JOURNAL AND PROCEEDINGS. 47 
away and resolved in the face of thousands of years of human 
admiration for the circle, to abandon it as an impossible orbit 
for the planetary system. By adopting the ellipse he was soon 
able to demonstrate that the circle as a planetary orbit was an 
illusion. Difficulties hitherto apparently insurmountable van- 
ished, and Kepler gave the world his first law, viz: that 
‘Planets revolve in elliptic orbits about the sun, which occupies 
the common focus of all these orbits.’’ Kepler conceived 
the idea that the planetary system was not an inde- 
pendent group of shining worlds but a fractional part of a 
system, immeasurably greater, to which it was joined by some 
common bond as natural and as certain as that which binds 
the planets to the sun. For seventeen years he wrought almost 
incessantly upon this problem. Once in his experiments he 
was on the right path but an error in his computation set him 
astray and he turned away almost in despair. After some 
months he set out in that same path again, discovered his error 
and corrected it, then toiled on. 
The mathematical formula on which he wrought was, 
‘The square of Jupiter’s period is to the square of Saturn’s 
period, as the cube of Jupiter’s distance is to a fourth term, 
which he prayed might prove to be the cube of Saturn’s dis- 
tance.’’ When he had finished, after testing for seventeen 
long years every conceivable theory, he compared the result 
with the cube of Saturn’s distance and found that they were 
the same. He went over the figures again and again. He 
tried the proportion, the square of Jupiter’s period with the 
square of Mars’ period as the cube of Jupiter’s distance with 
a fourth term. He compared it with the cube of Mars’ 
distance and found them the same. He tried other planets 
with the same result. [he man was frenzied with joy. He 
had discovered the law which makes a brotherhood of all the 
worlds. 
The squares of this periodic revolution are as the cubes of 
their distances, the struggle of seventeen long years was ended. 
His soul was so filled with ecstacy that in the excitement of his 
triumph he exclaims, ‘‘Nothing holds me, I will indulge my 
sacred fury, if you forgive me I rejoice, if you are angry, I can 
