavouring to determine the distance of a steeple or rock 15,000 feet, or nearly three miles, from him, with a base-line one foot in length, and you can conceive the task of astronomers who should attempt to apply the direct surveying method to determine the sun’s distance,—at least, you have one of their difficulties strikingly illustrated, though a number of others remain which the illustration does not indicate. For, after all, a base one foot in length, though far too short, is a convenient one in many respects: the observer can pass from one end to the other without trouble—he looks at the distant object under almost exactly the same conditions from each end, and so forth. A base 6000 miles long for determining the sun’s distance is too short in precisely the same degree, but it is assuredly not so convenient a base for the observer. A giant 36,000 miles high would find it as convenient as a surveyor six feet high would find a one foot base-line; but astronomers, as a rule, are less than 36,000 miles in height. Accordingly the same observer cannot work at both ends of the base-line, and they have to send out expeditions to occupy each station. All the circumstances of temperature, atmosphere, personal observing qualities, etc., are unlike at the two ends of the base-line. The task of measuring the sun’s distance directly is, in fact, at present beyond the power of observational astronomy, wonderfully though its methods have developed in accuracy.
We all know how, by observations of Venus in transit, the difficulty has been so far reduced that trustworthy results have been obtained. Such observations belong to the surveying method, only Venus’s distance is made the object of measurement instead of the sun’s. The sun serves simply as a sort of dial-plate, Venus’s position while in transit across this celestial dial-plate being more easily measured than when she is at large upon the sky. The devices by which Halley and Delisle severally caused time to be the relation observed, instead of position, do not affect the general principle of the transit method. It remains dependent on the determination of position. Precisely as by the change of the position of the hands of a clock on the face we measure time, so by the transit method, as Halley and Delisle respectively suggested its use, we determine Venus’s position on the sun’s face, by observing the difference of the time she takes in crossing, or the difference of the time at which she begins to cross, or passes off, his face.
Besides the advantage of having a dial-face like the sun’s on which thus to determine positions, the transit method deals with Venus when at her nearest, or about 25 million miles from us, instead of the sun at his greater distance of from 90½ to 93½ millions of miles. Yet we do not get the entire advantage of this relative proximity of Venus. For the dial-face—the sun, that is—changes its position too—in less degree than Venus changes hers, but still so much as largely to reduce her seeming displacement. The sun being further away as 92 to 25, is less displaced as 25 to 92. Venus’s displacement is thus diminished by 25/92nds of its full amount, leaving only 67/92nds. Practically, then, the advantage of observing Venus, so far as distance is concerned, is the same as though, instead of being at a distance of only 25 million miles, her distance were greater as 92 to 67, giving as her effective distance when in transit some 34,300,000 miles.
All the methods of observing Venus in transit are affected in this respect. Astronomers were not content during the recent transit to use Halley’s and Delisle’s two time methods (which may be conveniently called the duration method and the epoch method), but endeavoured to determine