1 88 THE WORLD MACHINE 



the confines of Egypt. If you forgive me, I rejoice ; if you are 

 angry, I can bear it ; 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 six thousand 

 years for an observer ! " 



The third law, announced in this exulting paean, came nine 

 years after the other two. It embodied his discovery of the 

 simple relationship which subsists between the distance of the 

 planets from the sun and the time of the planetary year that 

 is, that the cube of the distance is proportional to the square 

 of the time of revolution. Stated in other terms, the speed of 

 each planet in its orbit is inversely as the square root of its 

 distance from the sun. The product of the distance into the 

 square of the speed is the same for each planet ; the ratio of 



^2 for every planet is the same. 



Simplicity, predictability, mechanical fixity, the whole 

 scheme under the governance of law, in lieu of mystery or caprice 

 or the whims of the gods ! This is what the discoveries of 

 Kepler meant. They were among the earliest of the attempts 

 to reveal a single common principle at work throughout broad 

 groups of phenomena, among the first of those " laws of nature " 

 which measure the degree of progress attained in any branch of 

 natural inquiry. Archimedes, it is true, had established the 

 laws of equilibrium in a time long gone. Galileo was even 

 then at work on the " laws " of motion. But Kepler's were 

 the first of the great generalisations which, like mighty monu- 

 ments, mark the advance of the human mind. He was a 

 pioneer. His fame is just. 



He had triumphed ; he had established for all time a truth 

 the greatest work, says Taine, open to man. But he did not, 

 could not, see the further meaning of the laws he had unveiled. 

 He could not divine the cause, the mechanical necessity, which 

 lay beneath his laws of planetary motion ; before that could 

 come a new science must be developed ; it was even then being 

 developed, and, stranger than all, by his friend and correspondent 

 in the University at Padua. 



Still, it is amazing to find how near he came to divining it 

 all. We have seen that some idea of planetary attraction 

 floated vaguely before the mind of Coppernicus. With Kepler 



