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Updated: May 11, 2025
The first thing to do is to multiply the earth's distance from the sun, which may be taken at 93,000,000 miles, by 206,265, the number of seconds of arc in a radian, the base of circular measure, and then divide the product by the parallax of the star. Performing the multiplication and division, we get the following: 19,182,645,000,000 / .018 = 1,065,702,500,000,000.
Using improved determinations of the longitude of the various stations, and a selective judgment in dealing with their materials, which, however indispensable, did not escape adverse criticism, they brought out results confirmatory of the no longer disputed necessity for largely increasing the solar parallax, and proportionately diminishing the solar distance.
At one time we are nearer to a particular region of the heavens by a distance equal to the whole diameter of the earth's orbit than we were six months previously, and hence there ought to be a change in the relative position of the stars; they should seem to separate as we approach them, and to close together as we recede from them; or, to use the astronomical expression, these stars should have a yearly parallax.
Lest, however, a sudden bound of four million miles nearer to the centre of our system should shake public faith in astronomical accuracy, it was explained that the change in the solar parallax corresponding to that huge leap, amounted to no more than the breadth of a human hair 125 feet from the eye!
This system which I have explained to you is called finding the star's parallax, and perhaps it is easier to understand when we put it the other way round and say that the hair's-breadth is what the whole orbit of the earth would appear to have shrunk to if it were seen from the distance of these stars!
This determination was held by Professor Todd to be entitled to four times as much confidence as any previous one; and if the solar parallax of 8·758" deduced from it by Professor Harkness errs somewhat by defect, it is doubtless because Glasenapp's "light-equation," with which it was combined, errs slightly by excess.
They were as much puzzled about the meaning of the word parallax as I had been with regard to the word algebra, and only learnt what it meant when Brewster went to study for the kirk in Edinburgh. They were both very devout; nevertheless, Brewster soon gave up the kirk for science, and he devoted himself especially to optics, in which he made so many discoveries.
To avoid the possibility of further objection he carried out this demonstration separately for each of the systems of Ptolemy, Copernicus, and Tycho. For the new method he noticed that great accuracy was required in the reduction of the observed places of Mars to the ecliptic, and for this purpose the value obtained for the parallax by Tycho's assistants fell far short of the requisite accuracy.
The expectation was not fulfilled. The apparent shift of position of a star as viewed from opposite sides of the earth's orbit, from which the parallax might be estimated, is so extremely minute that it proved utterly inappreciable, even to the almost preternaturally acute vision of Herschel, with the aid of any instrumental means then at command.
Attempts have been made to ascertain the distance of some of the stars by calculations founded on parallax, it being previously understood that, if a parallax of so much as one second, or the 3600th of a degree, could be ascertained in any one instance, the distance might be assumed in that instance as not less than 19,200 millions of miles!
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