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Why Spinoza’s Method of Lens Polishing Might Have Been Integral

How The Clouded Glass Sphere Becomes Opened up to Light

Al Shinn has given me a link to work being done by Alvaro Amaro de Azevedo, which might explain why a hypothesized Spinoza lens polishing expertise could prove decisive in employing a single lens technique. First, Amaro de Azevedo approximated a simple, thread-melting techique thought to have been used by Van Leeuwenhoek, and achieved practical results of about x500 magnification and more, reaching those even achieved by Van Leeuwenhoek himself (x266 is I believe the highest magnification of an existing Leeuwenhoek lens, but Ruestow estimates that x500 could not have been “unusual” (14), noting that a recommended lens by Hartsoeker would “entail a magnification of x770”). Amaro de Azevedo even reached a magnification level of x1000 using soley the melted beads of glass thread, whose proximity to the specimen challenged most 17th century specimen staging capacities. If nothing more, this established the ease of dramatic single lens, beaded magnification achievement. Here his experiments are detailed.

Yet Mr. Amaro de Azevedo later learned that nearly all of existent Leeuwenhoek lenses had been ground lenses, and not simply beaded from melted glass. He set to grounding equally powerful lenses. As I have said, Johannes Hudde is reported to have ground his bead lenses (in salt), and Hooke too ground his bead lenses. It has consternated some modern analyzers of this method as to why a rather effective, tiny glass globule lens should prove insuffient? Why grind glass? The answer to this might help establish why an additional and otherwise guarded means of grinding technique might pave the way towards a more effective beaded lens.

Alvaro Amaro de Azevedo in his second round of experiments actual unveils some of the possibilities for these techniques (improvised on modern equipment), and produced results suggestive of the necessity of the additional polishing means. Here is his article, “The Challenge of Grinding Lenses for Single Lens Microscopes” (keeping a close eye upon the aspects that were feasible in the 17th century).

The first thing I notice is that the grinding abrasive required the use of mills, as Alvaro decides to use sand:

Anyone who has ever read about lens grinding techniques is aware that the main resource for succeeding is the grinding powders…I honestly have no idea where such powders could be found locally but the article mentions that Leeuwenhoek might have employed sand and graded it by levigation. So that was what I did. The sand was collected from a nearby beach and then washed thoroughly. After it had dried, the sand was put into a mill where it was crushed for one hour. The resulting flour was then suspended in water and through levigation six fractions were collected. I named them from 1 (the coarsest) to 6 (the finest).

As an simple point of correspondence, bought at the auction of Spinoza’s estate were various “mills” (molens):

and various instruments for grinding (‘en verscheidene slypgereedschap’) like mills (‘molens’, also plural!) and great and small metal dishes serving for them (‘groote en kleine metale schotels daartoe dienende’) and so on” (en so voort).

The plurality of mills suggests a gradation of grits produced, such as perhaps those used by Amaro de Azevedo. Whether these were of salt as Hudde is said to have used, or of sand, these mills speak to a particular technique of grinding and polishing, something that could be passed on through the equipment alone.

Next I noticed his search for a polishing agent:

For polishing purposes, I tried to find the jewelry rouge (iron oxide) but it was in vain. Then I tried to smash a hematite stone and I got a powder that was too coarse for a good polishing powder. Then I made many attempts to find a good substitute and at the end of the day I made a polishing tool that doesn’t need powder to carry on polishing.

His solution is certainly not one that Spinoza would use, though the iron oxide powder may have been something that Spinoza picked up in Amsterdam when he learned to grind glass, given the plethora of gem and diamond polishers that may have florished in his community (it was one for the few non-Guild regulated buisnesses available to Jews). Robert Hooke used “tripoli” (a diatomaceous material, getting its fineness from the remains of microscopic organisms). This was long used by Venetian spectacle makers, its use forwarded by instructional manuscripts written by Sirturus and then Rheita. Because Van Leeuwenhoek put tripoli under his microscope to examine it, it is quite likely that he used this as well.


Lastly though, as Amaro de Azevedo ground his smaller and smaller lenses, leaving behind a cut glass blank, and eventually grinding melted beads of glass themselves, as did Hooke and Hudde (and likely Van Leeuwenhoek), achieving greater and greater limits of magnfication, he comes to the vital point, illumination and focal distance:

The main advantage of ground lenses are that they can focus at longer distances compared to the same magnification from ball lenses and thus, I could capture images from already mounted slides that wasn’t possible before. I also noticed that ground lenses allow wider apertures and as consequence, the images seemed to be brighter and higher in resolution.

A modern maker of the two comparable lenses, that is, of the simple beads of glass spheres, and their tiny ground counterparts might not readily notice the distinct advantage that Amaro de Azevedo brings out here. The reason is, the quality of glass that is readily available to us simple was not makeable then. Glass, even the best of it, was bubbled, marred with striations, and considerably darker, tinged with colored. Any advantage in opening up the aperture and letting in more light was not simply a convenience, but rather probably marked the difference between being able to see a specimen or not. For instance, when Robert Hooke says that the single bead lens is simply too small, and that he fears for his eyesight, he means not only too small, but too small and too dark.

Aligned with this point was the techniques of lighting the specimen would prove most important. Ruestow infers that Hudde’s microscopic observations may have been impaired for many years for it did not occur to him to look directly at a light source, with the specimen in between, an improvement attributed to Van Leeuwenhoek (22, n.85). Is this why Hudde did not come up with any astounding discoveries despite owning the beading technique for more than decade before Van Leeuwenhoek comes upon the scene?

These three factors, rather poor occluding glass, just discovered techniques in lighting and specimen preparation, and in some cases guarded secrets in grinding and polishing techniques, all point to the difficulty of microscopic discovery, when using bead-lenses. What is suggested is that the best polishing of these tiny melted spheres would open up the aperture and clarity of an otherwise murky ball glass lens, when pushed to the greatest of magnifications. Thus the state of the technology may have demanded an adequate polishing means, one provided by the purchase of Spinoza’s equipment by the Huygenses.



How Much were Spinoza’s Lenses and Microscopes?

In the interest of making Spinoza’s lens-grinding, polishing, and telescope and microscope building more vivid to those considering his metaphysics, this evidence is posted as to the kinds of prices for those services one would expect.

Lueken and Lueken (1694)

E. G. Ruestow writes:

At a date I read to be late 1670’s: “…Johan van Musschenbroek in Leiden [sold micro-beaded lenses] forty for a gilder – roughly a day’s wages for skilled manual labor in the Netherlands. Musschenbroek otherwise advertised his cheapest simple microscope for 7½ gilders and his most elaborate, with nine seperate and interchangeable lenses, for nearly ten times as much” (The Microscope and the Dutch Republic, 28).

And the footnote reads: “Johan van Musschenbroek advertised six beads – “Glaze dropjes, en bolletjes” – for three stuivers, which, there being twenty stuivers to the guilder, was the price equivalent to forty for a guilder…Earlier in the century, Constanijn Huygens, Sr., had paid forty guilders for one of Drebbel’s microscopes.”

If indeed Spinoza made simple bead lenses, provided a buyer was available – which for these type lenses would be likely be infrequently – he could make a laborer’s day’s wages in about an hour (Ruestow points out that Swammerdam said he could make them at this rapid rate, 40 and hour). The prices of any primary grinding of lenses to specific focal lengths or uses for other salesmen or instrument makers of course are not reflected here. But perhaps a week’s wages could be made for his simplest microscopes.

Lenses not Rare

One can see from the depiction of a spectacle makers’ storefront, strewn with glimmering lenses and spy glasses, that by the late 17th century such devices are quite common. In fact, when Descartes writes his Dioptrics in 1637, when Spinoza is five years old, he mentions how common “flea glasses” have become. It is good to remember both the commonality of Spinoza’s trade, its brute, craftsman standing, but also the elite circulation of ideas which came about in applying these somewhat widespread devices, both in terms of theories about the nature of what was seen, but also changing techniques and optical conceptions on how to see it. Spinoza stood in both worlds.