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Updated: May 2, 2025
Louisa, half-asleep, tried hard to take an interest in the information, but the remarks which she ventured showed that she had understood not a word, and provoked Amalia to indignant exclamations and repetition of every detail. Old Euler, a clerk, tried to explain to Christophe the difficulties of a musical career.
Euler alone, he found, to be an exception to this general law, as the volume of its crater appeared to be twice as great as that of the mass surrounding it. It must therefore have been formed by several eruptions in succession, but in that case what had become of the ejected matter?
The only reason on this theory why anyone should want to satisfy these formulae is a sentimental regard for Galileo, Newton, Euler and Lagrange. The theory, so far from founding science on a sound observational basis, forces everything to conform to a mere mathematical preference for certain simple formulae.
Euler won the prize, but failed to explain the effect, and said: "It appears to be established by indisputable evidence that the secular inequality of the moon's mean motion cannot be produced by the forces of gravitation."
An observant eye perceives already some traces of their efforts in the writings of the mathematicians of the Alexandrian School. These traces, it must be acknowledged, are so slight and so imperfect, that we should truly be justified in referring the origin of this branch of analysis only to the excellent labours of our countryman Vieta. Descartes, to whom we render very imperfect justice when we content ourselves with saying that he taught us much when he taught us to doubt, occupied his attention also for a short time with this problem, and left upon it the indelible impress of his powerful mind. Hudde gave for a particular but very important case rules to which nothing has since been added; Rolle, of the Academy of Sciences, devoted to this one subject his entire life. Among our neighbours on the other side of the channel, Harriot, Newton, Maclaurin, Stirling, Waring, I may say all the illustrious geometers which England produced in the last century, made it also the subject of their researches. Some years afterwards the names of Daniel Barnoulli, of Euler, and of Fontaine came to be added to so many great names. Finally, Lagrange in his turn embarked in the same career, and at the very commencement of his researches he succeeded in substituting for the imperfect, although very ingenious, essays of his predecessors, a complete method which was free from every objection. From that instant the dignity of science was satisfied; but in such a case it would not be permitted to say with the poet: "Le temps ne fait rien
He ran to the garden fence. At the risk of being seen he was about to clear it. But when he looked at the window at which she had appeared, he saw that the shutters were closed. The house seemed to be asleep. He stopped. Old Euler, going to his cellar, saw him and called him. He retraced his footsteps. He thought he must have been dreaming.
There is a distinct little gap in the S. wall, easily glimpsed when it is close to the morning terminator, which probably represents a small crater. Euler has a bright central mountain, and is a centre of white silvery streaks. BRAYLEY. A very conspicuous little ring-plain E.S.E. of Euler, with two smaller but equally brilliant objects of the same class situated respectively E. and W. of it.
In the time of Huyghens and Euler a medium had been assumed for the transmission of the waves of light; but Newton raised the objection that, if light consisted of the waves of such a medium, shadows could not exist. The waves, he contended, would bend round opaque bodies and produce the motion of light behind them, as sound turns a corner, or as waves of water wash round a rock.
Is it not astonishing to find in the commensurability of the mean motions of two planets, a cause of perturbation of so influential a nature; to discover that the definitive solution of an immense difficulty which baffled the genius of Euler, and which even led persons to doubt whether the theory of gravitation was capable of accounting for all the phenomena of the heavens should depend upon the fortuitous circumstance of five times the mean motion of Saturn being equal to twice the mean motion of Jupiter?
In the midst of this apparent chaos there is one element which remains constant or is merely subject to small periodic changes; namely, the major axis of each orbit, and consequently the time of revolution of each planet. This is the element which ought to have chiefly varied, according to the learned speculations of Newton and Euler.
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