Rough Ways Made Smooth: A series of familiar essays on scientific subjects

by Richard A. Proctor

Now the case here imagined corresponds very closely with the circumstances of the recent attempt to correct our estimate of the sun's distance by Delisle's method. Our Government astronomers bethought themselves of this method as likely to give the best possible means for correcting, by observations of Venus in transit, the estimate of the sun's distance which had been deduced by Newcomb, and confirmed by Leverrier. While as yet their plans were not finally decided upon, reasons for questioning this conclusion were indicated to those officials by unofficial astronomers entertaining very friendly feelings towards them. Retaining, however, their reliance on the method thus called in question, they carried out their purpose, though fortunately making provision, very nearly sufficient, for the use of another method. Now, instead of the estimate of the sun's distance obtained from the observations by Delisle's method agreeing closely with Newcomb's mean value,—about 92,350,000 miles,—it exceeds this value by about a million miles. (See, however, note on the last page of this article.) According to various ways of considering the results sent in by his observers, the chief official astronomer obtains a mean value ranging from about 93,300,000 miles to about 93,375,000 miles. The last named estimate seems preferred on the whole; but if we take 93,350,000 miles, we shall probably give about the fairest final mean value. We have seen, however, that the results of observations by seven distinct methods give values ranging only between 92,250,000 miles and 92,850,000 miles,—the six best methods giving values ranging only between 92,250,000 miles and about 92,480,000 miles. The new value thus lies 500,000 miles above the largest and admittedly the least trustworthy of the seven results, 870,000 miles above the next largest, a million miles above the mean value, and 1,100,000 miles above the least value. It certainly ranges 500,000 miles above the largest admissible value from those seven trusted methods, dealt with most skilfully, cautiously, and laboriously, by such mathematicians as Newcomb and Leverrier.

Can we hesitate as to the inference we should deduce from this result? We need not for a moment call in question the skill or care with which the British observing parties carried out their operations. Nor need we doubt that the results obtained have been most skilfully and cautiously investigated by those to whom the work of supervision and of reduction has been entrusted. We need not even question the policy of devoting so large a share of labour and expense to the employment of a method held in little favour by most experienced Continental and American astronomers, and objected to by many in England, including some even among official astronomers. It was perhaps well that the method should have one fair and full trial. And it is certain that all who have taken part in the work have done their duty zealously and skilfully. Captain Tupman, to whom Sir George Airy, our chief official astronomer, entrusted the management of the calculations, has received, and justly, from his official superior, the highest commendation for his energy and discrimination. But beyond all manner of doubt the method employed has failed under the test thus applied to it. I do not say that hereafter the method may not succeed. Some of the conditions which at present render it untrustworthy are such as may be expected to be modified with the progress of improvement in the construction of scientific instruments. But as yet the method is certainly not trustworthy.

This might be safely concluded from the wide discrepancy between the new result and the mean of those before obtained. Yet if all the various observations made by the British observing parties agreed closely together, the circumstance, though it could hardly shake our inference on this point, would yet cause some degree of perplexity, since, of itself, it would seem to imply that the method was trustworthy. Fortunately we are not thus troubled by conflicting evidence. The indications of the untrustworthy nature of the method, derived from the discordance between the results obtained by it and those before inferred, are not a whit clearer, clear and convincing though they are, than are the indications afforded by their discordance inter se. The distance derived from northern and southern observations of the beginning of transit ought of course to be the same as that derived from northern and southern observations of the end of transit. If both sets of observations were exactly correct, the agreement between the results would be exact. The discordance between them could only be wide as a consequence of some serious imperfection in this method of observing a transit. But the discordance is very wide. The observations of the beginning of transit by the British parties give a distance of the sun exceeding by rather more than a million miles that deduced from the observations of the end of transit.

I am well assured that neither Continental nor American astronomers will accept the new estimate of the sun's distance, unless—which I venture to predict will not be the case—the entire series of transit observations should seem to point to the same value as the most probable mean. Even then most astronomers will, I believe, think rather that transits of Venus do not afford such satisfactory means of determining the sun's distance as had been supposed. This opinion, it is well known, was held by Leverrier, insomuch that he declined to support with the weight of his influence the proposals for heavy expenditure by France upon expeditions for observing the recent transit and the approaching transit of the year 1882.

I doubt whether many, even among British astronomers, will accept the new value. Already the Superintendent of the Nautical Almanac has given his opinion upon it in terms which cannot be regarded as favourable. 'It is well known,' he says (I quote at least from an article which has been attributed to him without contradiction on his part), 'that some astronomers have not expected our knowledge of the sun's distance to be greatly improved from the observations of the transit of Venus. Many, we can imagine, will regard with some suspicion' so great a value as 93,300,000 miles (I substitute these words for technical expressions identical in real meaning). 'Nevertheless, whatever degree of doubt might be entertained by competent authorities, it appears to have been felt by those immediately responsible for action, in different civilised nations where science is encouraged, that so rare a phenomenon as a transit of Venus could not be allowed to pass without every exertion being made to utilise it.'

Sir George Airy, very naturally, attaches more value to the result of the British expeditions, or at least of that part of the operations for which he was responsible, than others are disposed to do. In an address to the Astronomical Society, he expressed the opinion that 'the results now presented are well worthy of very great confidence.... Considering that the number of observers was eighteen, and that they made fifty-four observations, and considering also the degree of training they had, and their zeal, and the extreme care that was taken in the choice of stations, I think,' he said, 'that there will not be anything to compete with the value which has been deduced.' This is, as I have said, very naturally his opinion; and although ordinarily it is rather for the employers than for the employed to estimate the value of the results sent in, yet at least we cannot object to his just and generous praise of those who have worked under his orders.

Nevertheless, it must not be forgotten that on a former occasion when equal satisfaction was expressed with the result of a rather less costly but still a laborious and difficult experiment, the scientific world did not accept (and has since definitely rejected) the conclusion thus confidently advanced. I refer to the famous Harton Colliery experiment for determining the mass of the earth. The case is so closely analogous to that we are dealing with, that it will be instructive briefly to describe its leading features. Maskelyne, formerly the chief Government astronomer of this country, from observations of the effect of the mass of Mount Schehallien in deflecting a plumb-line, had inferred that the density of the earth is five times that of water. Bouguer from observations in Chimborazo, and Colonel James from observations on Arthur's Seat, had deduced very similar results. From pendulum observations on high mountains, Carlini and Plana made the earth's density very nearly the same. Cavendish, Reich, and our own Francis Baily, weighed the earth against two great globes of lead, by a method commonly known as the Cavendish experiment, but really invented by Michell. These experiments agreed closely together, making the earth's density about 5½ times that of water, or giving to the earth a mass equivalent to that which would be contained in 6,000 millions of millions of millions of tons. Now, from the Harton Colliery experiments, in 1854, in which the earth's weight was estimated by comparing the vibrations of a pendulum at the mouth of the mine with those of a similar pendulum at a depth of about 1,260 feet, it appeared that the earth's density is rather more than 6½ times that of water, corresponding to an increase in our estimate of the earth's mass by nearly 1,100 millions of millions of millions of tons, or by more than a sixth of the entire mass resulting from the most trustworthy former measurements. Sir G. Airy considered that 'this result will compete on at least equal terms with those obtained by other methods;' but nearly a quarter of a century has passed during which no competent astronomer has adopted this opinion, or even suggested any modification of the former mean estimate of the earth's mass on account of the unexpectedly large value deduced from the Harton experiment.

It appears to me probable that a similar fortune will attend the latest measurement of the sun's distance. But fortunately the matter will not rest merely on measurements already made. Many fresh measurements will be made during the next few years by methods already tried and not (like Delisle's transit method) found wanting. The recent close approach of the planet Mars was not allowed to pass without a series of observations specially directed to the determination of the sun's distance; and we know that observations of Mars are among the most advantageous means available for the solution of this difficult problem. It was indeed from such observations that the first really trustworthy measures of the sun's distance were obtained two centuries ago. The small planets which travel in hundreds between the paths of Mars and Jupiter have also been pressed into the service. And now so many of these are known that scarcely a month passes without one or other of them being favourably placed for the purpose of distance measurements. For this too their star-like discs make these bodies specially suitable.

The most probable inference respecting the results obtained by the British expedition is that their chief value resides in the evidence which they afford respecting the Delislean method of observation. They seem to demonstrate what had before been only surmised (though with considerable confidence by some astronomers), that this method cannot be relied upon to correct our estimate of the sun's distance. In the transit of 1882, which by the way will be visible in this country, we may be certain that other and more satisfactory methods of observation will be employed.