494 KANSAS CITY REVIEW OF SCIENCE. 
at work finding the relative distances of the planets from the Sun. They had 
Kepler's law and therefore knew that there was a certain relation between the 
squares of times and cubes of distances. Suppose them at work on the task of 
finding how many times more distant Jupiter is from the Sun, than is the Earth. 
They could ail see that Jupiter requires 11.8617 times greater period to revolve 
around the Sun than the Earth does. Then they squared 11.8617 and secured 
140.6 as a product. Here, then, astronomers had a number — 140.6, which they 
knew possessed valuable properties, since by the law, the distances — both unknown 
— of the Earth and Jupiter were involved in it. They knew that whatever were 
the distances of the Earth and Jupiter, the cube of Jupiter's distance divided 
by the cube of the Earth's, would give a quotient^i4o.6. After years of toil 
had passed away in observing Jupiter; in watching it in all parts of its orbit, 
measuring and recording its angular distances from the Earth and Sun, as well 
as its longitude from time to time, it was discovered by almost interminable 
labor, that its distance from the Sun is 5.2016 times greater than that of the 
Earth. Therefore, the distance of the earth from the Sun becomes equal to i. 
The relation of the Earth's distance from the Sun to Jupiter's distance is as i is 
to 5.2016. 
(We desire to use the word ratio instead of relation, but desist, for if we 
should, our version of the law would be true). 
As noted above, astronomers knew if they could find the relative distances 
of the Earth and Jupiter with accuracy, that the cube of Jupiter's divided by the 
cube of the Earth's distance would equal 140.6. But why carry the computation 
further? Why cube Jupiter's distance and divide by the cube of the Earth's, 
when the work was already performed? The number 140.6 flashed out as a 
resplendent light, for behold ! it is the cube of 5.2016. That is : — the square of 
Jupiter's time is equal to the cube of its distance, in the only units that could pos- 
sibly be known to the astronomers of that epoch. 
It would have been well if these founders of our science had erected a mon- 
ument of granite, more enduring than the pyramids, and carved thereon these 
words : " The squares of the times of revolution of all the planets are equal to 
the cubes of their mean distances from the Sun." We think no astronomer now 
living would desire to obliterate such an inscription. This eternal law is one of 
the foundation stones of astronomy and we think all text-books should word it 
as above, and that every student should so memorize it. If any man ask that 
we explain the third law of Kepler, we will tell him that squares of times are 
equal to cubes of distances. Should he ask how to find the times, we would say : 
the only known method of finding the time of a planet's revolution is to observe 
how much longer or shorter period it requires to make circuit than the Earth 
does, because the motions of the Earth alone give us any conception of the flow 
of time. He desires to find the distance of Mars from the Sun in miles. We 
say square its time and extract the cube root of the product. The period of this 
planet is 1.88, that is — it takes .88 longer time to go round the Sun than the 
Earth does. The square of 1.88=3.537, whose cube root is 1.5238. Now, we 
