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Spinoza’s Lens-Grinding Equipment


Door to the Hofwijck Estate where Spinoza likely strode

Door to the Hofwijck Estate where Spinoza likely strode


Spinoza Purchases Lens Grinding Laps


…A further reason why convex-concave glasses are less satisfactory, apart from the fact that they require twice the labour and expense, is that the rays, being not all directed to one and the same point, never fall perpendicular on the concave surface. – Letter 36, June 1666

This is what Spinoza writes to mathematician and microscopist Johannes Hudde, part of a correspondence that had begun before the end of the previous year, a correspondence which may have had its impetus in another lettered exchange: the on-going discussions on probability and actuary models between Hudde and Christiaan Huygens of that same year. Spinoza was getting to know his neighbor Huygens, and ends up writing to Hudde, someone he may have known since Rijnsburg and Leiden in the early 60’s.

The value of this letter for those investigating any potential lens-grinding practices Spinoza may have had is that here Spinoza cues that he had his metal shapes or laps made for him, at least at this time in the summer of 1666. The context of these remarks is Spinoza’s argument for the superiority of convex-plano lenses, using the same mathematical analysis of refraction that Hudde uses in his brief “Specilla circularia” (1655). Huygens, the previous summer, had personally calculated to a new degree of precision the phenomena of spherical aberration using convex-plano lenses (something Spinoza may have been privy to), and as Huygens has just left for Paris in April, Spinoza asks Hudde for both practical and theoretical optical advice.

I only wish to present to this context information about the kinds of workmen the Huygens brothers used over the years for their own telescopic lens-grinding projects:

View from the Huygens Estate, the Hofwijck

View from the Huygens Estate, the Hofwijck


Christiaan Huygens’ Marbler and Chimney-Sweep

There is no doubt that at first their work consisted solely in grinding and polishing the glass. Even the metal shapes, on which the lenses were ground, were obtained from the outside. Their first ones were of iron (in 1656 Caspar Kalthof supplied one of these, [OC1, 380-81]), later they used copper shapes but for many years they did not make any themselves. In 1662 Christiaan still stated quite emphatically that he had never bothered with making shapes, although he did correct and finish them (OC4 53), and in 1666 in Paris he had a copper shape supplied to him (OC6, 87). But by 1668 we hear that Constantijn makes small shapes (for eyepieces) himself, on a lathe (OC6, 209), and it would appear that later he learned to make larger ones as well, for the instructions for making Telescope-lens (written in 1685 by the two brothers together) contains  detailed instructions about this part of the work (OC21, 251).

“Christiaan Huygens and his instrument makers” (1979), J. H. Leopold


It is not entirely clear if the brothers made their own eyepieces around 1660, but they did not do so later on. Occasionally their correspondence contains references to local craftsman who prepared glass or ground eyepieces; the brothers focused on the delicate work of grinding object lenses.

In 1667 and 1668, Constantijn employed Cornelis Langedelf for polishing glass and grinding eyepieces, and in 1683 this same man delivered the tubes for one of Constantijn’s telescopes. From 1682 the brothers preferred the services of Dirk van der Hoeven, who lived nearby in The Hague. At the same time the brothers also did business with a marbler van der Burgh, who supplied them with grinding laps and glass. The relationships the brothers had with these two craftsmen were not identical. In the case of van der Hoeven – he was often simply referred to as Dirk or the chimney-sweeper – it was only his labour was hired. The brothers supplied the materials and tools, including the grinding laps. Van der Burgh, on the other hand, had a workshop of his own, and the Huygens[es] were were not his only clients. Moreover, one might expect this marbler to have been a more skillful grinder than his chimney-sweeping fellow citizen. So, it was probably was not the routine preparatory work that Constantijn asked of van der Burgh in April 1686, when he sent him two pieces of glass to be flattened 15.

“The Lens Production by Christiaan and Constantijn Huygens” (1999), Anne C. van Helden and Rob H. van Gent

What seems evident from both the Helden and Gent account, and the interpretation of Leopold is that it was not uncommon at all to hire-out for the production of the metal laps in which lenses would be ground. It seems clear from Spinoza’s letter 32 to Oldenburg in November of 1665 that the Huygenses were at least in the possession of a lathe that not only could grind lenses, but also laps or pans, for it is regarding this very (semi-automated) turning of the pans that Spinoza had his greatest doubts:


Whether anything good came of this Huygens lathe we cannot know. What is significant though in this combination of evidence, is that Spinoza seems to have made use of someone like the marbler Dirk van der Hoeven, at The Hague, just as the Huygens did, but also that Spinoza maintained a priority using the free had to either polish these purchased laps, or to polish lenses in them. That a chimney-sweep and a marbler would both be hired by someone as wealthy as the Huygens family, suggests a rather wide-spread and eclectic economic foundation for the procurement of these services and other related grinding services, something that did not require a specialist.

It is interesting to place Spinoza somewhere between the handyman Chimney-sweep and the savant Christiaan Huygens. Perhaps, if we take a more refined glance back through history, he seems to be between holding the straight-forward lathe experience of marbler-turner van der Hoeven and the specialized knowledge of Christiaan’s brother Constantijn, who spared no expense in carrying out Christiaan’s designs and theories.

As I have mentioned several times on this weblog, the picture is a bit more complicated than that. Christiaan Huygens had to bow to Spinoza’s assertion that the smaller objective lens makes a better microscope, and marveled at the polish that Spinoza was able to achieve in his microscopes, a polish achieved by “by means of the instrument” in a method that Christiaan did not seem to know. The speciality of knowledge did not restrict itself to just microscopes, but to telescope lenses as well. It is reasonable that the Huygenses purchased telescopes, microscopes and lathes from the Spinoza estate upon his death, and there does seem to have been something special about Spinoza’s laps (one’s he likely polished), as Constantijn used one in 1687, ten years after Spinoza’s death:

[I] have ground a glass of 42 feet at one side in the dish of Spinoza’s clear and bright in 1 hour, without once taking it from the dish in order to inspect it, so that I had no scratches on that side ” (Oeuvres completes vol. XI, p. 732, footnote). [cited by Wim Klever]

Spinoza, it would seem, used a man like van der Hoeven, but held at least to some particular degree both theoretical and craft advantages over Christiaan Huygens.

Approaching Huygens

Approaching Huygens