KEPLER'S THIRD LAW. 
ASTRONOMY. 
KEPLER'S THIRD LAW. 
EDGAR L. LARKIN. 
In the November issue of this Review we published an article with the 
above title in which we said, in speaking of the periods of revolutions of planets 
and their distances from the Sun, that, — "The squares of the times are equal to 
the cubes of distances." This is a statement of Kepler's law at variance with 
those given in astronomical works. Herschel's Outlines, p. 259, gives it in these 
words: " 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." 
On November loth we received a letter from Prof. H. S. Pritchett, St. Louis, 
Mo,, which said, — "As your statement of Kepler's law is calculated to mislead 
any one unacquainted with the subject, it is proper that you should make some 
correction of it in the next number." 
Thanking Prof. Pritchett for calling attention to this matter, we make the 
following explanation : 
In late computations wherein values relating to the earth become factors', 
such as its mass, volume, density, distance, velocity, and gravity, we find each 
made equal to i. This scheme has become nearly universal, and our object in 
so wording Kepler's law was to make it applicable to those who were in the 
habit of using ratios in place of crude numbers. Since no value but a ratio was 
inserted in the article, we thought our version of the law would be understood to 
apply to ratios. For fear that students might think otherwise we here show the 
exceptions to the law as we gave it. The main use of Kepler's third law is to 
find the relative distances of the planets from the Sun, which of course gives their 
relative distances from each other. 
For many years such use was made of it, until finally it fulfilled its destiny 
and actually revealed the distances of all the planets from the Sun in relation to 
the earth's distance. 
Kepler beheld the future with joy, because he was aware that if in coming 
years any astronomer should be so fortunate as to discover the distance of one 
planet from the Sun in miles, then all would be known, since the squares of times 
he knew, contained the secret of distances. Astronomers long ago made tables 
of the relative distances of the planets — including the Earth — from the Sun ; and 
then began an untiring search, awakening the admiration of the world — a search 
not yet ended — to find the distance of one planet — the earth — in miles. 
Let us imagine ourselves transported into the past, and watch astronome;s 
