MATHEMATICAL PHYSICS. 101 
importance of this Jaw in the development of dynamics and 
astronomy will forgive Kepler his exaggerated outburst of 
exultation at its discovery :—‘‘ What 16 years ago I urged 
as a thing to be sought—that for which I joined Tycho 
Brahé—for which i settled m Prague—for which I have 
devoted the best part of my life to astronomical contempla- 
tions—at length I have brought to light, and have recog- 
nised its truth beyond my most sanguine expectations. . 
It is now 18 months since I got the first glimpse of light, 3 
months since the dawn; a very few days since the unveiled 
sun burst upon me . . . . The die is cast—the book 
is written, to be read either now or by posterity, I care not 
which. It may well wait a century for a reader, as God has 
waited 6000 years for an interpreter of his works.” 
So much of Kepler. Many will readily admit that his 
laws “‘explain”’ nothing, but will add that the “ explana- 
tion”’ was left to Newton. The absurdity of this has 
already been pointed out. The real function of the laws of 
motion and of gravity is to sum up a vast number of other- 
wise isolated facts; and, of course, when looked at in this 
light, they appear among the grandest of Nature’s “ laws.’’ 
Thebuilding upof the lawof gravitation gaveemp oyment to 
many workmen besides Newton; Kepler, Bouillard, Wren, 
Halley, and Hooke among the others. Let us see how 
near Hooke came to victory in his speculations. After 
maintaining that the planets “must have some other causes 
beside the first’ impressed impulse to bend their motion 
into these curves,”’ he says that only two causes can be sug- 
gested for this curvature. The first is that the tendency 
towards the central sun is produced by a greater density in 
the ether near the sun. ‘The second may be from an 
attractive property of the body placed in the centre, whereby 
it continually endeavours to attract or draw it to itself.” In 
1674, in some observations on gravity, he says—‘‘I shall 
hereafter explain a system of the world differing in many 
particulars from any yet known, but answering in all things 
to the common rules of mechanical motions.”” This depends 
on three hypotheses—(1) that all celestial bodies gravitate 
towards one another; (2) the law of inertia; (3) that the 
law of gravity is such that “those atiractive powers are so 
much the more powerful in operating by how much the 
‘nearer the body wrought upon is to their own centres; but 
what these several degrees are I have not yet experimentally 
verified.” This is very remarkable. The law of the in- 
verse squares is alone wanting to complete the Newtonian 
