It is a memorable and a curious speculation to reflect, upon how slight grounds the doctrine of "thousands and thousands of suns, multiplied without end, and ranged all around us, at immense distances from each other, and attended by ten thousand times ten thousand worlds," mentioned in the beginning of this Essay, is built. It may be all true. But, true or false, it cannot be without its use to us, carefully to survey the road upon which we are advancing, the pier which human enterprise has dared to throw out into the vast ocean of Cimmerian darkness. We have constructed a pyramid, which throws into unspeakable contempt the vestiges of ancient Egyptian industry: but it stands upon its apex; it trembles with every breeze; and momentarily threatens to overwhelm in its ruins the fearless undertakers that have set it up.
It gives us a mighty and sublime idea of the nature of man, to think with what composure and confidence a succession of persons of the greatest genius have launched themselves in illimitable space, with what invincible industry they have proceeded, wasting the midnight oil, racking their faculties, and almost wearing their organs to dust, in measuring the distance of Sirius and the other fixed stars, the velocity of light, and "the myriads of intelligent beings formed for endless progression in perfection and felicity," that people the numberless worlds of which they discourse. The illustrious names of Copernicus, Galileo, Gassendi, Kepler, Halley and Newton impress us with awe; and, if the astronomy they have opened before us is a romance, it is at least a romance more seriously and perseveringly handled than any other in the annals of literature.
A vulgar and a plain man would unavoidably ask the astronomers, How came you so familiarly acquainted with the magnitude and qualities of the heavenly bodies, a great portion of which, by your own account, are millions of millions of miles removed from us? But, I believe, it is not the fashion of the present day to start so rude a question. I have just turned over an article on Astronomy in the Encyclopaedia Londinensis, consisting of one hundred and thirty-three very closely printed quarto pages, and in no corner of this article is any evidence so much as hinted at. Is it not enough? Newton and his compeers have said it.
The whole doctrine of astronomy rests upon trigonometry, a branch of the science of mathematics which teaches us, having two sides and one angle, or two angles and one side, of a triangle given us, to construct the whole. To apply this principle therefore to the heavenly bodies, it is necessary for us to take two stations, the more remote from each other the better, from which our observations should be made. For the sake of illustration we will suppose them to be taken at the extremes of the earth's diameter, in other words, nearly eight thousand miles apart from each other, the thing itself having never been realised to that extent. From each of these stations we will imagine a line to be drawn, terminating in the sun. Now it seems easy, by means of a quadrant, to find the arch of a circle (in other words, the angle) included between these lines terminating in the sun, and the base formed by a right line drawn from one of these stations to the other, which in this case is the length of the earth's diameter. I have therefore now the three particulars required to enable me to construct my triangle. And, according to the most approved astronomical observations hitherto made, I have an isosceles triangle, eight thousand miles broad at its base, and ninety-five millions of miles in the length of each of the sides reaching from the base to the apex.
It is however obvious to the most indifferent observer, that the more any triangle, or other mathematical diagram, falls within the limits which our senses can conveniently embrace, the more securely, when our business is practical, and our purpose to apply the result to external objects, can we rely on the accuracy of our results. In a case therefore like the present, where the base of our isosceles triangle is to the other two sides as eight units to twelve thousand, it is impossible not to perceive that it behoves us to be singularly diffident as to the conclusion at which we have arrived, or rather it behoves us to take for granted that we are not unlikely to fall into the most important error. We have satisfied ourselves that the sides of the triangle including the apex, do not form an angle, till they have arrived at the extent of ninety-five millions of miles. How are we sure that they do then? May not lines which have reached to so amazing a length without meeting, be in reality parallel lines? If an angle is never formed, there can be no result. The whole question seems to be incommensurate to our faculties.
It being obvious that this was a very unsatisfactory scheme for arriving at the knowledge desired, the celebrated Halley suggested another method, in the year 1716, by an observation to be taken at the time of the transit of Venus over the sun[50].
[50] Philosophical Transactions, Vol. XXIX, p. 454.
It was supposed that we were already pretty accurately acquainted with the distance of the moon from the earth, it being so much nearer to us, by observing its parallax, or the difference of its place in the heavens as seen from the surface of the earth, from that in which it would appear if seen from its centre[51]. But the parallax of the sun is so exceedingly small, as scarcely to afford the basis of a mathematical calculation[52]. The parallax of Venus is however almost four times as great as that of the sun; and there must therefore be a very sensible difference between the times in which Venus may be seen passing over the sun from different parts of the earth. It was on this account apprehended, that the parallax of the sun, by means of observations taken from different places at the time of the transit of Venus in 1761 and 1769, might be ascertained with a great degree of precision[53].
