"It is well known that the parallax of the sun can never exceed nine seconds, or the four-hundredth part of a degree(55)." "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 many ingenious endeavours of the most able opetators."(56).
(55) Ibid, p. 268.
(56) Phil. Transactions, Vol. XXIX, p. 456.
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(57). 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.
(57) See above, Essay XXI.
The result of the uncertainty which adheres to 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 semi-diameters; 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(58); some later astronomers, mentioned by Halley, as fourteen thousand; and Halley himself as sixteen thousand five hundred(59).
(58) They were about thirty and forty years younger than Kepler
respectively.
(59) Halley, apud Philosophical Transactions, Vol. XXIX, p. 455.
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.