198 



♦ KNO^A^LIl:DGE ♦ 



[Sept. 28, 1883. 



where we are this autumn, and commence anew the cycle 

 of changes I have indicated. Though these changes 

 amount to millions of miles, yet they are at the utmost 

 only a small fraction of the sun's distance. To superficial 

 observation the sun always seems the same size, and hence 

 there can be no great relative changes in its distance. 



There is no difficulty is understanding what is meant by 

 the average distance of the sun. To express the idea with 

 precision we may borrow the language of mathematics, and 

 say that the distance from the earth to the sun consists of 

 two parts — a large constant part and a small periodical 

 part. The important problem, and the difficult problem, 

 is the measurement of the large constant part. 



The early history of the subject is as easy to sketch as 

 the latter part is difficult. For fourteen centuries the 

 doctrines of Ptolemy were adopted on the distance of the 

 sun as on all other astronomical problems. The method 

 of Ptolemy might have succeeded if the sun's distance 

 could have been measured by thousands of miles instead of 

 by tens of millions. As matters stands, Ptolemy's method 

 was utterly inadequate to cope with the real difficulties of 

 the question. It led him to a conclusion which we now 

 know to have fallen far short of the truth. The real dis- 

 tance of the sun is twenty times as great as that which 

 Ptolemy deduced from his observations. But Ptolemy's 

 result was a great step in advance, notwithstanding the 

 tremendous error by which it was vitiated. It was, at all 

 events, an honest attempt to solve the problem by a direct 

 appeal to nature, and he succeeded so far as to demonstrate 

 the great truth that the sun is larger than the earth. 



It is somewhat remarkable that the first reasonable 

 approximation to the sun's distance was obtained by what 

 can only be described as a well-considered guess. The 

 illustrious Huyghens, in the seventeenth century, hazarded 

 a speculation, which seemed plausible at the time, and 

 which we now know to have been reasonably correct. 

 Huyghens compared the diameter of the planet Mars with 

 the sun. He compared the diameter of Venus with the 

 sun. The primitive instruments used were capable of 

 making these measures with some accuracy. Huyghens 

 knew that the earth was also a planet revolving outside 

 the path of Venus and inside that of Mars. Was it not 

 reasonable to assume that the bulk of the earth might be 

 comparable with that of its fellow planets, and inter- 

 mediate between the bulk of Venus and that of Mars 1 

 This assumption — and, of course, it was no more than an 

 assumption — gave the means of guessing the distance of 

 the sun, which was concluded to be about 100 million 

 miles. 



When guesswork came to be replaced liy measurement, 

 this estimate of the sun's distance was corrected. It was 

 found to be too large. It was amended first to 95,000,000 

 miles, then to 91,000,000 miles. This was subsequently 

 found rather too small, and it is now generally thought 

 that the sun's distance must be more than 92,000,000 

 miles but hardly so much as 9.3,000,000 miles. We 

 have here a range of one million miles. 



The problem in its present condition can now be dis- 

 tinctly stated. We require to determine the sun's dis- 

 tance accurately to within 100,000 miles, or, to speak in 

 round numbers, we desire to determine the distance of the 

 sun accurately to one-thousandth part of its total amount. 

 Is such a degree of accuracy obtainable ? I believe that 

 it is. I do not say that the problem has already been 

 solved with this precision, but an approach has been 

 made, and enough has been done to show that the 

 accuracy I have indicated may be attained. But this 

 margin is not really large when we reflect on the 

 stupendous magnitude of the sun's distance. 



A favourite illustration in books of astronomy states that 

 a journey to the sun in an express train running night and 

 day without stopping would consume about 300 years. 

 Before entering on such a journey it would, however, be 

 well to recall to mind a very interesting lecture on railway 

 accidents delivered by Sir F. Bramwell to this association a 

 few years ago. From the figures available he showed that 

 supposing a man made up his mind to be killed by a rail- 

 way accident it would usually be necessary for him to 

 travel day and night by express trains for 900 years before 

 he could be quite certain of achieving his purpose. One or 

 two return trips to the sun would no doubt suffice. 



There are certain conditions which any method of mea- 

 suring the sun's distance must fulfil. In the first place, it 

 is obvious that we cannot measure the distance directly. 

 We cannot take a tape and measure it as we would the 

 length of a field. We are compelled to resort to indirect 

 methods. In other words, instead of measuring the sun's 

 distance directly, we measure something else, from which 

 we derive the sun's distance by calculation. Whatever 

 that something else may be, there is one obvious condition 

 which must be fulfilled. The method by which the calcu- 

 lation is to be made must be absolutely unimpeachable. 

 The measurable quantity and the sun's distance must be 

 connected together by inexorable logic. The theory may 

 be difficult, but it must contain no trace of ambiguity or 

 of indefiniteness. No question of mere judgment or of 

 estimation should be admissible. The connection between 

 the two results must be as tight as a demonstration in 

 geometry. 



Another condition, alike obvious and important, must 

 be specified. Whatever be the measurable quantity, be 

 it the displacement of a planet, a lunar inequality, or the 

 co-efficient of aberration, our measurements are subject to 

 error. Sometimes the measured quantity will be too 

 large, sometimes it will lie too small. It is necessary to 

 have an organised plan of symmetrical measurement, so 

 that the number of measurements which are too great 

 shall be as nearly as possible equal to the number of 

 measurements which are too small. This condition is 

 secured by forethought in arranging the details, and by 

 vigilant suspicion of error from every conceivable source. 

 The observations or measurements can then be purged 

 from error by the well-known method of taking the mean. 

 The success of this operation depends upon the number 

 of observations that have been accumulated. It is, 

 therefore, desirable that any proposed method of finding 

 the sun's distance should admit of repeated application. 

 Once we are assured that the observations contain no pre- 

 disposition to be all too large or all too small, the mean 

 will afford a result vastly more accurate than the original 

 observations. It will do more than this — it will tell us 

 not only what the result is, but how far that result is 

 entitled to our confidence. 



Let me venture on an illustration to show how accu- 

 racy may be obtained from the mean of inaccurate results. 

 Suppose the question were to be asked this evening — What 

 o'clock is it 1 and suppose that every lady and gentle- 

 man were at the same moment to look at their watches, we 

 should have, I suppose, a thousand watches or so brought to 

 bear on the question. Perhaps I am not wrong in supposing 

 that, if the trial were made, the thousand watches would 

 exhibit some degree of variety. Some, no doubt, would be 

 right, some would be a minute or two wrong, some, perhaps, 

 would be five minutes wrong, or even more. But though 

 there may be a general tendency in watches to be wrong, I 

 believe no one can assert that as a whole they exhibit 

 any particular preference to being fast rather than slow. 

 There are, perhaps, some hundreds of watches in the 



