Lenses and Waves

1690 - TRAITÉ DE LA LUMIÈRE 245
First of all because he did not believe that Newton intended to explain
gravity by attraction:
“It would be a different matter if one supposes that gravity is a quality inherent to
corporeal matter. But that is what I do not believe Mr. Newton agrees with, because
such an hypothesis would lead us far from mathematical or mechanical principles”. 108
Secondly, Huygens had reason to believe that Newton’s concept of gravity
was not universal. His calculations yielded a degree of oblateness of the earth
that stood in sharp contrast to the value Newton had derived on the basis of
the supposition of gravitational attraction between its parts. 109 In addition,
these calculations agreed with the data gathered on the most recent test of
his clocks at sea. 110 Huygens had not examined Newton’s derivation in detail
“… because I likewise do not agree with a principle he supposes in that calculation and
elsewhere; which is that all the little parts, …, mutually attract or tend to approach one
another. That I would not know how to admit, because I believe to see clearly that the
cause of such an attraction is not explicable by any principle of mechanics, nor by rules
of motion.” 111
Huygens had no objections to Newton’s mathematical demonstrations
regarding the inverse-square law per se:
“Thus I have nothing against the Vis Centripeta, as Mr. Newton calls it, by which he
makes the planets be heavy towards the sun, and the moon towards the earth, but I
rather remain in agreement with that without difficulty: … I had not thought either of
that regular diminution of gravity, namely, that it is in reciprocal ratio to the squares of
the distances from the center: which is a new and very remarkable property of gravity,
of which it is well worth to seek the cause.” 112
In explicitly refraining from explaining the properties of gravity
mechanistically, Newton did not offer an alternative for spherical vortices.
Huygens would be happy to fill this gap by means of his alternative to
Descartes’ theory. Only, what did vortices explain? He could argue that his
spherical vortices were consistent with an inverse-square law. But could he
derive the properties of gravitational acceleration in the way he had derived
the properties of light rays? No, for he did not show that this kind of
movement follows from the behavior of single particles as he did for waves
in Traité de la Lumière. Moreover, in the light of book two of Principia,
108
OC21, 474 (Discours, 163). “Ce seroit autre chose si on supposoit que la pesanteur fust une qualité
inherente de la matiere corporelle. Mais c’est à quoy je ne crois pas que Mr. Newton consente, parce
qu’un telle hypothese nous eloignoit fort des principes Mathematiques ou Mechaniques.”
109
Smith, “Huygens’ empirical challenge”, 2-3.
110
Mahoney, “Determination”, 258-260.
111
OC21, 471 (Discours, 159). “… parce qu’aussi bien je ne suis pas d’accord d’un Principe qu’il suppose
dans ce calcul & ailleurs; qui est, que toutes les petites parties, …, s’attirent ou tendent à s’approcher
mutuellement. Ce que je ne sçavrois admettre, par ce que je crois voir clairement, que la cause d’une telle
attraction n’est point explicable par aucun principe de Mechanique, ni des regles du mouvement.”
112
OC21, 472 (Discours, 160). “Je n’ay donc rien contre la Vis Centripeta, comme Mr. Newton l’appele, par
la quelle il fait peser les Planetes vers le Soleil, & la Lune vers la Terre, mais j’en demeure d’accord sans
difficulté: … Je n’avois pensé non plus à cette diminution reglée de la pesanteur, sçavoir qu’elle estoit en
raison reciproque des quarrez des distances du centre: qui est une nouvelle & fort remarquable proprieté
de la pesanteur, dont il vaut bien la peine de chercher la raison.”