300 THE WORLD MACHINE 



refused. Lagrange went, and there he remained for twenty- 

 one years. It was at Berlin that he completed his great 

 MJcanique Analytique, a superb work, practically the foundation 

 of that especial science ; it would have given him an enviable 

 fame had he done nothing more. 



These two giants, Laplace and Lagrange, so largely mono- 

 polised the stage as to dwarf into a minor place an excellent 

 mathematician, a dreaming genius, Johann Heinrich Lambert, 

 tailor's apprentice of Miihlhausen, of whose majestic reveries 

 we shall hear hereafter. It was a discovery by Lambert one 

 that he did not live to solve himself that gave to Laplace and 

 Lagrange one of their most celebrated problems. 



Halley, who pointed out so much for others to think about, 

 had noted that the motion of Saturn was swifter than it ought 

 to be, according to the Newtonian theory, while that of Jupiter 

 was slower. Lambert found that Saturn in his day was moving 

 faster than in Halley's time. There was evidently a fluctuation 

 or disturbance of some sort at work. The situation was pretty 

 obviously the result of the pull of one planet on the other, 

 acting with or against the steady pull of the sun. But it was 

 a mathematical puzzle of a very intricate order the problem 

 of three bodies over again. In many doubting, hesitating 

 minds it was a stumbling-block to the acceptance of the theory 

 of gravitation. In that day, just as in our own, there were, in 

 abundance, types of minds which clung tenaciously to every- 

 thing which seemed a difficulty or an obstacle in the path of 

 any new idea. No doubt this type is of use, always ; it forms 

 a kind of check upon over-enthusiastic spirits, refuses to accept 

 any new result until it has been proven up to the hilt ; it is 

 of undoubted value in sifting out fact from hasty theory, and 

 in giving us a solid sense that what knowledge we may put by 

 when the opposition has been cleared away is of real and lasting 

 worth. 



The solution of the special case of Jupiter and Saturn proved 

 a clue to other and less important planetary perturbations. It 

 naturally was received with great acclaim by astronomers, 

 since it seemed to sweep away the last hindrance to the full 

 acceptance of the idea of attraction. This idea was no longer an 

 hypothesis. After the demonstrations of Lagrange and Laplace, 

 it would take rank as a theory beyond all cavil or doubt. Fifty 



