PHYSICO-MECHANICAL laws are, as it were, the telescope of our spiritual eye, which can penetrate into the deepest night of times past and to come. HELMHOLTZ, On the Interaction of Natural Forces. CHAPTER XXIII LAPLACE AND THE STABILITY OF THE SOLAR SYSTEM IN the history of intellectual development, more especially in the development of science, precedence among the nations seems to flit about in a lawless way. In the workaday world in which we live, one of the strongest forces is that of heredity; its workings are revealed not merely among families, but in the larger forms which we may call social, the inheritance from one generation to another of ideas, customs, beliefs. The fact is one of the foundation-stones of the growing science of sociology. But genius for discovery, for invention, for the grouping and generalisation of phenomena into broad and simple laws, seems to escape the force of heredity entirely. One would readily think that the career of a great man would mean the impregnation of a generation and a people with his ways of thinking and ways of doing, and that when he had gone there would arise a distinct progeny to carry on his work. But it does not seem to be so. Poland did not become the leader of the intellectual world because of Coppernicus, nor Germany because of Kepler, nor Italy because of Galileo. Newton had no successors among his own people nor in the generation that followed. It was the mathematicians of France who were destined in the obscure order of events to take up his work. There remained when he died a number of minor but none the less important problems; subsequent facts, as they came to light, suggested several more. There was one of extreme intricacy which Newton may have pondered but which he never ventured to solve. The slow sway of the earth's axis, pointed out by Coppernicus and explained by Newton, was clearly a periodical disturbance. So was the secondary nodding or nutation of the axis discovered by Bradley. Their effects might be momentous-they might determine changes of climate, for example-and so men came afterwards to perceive. But they were not permanent. It was clear that some time or other the earth would return to precisely the same conditions as that which had once prevailed; it was merely making a round. But the fact that there could be any such deviation from seeming regularity must have very soon suggested that there might be other changes whose effect was progressive and cumulative. Men came to wonder whether the seeming permanent arrangement of the planets formed a stable system, or whether it might one day go all awry. Has this little patch of the universe which we call the solar system always existed more or less in its present form? Were the planets always arranged in the same order and same distance and with the same speeds as we perceive them now, or is there underneath all this apparent regularity, this machine-like motion, a subtle deviation which in the course of uncounted ages will change it utterly. There was a curious fact turned up by Halley. Studying the records of some of the old eclipses, he found that the calculation, so far as he could perceive, of the times in which they should have occurred did not agree with the records at all. In the pages of Ptolemy and others he found accurate descriptions of eclipses which had taken place far back in the old Babylonian and Chaldean days. They did not tally with his computations by nearly two hours. This in a period of twentyfour hundred years is not a great variation; there was always a chance, of course, that his calculations, or the ideas upon which he based them, were wrong. But the new methods brought in by Newton had reduced planetary motion to a science of marvellous accuracy. So, when the estimates had been carefully checked up and found flawless, astronomers were able to lay hold of any such discrepancy as a distinct and significant fact; they could go hunting for the reason, rather than put the matter aside as something inexplicable or the mere product of error. Halley did not find the solution of the problem he had posed. Before it could come it was needful to clear up a difficult and highly recondite problem, the pull of the planets on each other, their mutual perturbations, as it is known-in more technical phrase, the problem of three bodies. For this, in turn, mathe matical analysis had to grow to new powers. Newton had lent a powerful aid with his invention of fluxions. The philosopher Leibnitz had made very near the same discovery. Together they had produced the new calculus. It was the new weapon of analysis which, when the "Mathematical Principles," the Principia, finally had taken hold, gave such a tremendous impetus to the mathematical treatment of scientific problems, and especially those of astronomy. There seemed to spring up a whole school of calculating geniuses to whom an unsolved problem was as meat and drink. The foremost of the earlier ones was Euler, a Swiss. It is related of him that when in middle life he lost one of his eyes, he remarked that henceforth he would have less to distract him from mathematics. Later on he lost the use of the other; but it seemed to make no difference in his astonishing activity. Princes of the mind were then high in the favour of princes of the land. Euler roamed about the courts of Europe, joining first in the organisation of the newly created Academy of Sciences in St. Petersburg, then in Frederick's reorganisation of the Academy at Berlin, then back again. All the while he was turning out with an incredible rapidity papers upon new methods of analysis, abstract dynamics, optics, the motion of fluids, the movement of the planets; every branch of physical investigation seemed grist for his mill. Altogether he left some eight hundred memoirs, besides several respectable volumes, and a charming series of letters on the study of nature, addressed to a princess friend. His versatility was amazing. It may be noted in passing that this seems a characteristic of minds of the highest order. It was particularly true in the first two centuries after Galileo, before the sciences had become so intricate and highly specialised that mastery in more than one narrow field should make a Helmholtz a marvel to his kind. Euler's association with the Bernouillis was so close that he might almost be regarded as a member of that famous family of mathematicians, two of whom were rivals of Newton, and one of whom, Daniel Bernouilli, was the first important Newtonian among mathematicians outside of Great Britain. Euler and the latter found a keen competitor in the precocious genius of Clairaut. He is remembered now, if he is remembered at all, chiefly for his classical investigations into the figure of the earth; but in his own time his celebrity was considerable, |