Descartes and Lenses

Descartes other friend beside Father Mersenne was Mr. Mydorge.

Mydorge made lenses for Descartes in Paris in 1627 and 1628, when they enjoyed each other’s company at leisure.

Nothing in the world was more useful to him than these lenses to know and to explain, as he has since done in his dioptrics, the nature of light, vision, and refraction.

Mydorge had him make parabolic and hyperbolic ones, oval and elliptical ones.

And as he had a hand as sure and as delicate as his subtle mind, he wanted to describe the hyperbolas and ellipses himself. This was of marvelous help to Mr. Descartes not only to better understand than he had until then the nature of the ellipse and the hyperbola, their property regarding refractions, the manner in which they must be described; but also to confirm himself in several beautiful discoveries he had already made before regarding light, and the means to perfect vision.

Descartes mastered the art of cutting lenses in a very short time.

This is what he made known 10 years later, to one of his friends who had sent him a lens to examine. In pointing out the defects of this lens cut by a Dutch turner, he speaks to him in these terms, of the way he had had one cut in Paris by means of the lathe. “The lens,” he says, “that I had cut eight or nine years ago, succeeded perfectly well.

For although its diameter was no larger than half of yours, it did not cease to burn with a lot of force at a distance of eight inches: and having put it to the test of a piece of cardboard with small holes, one could see that all the rays that passed through these holes approached proportionally up to a distance of eight inches, where they were very exactly assembled into one. But I will tell you the precautions that were used to cut it.

First, I had three small triangles cut, all equal, which each had a right angle, and the other of thirty degrees, so that one of their sides was double the other.

They were one of rock crystal, the other of crystalline or Venetian glass, and the third of less fine glass. Then, I also had a copper rule made with two sights, to apply these triangles to it, and measure the refractions: and from there, I learned that the refraction of rock crystal was much greater than that of the crystalline; and that of the crystalline than that of the less pure glass. After that Mr. Mydorge, whom I hold to be the most exact at well tracing a mathematical figure that is in the world, described the hyperbola that related to the refraction of Venetian crystal on a large, well-polished copper sheet, and with compasses whose steel points were as fine as needles. Then he filed this sheet exactly according to the shape of the hyperbola, to serve as a pattern, on which a maker of mathematical instruments named Ferrier cut on the lathe a rounded copper mold, of the size of the lens he wanted to cut. And so as not to corrupt the first model by adjusting it often on this mold, he only cut pieces of cardboard on it, which he used in its place, until having brought this mold to its perfection, he attached his lens to the lathe, and applying it with sandstone in between, he cut it very fortunately. But wanting afterwards to cut a concave one in the same way, the thing was impossible for him, because the movement of the lathe being less in the middle than at the ends, the glass wore out less there, although it should have worn out more. But if I had then considered that the defects of the concave lens are not of as great importance as those of the convex, as I have since done, I believe that I would not have failed to have him make quite good telescopes with the lathe.”

This Ferrier of whom Mr. Descartes speaks, and who had apparently been directed to him by Mr. Mydorge, was not a simple craftsman who only knew how to move his hand. He also possessed the theory of his profession, and knew optics and mechanics as surely as a professor of the royal college. He was not completely ignorant in the rest of mathematics; and notwithstanding his condition, he was received among the learned, as if he had been one of them. He particularly attached himself to Mr. Descartes who took him into affection, and who, not content with employing him in a way to enhance his fortune, also wanted to teach him the means of perfecting himself in his art. One of the most excellent instruments he had him make was a new telescope composed of hyperbolic lenses, to which nothing similar had yet been seen. Mr. de Ville-Bressieux, who had seen it, and who had moreover been present at its manufacture, assured that by its means one could distinctly discover the leaves of plants at a distance of three leagues.

One can consider what happened to Mr. Descartes during this space of three and a half years that he spent in Paris, as a summary of the revolutions that his mind had suffered until then, and that he still suffered since regarding his studies and the occupations of his life. He had engaged again in the depths of abstract sciences, which he had previously renounced: but the few people with whom he could communicate, even in the middle of this great city, had disgusted him with it a second time. He had resumed the study of man that he had cultivated so much during his travels. This study of our nature and our state had still persuaded him more than before that these abstract sciences are not too suitable for us, and it had made him perceive that he himself, in penetrating them, strayed even more than other men in being ignorant of them.

He had believed he would find at least among so many honest people many companions in the study of man, since it is the one that suits us the most. But he had seen himself deceived, and he had noticed that in this city which passes for the summary of the world, as in Rome, in Venice, and everywhere he had been, there are even fewer people who study man than geometry.

This made him resolve again quite newly to do without anyone but himself as much as he could, and to be content with a small number of friends for the relief of life. But his reputation was a great obstacle to this resolution. It had made the house of Mr. Le Vasseur a kind of academy, by attracting a great number of people who introduced themselves to his home with the help of his friends. The curious of literature did not fail to slip in among the others: and joining with those of his friends who took the most pleasure in spreading his reputation, they risked proposing to him to take up the pen to share his knowledge and his discoveries with the public. The booksellers themselves, who only seek to trade in the reputation of authors, seemed to want to also be part of the conspiracy of those who were besieging him at Mr. Le Vasseur’s. He himself teaches us that from that time there were people of this profession who solicited him, and offered him presents to engage him to promise them the copy of what he could compose, not being ashamed to want to buy the honor of serving him.

These companies began to make his stay in Paris burdensome to him, and to make him feel his own reputation as an unbearable weight. It is not that, being a man, he did not have a great enough idea of the rest of men to wish to see himself in the esteem of the whole human race if he had been known to it. He has always carried so high the greatness and the force of the reason of man, that one must not doubt the passion he would have had to find himself advantageously placed there. But he did not pretend that this esteem should be accompanied by so many inconveniences: and to begin to deliver himself from the importunities of those who frequented him too often, he left the house of Mr. Le Vasseur, and went to stay in a quarter where he was to hide from their knowledge, and make himself visible only to a very small number of friends who had his secret. Mr. Le Vasseur to whom he had not judged it appropriate to communicate it was for some time in anxiety, finding no one who could give him news of him. But chance having made him meet his valet de chambre in the streets after five or six weeks, he stopped him on the spot, and obliged him after much resistance to discover to him the residence of his master. The valet after having thus revealed the main part of his secret to him, no longer had any difficulty in declaring the rest to him. He told him all the ways in which his master governed himself in his retreat, and told him among other things that he was accustomed to leaving him in bed every morning when he went out to execute his commissions, and that he hoped to find him there again on his return.

It was almost eleven o’clock, and Mr. Le Vasseur, who was returning from the palace wanting to be sure on the spot of Mr. Descartes’s residence, obliged the valet to become his guide, and had himself led to Monsieur Descartes’s.

When they arrived there, they agreed that they would enter without noise, and the faithful guide having gently opened the antechamber to Mr. Le Vasseur, left him as soon as possible to go order dinner.

Mr. Le Vasseur having slipped against the door of Mr. Descartes’s room began to look through the keyhole, and saw him in his bed, the windows of the room open, the curtain raised, and the side table with some papers near the head of the bed. He had the patience to consider him for a considerable time, and he saw that he got up halfway from time to time to write, and then lay down again to meditate. The alternation of these postures lasted for almost half an hour in the sight of Mr. Le Vasseur. Mr. Descartes having then got up to dress, Mr. Le Vasseur knocked on the door of the room like a man who had just arrived and was going up the stairs. The valet who had entered by another door came to open, and pretended to be surprised.

Descartes was surprised when he saw the person he expected the least.

Mr. Le Vasseur made him some reproaches on the part of Madame Le Vasseur who had felt despised in the way he had abandoned her house. As for him, he was content to ask him for dinner in order to reconcile together.

In the afternoon, they went out together to go find Madame Le Vasseur, to whom Mr. Descartes gave all the satisfaction she could expect, not from a philosopher, but from a gallant man who knew the art of living with everyone. After his return, he had the pleasure of regretting the sweetness of his retreat, and of looking for the means to repair the loss of his freedom: he could not turn away the course of his bad fortune, and he saw himself in a few days fallen back into the inconveniences from which he had delivered himself by hiding.

The displeasure he had from it drove him from his quarter, and gave him the desire to go see the siege of La Rochelle.