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Extracts from Maupertius' account of his expedition can be found in Fauvel and Gray (1987), ^ p. 455 (see also Terrall (1992, 2003)).

L'eiemens de la philosophie de Newton. This work was translated immediately into English

(Voltaire (1967)). For more details on Voltaire's advocacy of Newtonianism and the Elements in particular, see for example, Teske (1972).

Madame du Chatelet's achievements in natural philosophy and mechanics are described in

Theoria philosophiae naturalis (1758) was published in Vienna. An English translation of the

1763 edition published in Venice can be found in Boscovich (1966).

they allowed the theoretical determination (based on mathematics) of all sorts of apparently unrelated phenomena. Kepler's three laws had been shown to follow from a single general principle, and the same principle could be used to explain phenomena as diverse as the tides and the precession of the equinoxes. This was a state of affairs not even dreamed of before Newton. In the words of

Voltaire: 'Before Kepler, all men were blind. Kepler had one eye, Newton had

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two.

One thing that the Principia did not bring about was an immediate increase in the accuracy of planetary tables. Well into the eighteenth century, such tables were essentially Keplerian in nature, with improvements due to the more accurate value of solar parallax and the eccentricity of the Earth that Horrocks had introduced, and more sophisticated observation techniques, including better corrections for refraction. Universal gravitation held the key to a step change in the accuracy of theoretical predictions, but astronomers had to wait until mathematicians had devised methods for determining quantitatively the effect of one planet on another's orbit before such a change could be realized.

There were many imperfections in Newton's demonstrations, some of which have been mentioned above, and other people were quick to latch on to them in order to help discredit the overall theory. In another way, these imperfections aided the advance of Newtonianism in that, as they were removed one by one by improved techniques, the impression was gained that there was nothing that universal gravitation could not explain, given sufficient mathematical ingenuity. One of the prime examples of this was the lunar theory, which, as we have seen, gave an erroneous value for the advance of the apsidal line and which was considered a serious objection to accepting the attraction theory. It took half a century before universal gravitation was reconciled with the motion of the lunar apogee, but with that achievement the Newtonian framework became virtually unassailable.

### The demise of the vortex theory

As far as Cartesian physics is concerned, the period between the publication of the Principia and Newton's death in 1727 was characterized by attempts to explain the quantitative details of planetary theory, rather than simply being satisfied with an overall qualitative world view.

One year before the publication of the Principia in 1687, Bernard Fontanelle published his L'entretiens sur la pluralité des mondes, which described the

Quoted from Brackenridge (1995), p. 10.

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