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 suni.

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. But the parallax of the sun is so exceedingly small, as scarcely to afford the basis of a mathematical calculation'. 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 m.

But the imperfectness of our instruments and

1 Philosophical Transactions, Vol. XXIX, p. 454.

k

* Bonnycastle, Astronomy, 7th edition, p. 262, et seqq.

1 Ibid, p. 268.

in Phil. Transactions, Vol. XXIX, p. 457.

means of observation have no small tendency to baffle the ambition of man in these curious investigations.

"The true quantity of the moon's parallax," says Bonnycastle, "cannot be accurately determined by the methods ordinarily resorted to, on account of the varying declination of the moon, and the inconstancy of the horizontal refractions, which are perpetually changing according to the state the atmosphere is in at the time. For the moon continues but for a short time in the equinoctial, and the refraction at a mean rate elevates her apparent place near the horizon, half as much as her parallax depresses it"."

"It is well known that the parallax of the sun can never exceed nine seconds, or the four-hundredth part of a degree"." "Observations," says Halley, "made upon the vibrations of a pendulum, to determine these exceedingly small angles, are not sufficiently accurate to be depended upon; for by this method of ascertaining the parallax, it will sometimes come out to be nothing, or even negative; that is, the distance will either be infinite, or greater than infinite, which is absurd. And, to confess the truth, it is hardly possible for a person to distinguish seconds with certainty by any instruments, however skilfully they may be made; and therefore it is not to be wondered at, that the excessive nicety of this matter should have eluded the

"Astronomy, p. 265.

。 Ibid,

p.

268.

many ingenious endeavours of the most able operators P.

Such are the difficulties that beset the subject on every side. It is for the impartial and dispassionate observers who have mastered all the subtleties of the science, if such can be found, to determine whether the remedies that have been resorted to to obviate the above inaccuracies and their causes, have fulfilled their end, and are not exposed to similar errors. But it would be vain to expect the persons, who have "scorned delights, and lived laborious days" to possess themselves of the mysteries of astronomy, should be impartial and dispassionate, or be disposed to confess, even to their own minds, that their researches were useless, and their labours ended in nothing.

It is further worthy of our attention, that the instruments with which we measure the distance of the earth from the sun and the planets, are the very instruments which have been pronounced upon as incompetent in measuring the heights of mountains. In the latter case therefore we have substituted a different mode for arriving at the truth, which is supposed to be attended with greater precision but we have no substitute to which we can resort, to correct the mistakes into which we may fall respecting the heavenly bodies.

The result of the uncertainty which adheres to

P Phil. Transactions, Vol. XXIX, p. 456.

See above, p. 392.

all astronomical observations is such as might have been expected. Common readers are only informed of the latest adjustment of the question, and are therefore unavoidably led to believe that the distance of the sun from the earth, ever since astronomy became entitled to the name of a science, has by universal consent been recognised as ninety-five millions of miles, or, as near as may be, twenty-four thousand semi-diameters of the earth. But how does the case really stand? Copernicus and Tycho Brahe held the distance to be twelve hundred semidiameters; Kepler, who is received to have been perhaps the greatest astronomer that any age has produced, puts it down as three thousand five hundred semi-diameters; since his time, Riccioli as seven thousand; Hevelius as five thousand two hundred and fifty'; some later astronomers, mentioned by Halley, as fourteen thousand; and Halley himself as sixteen thousand five hundreds.

The doctrine of fluxions is likewise called in by the astronomers in their attempts to ascertain the distance and magnitude of the different celestial bodies which compose the solar system; and in this way their conclusions become subject to all the difficulties which Berkeley has alleged against that doctrine.

r

Kepler has also supplied us with another mode

They were about thirty and forty years younger than Kepler respectively.

S

* Halley, apud Philosophical Transactions, Vol. XXIX, p. 455.