Lenses and Waves

1690 - TRAITÉ DE LA LUMIÈRE 243
What difficulties Huygens was thinking of, is not clear. I suspect the
letters of Pardies had given him the idea that Newton’s theory presupposed
an emission conception of light. This he could not accept, as it conflicted
with his basic notions about the nature of light. Did he fear a diversity of
‘lights’ would undermine his understanding of the nature of light? His (later)
view of light being an action propagated with a velocity depending only upon
the nature of the medium, cannot be reconciled with such a diversity. On the
other hand, around the same time he had suggested the idea that double
refraction, including its odd absence in a second crystal, is caused by two
undulations linked to two kinds of particles in Iceland crystal. I think there
was a good deal of rhetoric in Huygens’ remark, and I do not believe he had
considered the issue in any great detail at this point. It appears that he
considered the mere semblance of being unclear in terms of the mechanistic
nature of light sufficient to request clarification on this point. As long as
Newton had not done so Huygens could not accept his conclusions about
the nature of light on the basis of the ‘accident’ of different refrangibility.
The dispute, 15 years later, over Principia followed a similar course.
Huygens accepted the ‘accident’ of the inverse-square law, but rejected
Newton’s conclusions regarding universal gravity. Principia did what Huygens
had not been able to do: to unify all forms of accelerated motion. 100 He did
so by means of a new, mathematized concept of force. Newton considered
circular motion in terms of a force that seeks the center and coined the term
centripetal force. With this force he could treat all frictionless motions of
point masses. Book one of Prinicipia laid down ‘the science of motions that
result from any forces whatever’ as they can be investigated from the
phenomena. 101
The aim of Principia went beyond a mere science of motion. The laws and
conditions of motions and forces established in book one were the principles
of a philosophy from which the phenomena of nature were to be derived.
“For many things lead me to have a suspicion that all phenomena may depend on
certain forces by which the particles of bodies, by causes not yet known, either are
impelled toward one another and cohere in regular figures, or are repelled from one
another and recede.” 102
In book three, Newton gave an example of this by unfolding a system of the
world founded upon the force of gravity. He showed that the force that
holds satellites in their orbit is the same as the force that causes an apple to
fall on earth. The centripetal force established mathematically in book one
formed the basis. He correlated the centripetal acceleration of the moon and
the acceleration of gravity and showed that both are instances of a force that
varies inversely as the square of the distance.
100 Westfall (Force, 178-179) discusses a paper from about 1675 (OC18, 496-498) that was the start of a
generalised theory of accelerated motion, but in which Huygens failed to see the dynamical equivalence of
change of direction and change of linear velocity.
101 Newton, Principia, 382.
102 Newton, Principia, 382-383.