DISTANCE OF THE SUN.
ANE1V Estimate of the Sun's Distance reminds us that this important astronomical element still remains unsatisfactorily determined. The discovery made, not many years ago, that the accepted value of the sun's distance was some three millions of miles too great, was reluctantly admitted by astronomers. It was easy, indeed, to show that they might justly be proud of having determined the sun's distance even within this apparently enormous range of error. But none the less, it was unpleasant to have to admit that they had largely over-valued the accuracy of their calculations—or rather of the observations on which their estimates had been founded.
That astronomers should have been in error on this point, and yet that astronomy should be spoken of as the most exact of the sciences, may seem perplexing to those who are not familiar with the true quality of that exactness which is sought after by astro- nomers. It resembles in a sort the accuracy of the horologist's art. We know that this is in no way dependent on the scale upon which clocks or watches may be constructed. The great bands which sweep over the dial-plate of a cathedral clock, and the delicate hands of a pocket chronometer, are equally well adapted to indicate the flight of time. And, in like manner, the scale of the Solar system might have been many times greater or many times less than it actually is, and yet the planets would have swept on their stately courses precisely as at present.
It may not be amiss to point out briefly what is the nature of the problem astronomers have sought to solve :-
Imagine a prisoner confined within a room which has a single circular window, only six inches in diameter. Suppose him to be provided with accurate instruments, and conceive that directly in front of the window, and somewhat more than a mile off, there is an object—say a steeple—whose disance he wishes to determine. Then a moment's consideration will show that whatever tha accuracy of his instruments, and whatever his skill in using them, yet, with his base line of only six inches, he could not expect an error of less than at least half a mile in his result.
The position of such a prisoner corresponds closely with that of the inhabitants of the earth, limited to their little globe, less than 8,000 miles in diameter, as a base from which to estimate the distance of the sun, upwards of ninety millions of miles away.
But in some respects our prisoner is better situated than the inhabitants of the earth. A single observer, using, in one place, a single set of instruments, is not troubled with the numerous important considerations which affect the value of the work done in two observatories situated on opposite sides of the earth. Different observers—each with his peculiar, perhaps variable, "personal equation "—must be employed ; or else a single observer, having completed a series of observations in one hemisphere, must commence a new series (when, perhaps, important changes may have occurred in his observing qualities) in another. Different instruments, each with its peculiar " instrumental equation," must be employed, or else the same instrument must be transported at the risk of all sorts of changes in its performance from one to another hemisphere of the globe. Differences of climate have also to be considered. And, in fact, the attempt to obtain any approach to a knowledge of the sun's distance simply by making use of a base line on our small earth may be pronounced absolutely hopeless.
Now, to return for a moment to our prisoner. If there were objects intervening between him and the steeple, and if he had by any means obtained a certain knowledge of the relative distances of the steeple and of these objects, it is clear his power over his problem would be greatly increased. Let the reader look from opposite sides of a window at objects unequally distant but nearly in the same direction, and he will immediately see the sort of use our prisoner might make of the knowledge we have spoken of. He may not, indeed, know the exact mathematical principles involved in the problem, nor would this be the place to explain them, but he will see that there is something tangible and appre- ciable in the new form of observation.
Now, the observer on earth has, at long intervals, an opportunity of grasping at some such aids as we have conceived available to our prisoner. Venus and Mercury occasionally pass between the Earth and Sun, and by observing their transits carefully from differ- ent parts of the earth, astronomers have been able to gain juster conceptions of the sun's distance than they could otherwise have obtained. All the difficulties, however, which we have mentioned above are involved in the solution of this form, also, of the problem.
Yet, with no other aid, and with the comparatively inefficient instruments of the last century, astronomers managed to determine the sun's distance with what may fairly be termed wonderful accuracy—certainly within one-thirtieth part of the true distance. This is as if our prisoner should determine the steeple's distance within fifty or sixty yards.
But the astronomers of the present day, using a variety of delicate methods, into whose nature we need not here enter, have arrived at more trustworthy results. It is hoped that during the transits of Venus in 1874 and 1882 these results may be improved upon. Yet, even now, we may note as a great achievement of modern science the following series of values, differing little (pro- portionately) among themselves, though well separated from the old determination, 95,274,000 miles :—The German astronomer Hansen, making use of a peculiarity in the moon's motion as a guide, was led to the value 91,700,000 miles ; Stone, of the Greenwich Observatory, was led by the same means (only the peculiarity was estimated by other instruments), to the value 92,400,000 miles. Winnecke and Stone, from observations of Mars, obtained, respectively, the values 91,300,000 miles and 91,500,000 miles. Estimates founded on a comparison of the velocity of light as determined by the experiments of Fizeau and Foucault with the astronomical determination, give a value of 91,500,000 miles. A method employed by Leverrier, and founded on a peculiarity of the earth's motion, gives 91,600,000 miles. And lastly, the new estimate obtained by Mr. Simon Newcombe (U. S.), founded on observations of Mars in 1862, make the sun's distance 92,400,000 miles. The mean of these values is 91,771,000 miles, or nearly 630,000 miles less than the greatest estimate.
From the above results it will be seen that astronomers over- estimated the accuracy of their calculations, when they expressed the sun's distance as if it were known correctly within a thousand miles. But we may justly wonder at the results recorded. Returning to our illustrative prisoner, it is as if his estimates of the steeple's distance differed from their mean by less than four- teen yards.
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