Lenses and Waves

154 CHAPTER 4
left aside the possible physical implications of his Cartesian analysis of
strange refraction. It remains to be seen how seriously he took his proposal.
In view of his commitment to a wave conception one might say that
Huygens was just taking considerable liberty of reasoning in order to see
how far he could get at fathoming the oddities of strange refraction.
Huygens also afforded himself liberty in another respect. In his notes, he
did not explain his motives for proposing an alternative to Bartholinus’ law.
Like Bartholinus, he extended the mathematical structure of the sine law
through rational analysis. He did not question Bartholinus’ data and confined
his study to mathematical analysis. 152 Also, irrespective of the virtues of
Bartholinus’ verification, Huygens made no effort to justify his conclusions
empirically. If his alternative was more general, he did not check whether it
was anywhere near the truth. Huygens was familiar with such an approach of
mathematical reasoning and it had been successful several times. Although in
his optical studies in De Aberratione it had led him somewhat astray, in his
studies of motion this strategy had been very rewarding. As mentioned in
chapter three, an empirical study of gravitational acceleration had got him
nowhere. The breakthrough had been effected by mathematical analysis of
circular motion.
In his correction of Descartes’ rules of impact, Huygens likewise relied on
rational analysis. He built upon the established, Galilean laws of motion to
find the true laws of impact by means of rational analysis, a strategy he also
chose in his analysis of strange refraction where he built upon the established
law of ordinary refraction. Huygens carried out his study of impact between
1652 and 1656. It has been discussed in full detail by Westfall. 153 He had
found out that Descartes’ rules of impact - a crucial topic in mechanistic
philosophy - where wrong save for the first. In particular in the case of
unequal bodies or speeds, the rules proved inconsistent and failed to obey
Galileo’s principle of relativity. Huygens’ solution lay in rigorously applying
this principle, in combination with the principle of inertia. In so doing, he
converted the study of impact into an extension of Galileo’s theory of
uniform motion, namely, the inertial motion of the center of gravity of two
colliding bodies. 154 As Westfall shows elaborately, the main thread in
Huygens’ study of impact was an increasing desire to treat impact in terms of
velocities instead of forces, which in his view defied mathematical clarity. As
we shall see in the next chapter, the concept of velocity would be crucial to
Huygens’ understanding of the mechanistic causes of natural phenomena. In
his study of impact Huygens repeatedly solved problems by transforming
them into problems subject to known principles. The principle of relativity
made possible the treatment of all collisions of equal bodies. Collisions of
152 There is no way Ziggelaar’s observation that “Huygens repeats carefully the experiments of Bartholin
on the crystal, measures more exactly, …” can be substantiated. Ziggelaar, “How”, 182.
153 Westfall, Force, 149-155.
154 Westfall, Force, 152-153.