KEPLER'S THIRD LAW. 433 
But the squares of the times are equal to cubes of distances ; whence the cube 
roots of the numbers in the second column, (Table i,) are equal to all planetary 
distances from the Sun. In Table II we give the squares of the times in the first 
column, and their cube roots in the second; which roots are the distances of all 
the planets from the solar globe. 
TABLE 11. 
Squares of Cube Roots of 
their Squares of Times, 
Names of Planets. Periodic Times. or Mean Distances. 
Mercury .058039 -3872 
Venus -378458 -7233322 
The Earth i. i. 
Mars. 3-53748 1.5238 
Jupiter 140.7 5.2016 
Saturn 867.516 9-5371 
Uranus .... .... 7058. 4311 19 182 
Neptune 27098. ' 30.036 
The relations of the numbers in both tables can be easily seen ; thus : Nep- 
tune revolves around the Sun in 164.615 years, whose square is 27098, the cube 
root of which is 30.036; hence we know that this distant world is 30.036 times 
farther from the Sun than is the earth. 
The truth of the law is demonstrated by elongations of Mercury and Venus, 
without knowing their, or the earth's distance from the Sun. Kepler did not 
know the distance from the earth to the Sun; but he knew ratios. He was aware 
that the distance from the Sun to Mercury is .3872 ; to Venus .723 and .1 to the 
earth ; and from these facts detected the third law. This law of nature is one of 
the most important elements of knowledge, and is capable of wide generalization. 
Not only do planets and satellites obey it, — bodies moving on orbits of small 
eccentricity, — but likewise comets, which traverse paths of the greatest possible 
elongation. All bodies whatever, that revolve around one another in cosmic 
space, must obey this inexorable rule. If suns wheel about their common centres 
of gravity, then the squares of their periods of revolution must be equal to the 
cubes of their distances apart ; but the units of measures for times and spaces are 
peculiar to each system of revolving bodies, only determined by their masses. 
When we observe a fact in nature, we know that it depends on another immedi- 
ately preceding it; law stands on law; every law has an antecedent and exists 
as a consequent. Now what great law of nature is next preceding the third of 
Kepler ? What makes it follow of necessity ? What is the cause of the fact that 
squares of times equal cubes of spaces ? We are almost on metaphysical ground, 
since we are dealing with such abstractions as time, space, and motion. The 
reason why the law of Kepler exists is because every particle of matter attracts 
every other with an intensity which is directly proportional to the quantity of 
matter they contain, and inversely proportional to the square of the distance 
between them. 
