432 KANSAS CITY REVIEW OF SCIENCE. 
KEPLER'S THIRD LAW. 
EDGAR L. LARKIN. 
This law is one of the corner-stones of modern astronomy ; and its discovery 
a turning-point in the history of the science. Its first presentation to students is- 
usually attended with more or less difficulty, and with the hope of aiding such 
we endeavor to give a simple exposition of the great law. It is given in different 
words by astronomers; and here are several versions: 
I. " The square of the time of revolution of each planet is proportional to the 
cube of its mean distance from the sun." Newcomb and Holden's Astronomy, 
p. 125. 
II. " The squares of the periodic times of any two planets are to each 
other in the same proportion as the cubes of their mean distances from the sun." 
Herschel's Outlines of Astronomy, p. 259. 
III. " The squares of the times are as the cubes of the mean distances 
from the sun." Ray's Elementary Astronomy. 
IV. "The squares of times of revolutions are to each other as the cubes of 
the distances from the sun." Robinson's University Astronomy. 
V. "The squares of the times of revolution of the planets around the sun 
a^-e proportional to the cubes of the major axis of their orbits." Guillemin's The 
Heavens. 
VI. " The squares of the periodical times are as the cubes of the major 
axes of the orbits." Olmstead's Astronomy, p. 99. 
It seems that matters might be simplified by using the word equal, thus : — 
VII. The squares of the times are equal to the cubes of distances. 
It follows then that if we square the periodic time of any planet, we know 
that the square is equal to the cube of its distance from the Sun, and to find the 
distance we extract its cube root. 
Table I gives the periodic times of all the planets, and their squares. Col- 
umn I gives the times of revolutions around the sun, and II the squares of 
these numbers : 
TABLE I. 
Names of Planets. Periodic Times. Periodic Times 
Squared. 
Mercury 24084 .058039 
Venus 61519 .378458 
The Earth i. i. 
Mars 1. 880819 3-53748 
Jupiter 1 1. 86 1 7 140- 7 
Saturn 29.456626 867.516 
Uranus 84.01447 7058. 431 1 
Neptune 164.615 27098. 
