100 PROCEEDINGS OF SECTION A. 
thought it well to give himself a loophole of escape. At any 
rate, he was ready to admit that his hypothesis might be 
quite wrong; all he cared for was that it enormously simpli- 
fied the description of celestial phenomena, rendering simple 
and intelligible many things that were formerly obscure and 
unconnected—the change of seasons, the varying brightness 
of the planets, their progressions and retrogressions, &c. 
Look next at the development of Kepler’s laws of plane- 
tary motion. He begins with the hypothesis that the 
distances of the planets from the Sun are determined by the 
six regular solids of geometry. ‘The Earth’s orbit is the 
sphere, the measurer of all. Round it describe a dodeca- 
hedron; the circle including this will be (the orbit of) Mars. 
Round Mars describe a tetrahedron ; the circle including this 
will be Jupiter. Describe a cube round Jupiter; the circle 
including this will be Saturn. Then inscribe in the (orbit 
of the) Earth an icosahedron ; the circle described in it will 
be Venus. Describe an octahedron round Venus; the circle 
inscribed in it will be Mercury.” This “law”’ seems fanci- 
ful enough; but the only sound objection that could have 
been advanced against it at the time was that it did not 
harmonise well with the results of experiment. Kepler was 
at first well satisfied. He declared that he ‘“ would not 
barter the glory of the invention for the whole Electorate 
of Saxony.” His ardour was somewhat cooled by Tycho’s 
advice, “first to lay a solid foundation for his views by 
actual observation.” So he turned aside from these specula- 
tions, and next gave his mind to pondering over the forms of 
the planetary orbits. Naturally, he tried circles first, but 
Tycho’s observations convinced him that, at least in the 
case of Mars, there was a considerable departure from the 
circular form. He therefore tried curves of all sorts, test- 
ing them by Tycho’s observations, until he hit upon the 
ellipse. Thus he discovered his second law. His next step 
was to generalise both his laws by extending them to ail the 
planets, and he found them still true. This great success 
revived his interest in the problem that had first aroused 
his enthusiasm—that of the planetary distances. He tried 
hypotheses of all sorts. He compared the planetary dis- 
tances with the intervals of the notes on the musical scale, 
an idea suggested by the venerable notion of the music of 
the spheres. At last, in 1618, he conceived the idea of 
comparing the powers of the different numbers that repre 
sent the distances of the planets with the powers of the 
numbers representing their periodic: times. Thus he hit 
upon his third great law ; and those who realise the immense 
