Lenses and Waves

50 CHAPTER 2
most part derived from Huygens’ dioptrical theories, and I will not discuss
them in further detail. 164
Huygens’ position
Picard’s dioptrical fragments bring us back to Huygens. What had he been
doing in the meantime? In Systema saturnium he had alluded to an elaborate
theory of dioptrics, which we know he possessed indeed. Yet, despite
ongoing requests to publish it, he had kept it to himself. It may be clear by
now that Tractatus is a unique work in the development of seventeenthcentury
dioptrics. Huygens was the first and only man to follow the lead of
Dioptrice. Like Kepler, he combined the two things necessary to develop a
theory of the telescope: mathematical proficiency and an orientation on the
instrument. Unlike Kepler, he had the exact law of refraction and thus he
could rigorously develop an exact theory of the telescope.
But did Huygens really follow Kepler? Did he want to understand the
telescope in view of its use in astronomy? Tractatus came into being well
before Huygens commenced his practical activities of telescope making and
astronomical observation (discussed in the next chapter). Unlike Flamsteed
and Picard, he did not seek answers to questions that had arisen in practice.
Nevertheless, his orientation on the telescope is clear. He passed by all those
sophisticated problems not relevant to the understanding of the telescope
that preoccupied mathematicians like Barrow. However, nowhere does
Huygens mention Kepler as an example. It looks as if developing a theory of
the telescope on the basis of the sine law was to him an interesting
mathematical puzzle, maybe just to correct Descartes’ useless approach to
dioptrics. The problem had not yet been solved and Huygens only too gladly
seized the opportunity. Which makes his exclusive orientation on the
instrument all the more interesting.
The transformation of the telescope into an instrument of precision
brought back an interest in the dioptrical properties of the telescope. In this
regard, one might say that Kepler had prematurely raised the question after a
mathematical understanding of the telescope. In 1611, it was a qualitative
instrument and remained so for another half century. To understand its
working, a qualitative account of the effects of lenses therefore sufficed.
Similarly, we can ask whether an exact theory like Huygens’ was really
needed. It seems that Kepler’s or Keplerian theories satisfied the needs of
men like Flamsteed and Molyneux pretty well. They lacked sufficient
proficiency in mathematics to treat lenses in exact terms, but they may also
have been perfectly satisfied with their approximate results.
Huygens himself did not put much work in applying his theory to the
questions that occupied Picard and Flamsteed. The principle of the
micrometer may or may not have been the result of his theoretical
understanding, in Systema saturnium he explained it only briefly. Huygens did
164 Blay, “Travaux de Picard”, 340.