A Method of Grinding Small, Spherical Lenses: Spinoza

Van Gutschoven’s Design for Grinding Small Lenses: Letter No. 1147

We have in a letter written to Christiaan Huygens by G. van Gutshoven, descriptions and diagrams of the essential processes for grinding small spherical lenses, as they were likely shared by most contemporaries of the age. The letter is surely a response to a request from Christiaan who may have been in need of smaller lens grinding techniques, either due to his future interest in compound eye-pieces for telescopes, or in regard to the question of the best lenses for microscopes which would later arise in discussions between himself and Johannes Hudde and Spinoza as well. In any case, van Guschoven an Antwerp mathematician, was Huygens’ initial teacher of the complete essentials of lens grinding in the first place, which he gave to him ten years before in a letter dated Feb. 10, 1653. It was by the aid of these instructions, among others,  that Huygens was able to grind one of the most powerful lenses in Europe, and discover the rings of Saturn in 1656.

This letter is dated only as 1663 by the editors of Huygens’s Oeuvres. 1663 was the year that Spinoza had moved to Voorburg, where the Huygens family kept their Hofwijck country estate. That spring Spinoza rented rooms in the home of master painter Daniel Tydeman, but a five minute walk from the Hofwijck. But Christiaanwas not yet there. He was living in Paris with his father who was attempting to curry the diplomatic favor of King Louis XIV, an effort which would result in Constantijn Sr.’s son becoming the secretary to Louis’ Royal Academy of the Sciences, in 1666.

None of this has occurred yet. Christiaan and Spinoza have not yet met (unless they crossed paths momentarily in the summer of 1663, when a traveling Christiaan took leave of Paris to go to London in the off-season). Huygens would not arrive in Holland and develop his relationship to Spinoza until after May of 1664.

What this letter reveals to us though is the basic mechanism and techniques used in the grinding of small lenses. We know that Spinoza made microscopes (and telescopes) at least since the year of 1661, and in his coming debates over techniques and optics with Christiaan he would champion much smaller, more highly curved lenses for microscopes, against Huygens’ designs of lesser magnification. One would think that from van Gutschoven’s descriptions we can receive a sense of the physical practices that preoccupied Spinoza for many of his daylight hours, specializing at times in these smaller lenses.

It should be noted that the Huygens brothers by this time are among the best lens-grinders in Europe, and Christiaan had already worked on several sophistocated semi-automated designs of grinding machines. These instructions must have been experienced as extremely rudimentary to Christiaan (or perhaps, it is from another date).

The letter has three figures, pictured below. The first of these shows a vertical grinding form that is likely of iron or copper. One can see the core movement of a lathe, as foot petal likely drove the strap that turns the shaft, spinning the form concentrically. For larger lenses the form would be hollow, holding the concavity of a curvature that one would want the glass to have. Here though, the small lens is to be ground in the “canal” near its lip:

“Now in this hollowed out canal C D you will grind glasses affixed to a handle and pressed into the canal, with the handle in the hand continuously; while grinding the glass you would turn it until all parts of the glass are equally ground.”

After this equanimity is roughly achieved, attention is turned to the “laminate” or layered strip A B, which turns so the top of it is horizontal to the turner’s bench. By van Gutschoven’sdirection, the laminate is of a soft wood, polar or willow. (Other techniques of the day call for paper.) The roughness of dimples are by hand ground away, and Tripoli, which is a chalky substance made of the remains of microscopic marine life, is added to the laminate to smooth the way.

After this, there is a third process recommended which can either be done in a concave wooden form G H, it too aided by Tripoli, pictured here:

Or, what seems to be a pillow (plombae), affixed to a lathe shaft EG:

There are several things of interest here. The date of the letter makes this description contemporaneous with Spinoza’s own practices, so one might assume a basic correspondence. The grooved canal method strikes one as similar to those a-centric grinding techniques discs used by diamond polishers which Spinoza may have come in contact with either briefly as a merchant of gems, or simply by growing up in a community where gem polishing. The process remained unchanged for several hundred years as late 19th century illustration below shows:

Like the diamond polisher, it is quite possible that Spinoza’s form was oriented horizontally, and not as van Gutschoven suggests, vertically. This was part of a gradual change in lens grinding techniques, much of it initiated by gem polishing influences. The horizontal mould simply made the glass easier to control, and the variable polishes to be administered more cleanly. For this reason, any polishing with Tripoli also occurred on a horizontal, turning wheel. The grinding forms designs that I have seen that the Huygens were using now all had a horizontally oriented lap. 

The second thing to note that in 1667 and 1668, after Christiaan had come to know Spinoza and become familiar with Spinoza’s techniques, he clearly did not still feel comfortable with the limits of van Gutschoven’s design, whenever he had received it, as he in repeated letters urged his brother about the fineness of Spinoza’s small lens polishing. Spinoza’s technique was not that of van Gutschoven. It is my feeling that he had developed, either though his associations in the community he grew up in, those influenced by the practices of gem polishing, means of polishing that were not common to the rest of Europe. Whether these be methods of grit application, the use of diamond dust, particular designs of a simple but effective lathe, one can only surmise. But it seems that Spinoza’s glasses were of a quality and luminosity that made them distinct.

Here is the Latin Text of van Gutschoven’s letter: The Text of van Gutschoven’s Letter to Huygens No. 1148

Conclusion

Aside from this I would want our investigative imagination to extend itself to the physical understanding of these practices, and the conceptual impression they would leave upon a thinking man who engaged in them repeatedly. This has been a theme of my thinking, that if Spinoza had been a potter we may do well to think about his metaphysics and arguments in terms of the potter’s wheel with which he was familiar. The grinding lathe is not so different from the potter’s wheel, and van Gutshoven’s diagrams give us a visual vocabulary for the kinds of effects and exertions that Spinoza produced in perfecting his craft. What in particular these diagrams allow, apart from the general understanding of the grinding lathe, is the picture of a grooved grinding practice, the canal, which varies from the greater method of placing a glass blank within a concave metal form. If indeed Spinoza used this method for his small objectives for microscopes, we can think along with him in the craft of it, and see him bent over the lip of the spinning canal.

As pictured here before, here is an example of a foot petaled lathe from the year 1647, that used by Hevelius. It may give us a dynamic sense of the physical engagement:

Here is a closer look at the Hevelius Lathe: Spinoza’s Grinding Lathe: An Extended Hypothesis

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