[17] There is, however, a much more perfect way of determining this
proportion, by applying the law which Kepler found to connect the
distances of the planets from the sun with the times in which they
complete the circuits of their orbits. The law is that, if we take any
two planets, and write down the numbers expressing their periods of
circuit (say in days), and the numbers expressing their distances from
the sun (say in miles) in the same order; then if we multiply each
number of the first pair into itself, and each number of the second pair
twice into itself, the four numbers thus obtained will be proportional;
that is to say, as the first is to the second, so will the third be to
the fourth. Now, as every one knows who has worked sums in the rule of
three, when any three are given out of four proportionals, the fourth
can always be found; but we know the periods of circuit both of the
earth and Venus (365·2564 days and 224·7008 days respectively) very
exactly indeed, because they have traversed their orbits so many times
since they began to be observed by astronomers. We can call the earth's
distance 100, and then applying the rule just stated, we get Venus'
distance relatively to the earth's. The reader who cares to work out
this little sum will find no difficulty whatever--if at least he is able
to extract the cube roots of any number. The proportion runs thus:--
365·2564 × 365·2564 : 224·7008 × 224·7008
:: 100 × 100 × 100 : (Venus' distance cubed.)
Work out this sum and we get for Venus' distance 72·333. The ratio of
Venus' distance to the earth's is almost exactly expressed by the
numbers 217 and 300.
Hazell, Watson, and Viney, Printers, London and Aylesbury.
* * * * *
Transcriber's Notes:
Italic text is denoted by _underscores_.
Obvious printer's errors corrected.
Every effort has been made to replicate this text as faithfully as
possible, including non-standard punctuation, inconsistently hyphenated
words, and other inconsistencies.