496 KANSAS CITY REVIEW OF SCIENCE. 
made equal to i ; then we see no reason why 92,882,000 may not be represented' 
by I, and Kepler's law be allowed to stand in simplicity and sublimity. 
This reasoning appears to us satisfaqjiory, that we have a right to make the 
Earth's distance unity, and then word the law as we did. 
Now for the exceptions — of which there are five, as follows: The squares 
of the times expressed in months, weeks, days, hours, and minutes, do not equal 
the cubes of distances in furlongs, rods, yards, feet, and inches. But since no 
one wants to use the law by handling these units, we did not make mention of 
them in the Kansas City Review. Yes, we omitted the units — years, because if 
we used j'^arj', the number I would appear ; and distance would have to come 
into the list as i, spoiling the scheme, since squares of times at once become equal 
to cubes of distances. 
We would much rather teach that squares of times equal cubes of distances ; 
than that they are simply proportional. We would teach equality first, and 
make secondary the fact of proportion. We would exalt this equality^ and class 
the proportions existing among these numbers as mathematical curiosities like 
others that may be deduced by different combinations of values of time, velocit- 
ies, distances and the like. Here is a table of proportions existing in the solar 
system, beginning with Mercury and extending to Neptune. 
The square of Venus' Time 
The cube of Venus' Distance 
■by the square of Mercury's Time = 6.5, 
by the cube of Mercury's Distance =6.5 
The square of the Earth's Time -f-by the square of Venus' Time = 2.64 
The cube of the Earth's Distance-=-by the cube of Venus' Distance = 2.64 
The square of Mars' Time -f-by the square of the Earth's Time = 3-537 
The cube of Mars' Distance ^by the cube of the Earth's Distance = 3.537 
The square of Jupiter's Time 
The cube of Jupiter's Distance 
The square of Saturn's Time 
The square of Uranus' Time 
The square of Neptune's Time - 
The cube of Neptune's Distance- 
-by the square of Mars' Time ^39.8 
■by the cube of Mars' Distance =39.8 
•by the square of Jupiter's Time = 6. i6' 
The cube of Saturn's Distance -^-by the cube of Jupiter's Distance = 6. 16 
-by the square of Saturn's Time = 8. 13. 
The cube of Uranus' Distance -^-by the cube of Saturn's Distance = 8.13, 
-by the square of Uranus' Time = 3.83. 
-by the cube of Uranus' Distance = 3.83, 
Quite a number of similar tables might be made by beginning the series with 
each of the planets; and then by different combinations arranging the numbers in 
all possible ways. We might begin with Saturn and compare with the other 
planets \ and then with Uranus, and so on, completing the work probably in six 
months. But then what would the tables be good for, simply to satisfy a curios- 
ity that might be awakened in a morbid mental condition. 
Nearly every work on astronomy fails to quote Kepler's law correctly; all 
astronomers know that as Herschel gives it, it is not absolutely perfect. The 
words, " when the masses of the planets are considered " should have been added. 
The third law is not true with mathematical precision unless the mass of each 
