f
Mars, observed in 1672 by Richer at Cayenne in concert with Cassini in
Paris, that the first scientific estimate of the sun's distance was
derived. It appeared to be nearly eighty-seven millions of miles
(parallax 9.5"); while Flamsteed deduced 81,700,000 (parallax 10") from
his independent observations of the same occurrence--a difference quite
insignificant at that stage of the inquiry. But Picard's result was just
half Flamsteed's (parallax 20"; distance forty-one million miles); and
Lahire considered that we must be separated from the hearth of our
system by an interval of _at least_ 136 million miles.[750] So that
uncertainty continued to have an enormous range.

Venus, on the other hand, comes closest to the earth when she passes
between it and the sun. At such times of "inferior conjunction" she is,
however, still twenty-six million miles, or (in round numbers) 109 times
as distant as the moon. Moreover, she is so immersed in the sun's rays
that it is only when her path lies across his disc that the requisite
facilities for measurement are afforded. These "partial eclipses of the
sun by Venus" (as Encke termed them) are coupled together in pairs,[751]
of which the components are separated by eight years, recurring at
intervals alternately of 105-1/2 and 121-1/2 years. Thus, the first
calculated transit took place in December, 1631, and its companion
(observed by Horrocks) in the same month (N.S.), 1639. Then, after the
lapse of 121-1/2 years, came the June couple of 1761 and 1769; and again
after 105-1/2, the two last observed, December 8, 1874, and December 6,
1882. Throughout the twentieth century there will be no transit of
Venus; but the astronomers of the twenty-first will only have to wait
four years for the first of a June pair. The rarity of these events is
due to the fact that the orbits of the earth and Venus do not lie in the
same plane. If they did, there would be a transit each time that our
twin-planet overtakes us in her more rapid circling--that is, on an
average, every 584 days. As things are actually arranged, she passes
above or below the sun, except when she happens to be very near the line
of intersection of the two tracks.

Such an occurrence as a transit of Venus seems, at first sight, full of
promise for solving the problem of the sun's distance. For nothing would
appear easier than to determine exactly either the duration of the
passage of a small, dark orb across a large brilliant dis