Simple or Compound: Spinoza’s Microscopes

Smaller Objective Lenses Produce Finer Representations

A very suggestive clue to the kinds of microscopes Spinoza may have produced is Christiaan Huygens’ admission to his brother Constantijn in a May 11 1667 letter that Spinoza was right in one regard, that smaller objective lenses do produce finer images. This has been cited by Wim Klever to be a sign of Huygens making a concession to Spinoza in a fairly substantial question of lensed magnification:

After some disagreement he had to confess in the end that Spinoza was right: “It is true that experience confirms what is said by Spinoza, namely that the small objectives in the microscope represent the objects much finer than the large ones” [OC4, 140, May 11, 1668]

Cambridge Companion to Spinoza, Wim Klever, “Spinoza’s Life and Works” (33)

And this is how I have read the citation as well, not having access to the original context. But some questions arise. Does this admission allow us to conclude that Spinoza was specifically making compounded microscopes, the kind that Huygens favored? Or are “objective” lenses to be understood to be lenses both of single and compound microscopes. What makes this interesting is that if we accept the easiest path, and assume that Huygens is talking about compound microscopes, then there may be some evidence that clouds our understanding of what Huygens would mean.

Edward Ruestow tells us that be believes that Christiaan Huygens in his 1654 beginnings already had experience constructing microscopes using the smallest lenses possible. If so, Spinoza’s claim regarding compound microscopes would not be new to him (or his brother). Ruestow puts the Huygens account in the context of the larger question of the powers of small objective lenses:

It was not obvious in the early seventeenth century that the smaller the lens – or more precisely, the smaller the radius of its surface curvature – the greater its power of magnification, but smaller and more sharply curved lenses were soon being ground as microscope objectives, at first apparently because, with their shorter focal lengths, they allowed the instrument to be brought closer to the object being observed. The curvature of a small cherry ascribed by Peirsec to the objective of Drebbel’s microscope was already a considerable departure from a spectacle lens…

Whatever the intial reason for resorting to smaller objective lenses, however, it was not such as to produce a continuing effort to reduce their size still further. (A lens, after all, could come too close to the object for convenience.) In 1654 a youthful Christiaan Huygens, already making his own first microscopes or preparing to do so, appears to have ordered a lens as sharply curved as a local lens maker could grind it, and it may indeed have been a planoconvex objective lens with which he worked that year whose curvature, with a radius of roughly 8mm, was still to that of Drebbel’s (i.e. to the curvature one might ascribe to a small cherry). Fourteen years later, however, Christiaan was inclined to lenses with a focal distance of roughly an inch, and he pointedly rejected small lenses as objectives – primarily it seems, because of their shallow depth of focus…In 1680 members of the Royal Society were admiring a biconvex lens no more than one-twentieth of an inch in diameter, and Christiaan Huygens, now with a very altered outlook, would write that the perfection of the compound microscope (of two lenses) was to be sought in the smallness of its objective lens. He claimed at the end of his life that the magnification such instruments could achieve was limited only by how small those lenses could be made and used [note: On the other hand, he also recognized that there was an absolute limit for the size of any aperture, beyond which the image become confused.] (13)

[Ruestow footnotes that the 1654 microscope described as constructed by Christiaan above, is thought by J. van Zuylen is rather the Drebbel microscope purchased by Christiaan’s father, Constantijn Sr.]

The Microscope in the Dutch Republic, Edward G. Ruestow

Not only is Huygens’s turn around described, no doubt fueled by his own famed success with the single lens, simple microscope, just after Spinoza’s death, but also Ruestow suggests that Huygens indeed already knew what Spinoza’s claimed, that smaller objectives indeed do make larger magnifications, his objection being not that the magnification is inferior, but simply that the depth of field makes observation problematic. It is unclear if Ruestow’s reading of the 1654 for is correct, so we cannot say for certain that Huygens had this experience with smaller objectives, but it is interesting that Ruestow cites the same year as his concession to Spinoza, (1668, “fourteen years later” without direct citation), as the year when Huygens makes clear what his objection to smaller objectives is. This raises the question: Is the “confession” in context part of an admission of the obvious between Christiaan and his brother, something of the order, “As Spinoza says objectives represent objects with greater detail, but the depth of field is awful? (Again, because I do not have the text I cannot check this.) 

Or, does Ruestow make a mistake? Is it not letters written 14 years, but only 11 years later, when Huygens in his debate with Johannes Hudde seems to have readily accepted the possibility of greater magnification, but makes his preference in terms of depth of field. As Marian Fournier sums: 

Hudde discussed the merits of these lense with Huygens [OC5, April 5, 10 and 17 1665: 308-9, 318, 330-1], who declined their use. He particularly deplored their very limited lack of depth of field. He found it inconvenient that with such a small lens one could not see the upper and underside of an object, a hair for instance, at the same time. The compound microscope had, because of the much smaller magnification, greater defintion so that the objects were visible in their entirety and therefore the compound instrument was more expedient in Huygens’ view (579) 

“Huygens’ Design of the Simple Microscope”

It is important that Hudde is not only championing smaller objectives, he is attempting to persuade Huygens that the very small bead-lenses of simple microscopes are best. Hudde had this technique of microscopy from as early as 1663, perhaps as early as 1657, and he taught it to Swammerdam. In the context of these letters, apparently written just as Huygens and Spinoza are getting to know each other in Voorburg, Huygens’ 1668 brotherly admission reads either as a distinct point in regards to compound microscopes, or signifies a larger concession in terms of his debate with Hudde. There are some indications that Hudde and Spinoza would have known each other in 1661, as they both figure as highly influential to Leiden Cartesians in Borch’s Diary. And Spinoza was a maker of microscopes, as Hudde was an enthusiast of the instrument even then. It makes good that there would have been some cross-pollination in the thinking of both instrument maker’s techniques in those days, but of this we cannot be sure. 

Against the notion that Spinoza has argued for simple microscope smaller objectives with Huygens is perhaps the compound microscopes achieved by the Italian Divini. Divini, in following Kepler’s Dioptice, realizes a compound microscope whose ever descreasing size of the objective increases its magnification. I believe that there is good evidence that Spinoza was a close reader of Kepler’s (see my interpretation of Spinoza’s optical letters: Deciphering Spinoza’s Optical Letters ). If Spinoza was making compound lenses, and he had argued with Huygens that the smaller the objective the better, it seems that it would have been the kind of microscope described below, following the reasoning of Kepler, which he would have made. 

First, Silvio Bedini sets out the principle of Divini’s construction: 

Divini was an optical instrument-maker who established himself in Rome in about 1646 and eventually achieved note as a maker of lenses and telescopes. In a work on optics published in Bologna in 1660 by Conte Carlo Antonio Manzini, the author describes a microscope which Divini had constructed in 1648, based on Proposition 37 of the Dioptrice of Johann Kepler. This was a compound instrument which utilized a convex lens for both the eye-piece and as the objective was reduced so were the magnification and the perfection of the instrument increased (386).

Then he typifies a class of microscope of which Divini was known to have constructed with this line of analysis:

One form consisted of a combination of four tubes, made of cardboard covered with paper. Each tube was slightly larger than the previous one, and slid over the former. An external collar at the lower end of each tube served as a stop to the next tube. The ocular lens was enclosed in a metal or wooden diaphragm attached to the uppermost end of the largest tube. The object-lens was likewise enclosed in a wooden or metal cell and attached to the bottom of the lowermost or smallest tube. The rims of the external collars were marked with the digits I, II, and III, in either Roman or Arabic digits, which served as keys to the magnification of the various lengths as noted on each of the tubes. The lowermost of the tubes slid within the metal socket ring of the support and served as an adjustment between the object-lens and the object. The instrument was supported on a tripod made of wood or metal. It consisted of a socket-ring to which three flat feet were attached (384).

 And lastly he presents an example of this type, which he calls Type A:

(Pictured left, a 1668 microscope attributed to Divini):The socket-ring and feet are flat and made of tin, and the cardboard body tubes are covered with grey paper, with the digits 1, 2, and 3 inscribed on the collar tubes. The lowermost tube slides with the socket-ring for adjustment of the distance between the object-lens attached to the nose-piece in a metal cell, and the object. The ocular lens is enclosed in a metal holder at the upper end of the body tube. It consists of two plano-convex lenses with the convex surfaces in contact. The original instrument had a magnification of 41 to 143 diameters. The instrument measured 16 1/2 inches in height when fully extended and the diameter of the largest body tube was 1 1/2 inches. A replica of this instrument, accurate in every detail, was made by John Mayall, Jr., of London in 1888 (385-386).

“Seventeenth Century Italian Compound Microscopes” Silvio A. Bedini

 This 16 1/2 inch compound microscope indeed may not have been the type that Huygens’ comment allows us to conclude that Spinoza built, but it does follow a Keplerian reasoning which employed the plano-convex lenses that Spinoza favored in telescopes, one that imposed the imparitive of smaller and smaller objective lenses. It is more my suspicion that Spinoza had in mind simple microscopes, but we cannot rule out the compound scope, or even that he was thinking about both.

Futher, Spinoza’s favor of spherical lenses and his ideal notion that such spheres provide a peripheral focus of rays (found in letters 39 and 49), seems to be in keeping with the extreme refraction in smaller objectives in microscopes, although he attributes this advantage to telescopes. More than in telescopes, the spherical advantage in conglobed, simple lensed microscopes, would seem to make much less of the prominent question of spherical aberration. But in the case of either compounds or simples, the increase curvature, and minuteness of the object lens would fit more closely with Spinoza’s arguments about magnification, and Descartes’ failure to treat it in terms other than the distance of the crossing of rays.

To Understand Spinoza’s Letter 32 to Oldenburg

It is November of 1665, and Spinoza has just that summer likely spent much time in communication and possible visitation with the esteemed Christiaan Huygens, whose estate is a mere 5 minutes walk from where he lives. The two of them are ensconced in the quiet village of Voorburg, but it was a summer in which plague was ravaging London at a rate of nearly 6000 a week, and the secretary of the Royal Society of England, Oldenburg, has begged Spinoza for an update on the discoveries and devices of Huygens, as if upon such innovations the figurative health of society depends.

Spinoza responds with some telling remarks, upon which I have already registered some thoughts: Spinoza’s Comments on Huygens’s Progress. Here though, I want to post some relevant illustrations from Huygens’s notebooks, which make much more clear just what Spinoza may find objection to in Huygens’s fabrica. What Spinoza writes is this:

The said Huygens has been a totally occupied man, and so he is, with polishing glass dioptrics; to that end a workshop he has outfitted, and in it he is able to “turn” pans – as is said, it’s certainly polished – what tho’ thusly he will have accomplished I don’t know, nor, to admit a truth, strongly do I desire to know. For me, as is said, experience has taught that with spherical pans, being polished by a free hand is safer and better than any machine.

(This was the summer that Huygens will have solved the issue of spherical aberration using a solely combination of spherical lenses. But Spinoza does not know this.) We can assume that Spinoza has seen the machine that Huygens is fast at using. In order to see with Spinoza what this machine likely entailed, one must turn to several illustrations. Since the 1650s Huygens had experimented with (and likely used) an assisted means of steadying the glass blank against the spinning metal grinding form. The nature of this technical strategy was a long “bâton” which would restrict the kinds of movements the blank was capable of:

This is a detail of the device, followed by the wide view:

Oeuvres Complètes, XVII (p.300)

Oeuvres Complètes, XVII (p.299)

As one might see, the glass blank can toggle to a degree. This is what professor Graham Burnett writes of it in his Descartes and the Hyperbolic Quest: Lens Making Machines and Their Significance in the Seventeenth Century:

In the late 1650s, [Huygens] outlined the improved “bâton” technique for handling the lens in the forming pan [above illustrations cited]. Previously, the lens blank had been afixed by means of pitch or rosin to a short wooden or stone handle called a mollette. This short handle and wide distribution could lead to a rocking of the blank as it guided over the form, resulting in distortions of shape. Huygens’s improvement made use of an iron pin which acted as a bearing in the center of a piece of wood sitting over the glass. The pin was affixed to a wooden shaft that was suspended from above. This arrangement did not necessitate the use of pitch to attach the lens, and thus avoided fouling the abrasive with fragments of rosin. The technique must have worked well, because Huygens referred to using it into the early 1660s and even dedicated to it several pages in his extensive De Vitris Figurandis…representing work done in the 1670s and 1680s (97 – 98 )

Whatever the fabrica that Spinoza saw and commented on, it most surely employed something of the bâton mechanism. And it is likely that it is at least in part this that Spinoza is commenting on when he says: “experience has taught that with spherical pans, being polished by a free hand is safer and better than any machine”. But the automated potential of Huygens’s machine exceeds this semi-assisted mechanism, for there is a long history of Huygens’s conceptual experimentation with a fully automated device which would both hold the glass blank, but also turn and grind it. In these the glass blank and the forming pan apparently spun against each other in opposing directions. Here are several of these prospective machines:

Oeuvres Complètes, XVII (p.303)

 Oeuvres Complètes, XVII (p.304)

As Graham Burnett describes:

They are gear- and belt- driven, imparting both rotary and epicyclic motion to the glass blank, and they are all represented as self-contained boxes out of which lenses would emerge more or less by the turn of the crank. In fact in [the figure from page 303 of OC], it appears that the crank itself was forgotten and had to be added as an afterthought – a pentimento that speaks volumes concerning the preoccupation with excessive of the process (98 )

Burnett’s global point, if I read him right, is that Huygens’ plans for a completely mechanized production of mathematically exact lenses, purged from the human errors of the craftsman, is in the heritage of Descartes own, highly unrealistic schemata for a hyperbolic lens-grinding machine, symptomatic perhaps of a tendency to divorce body from mind. Burnett is quick to point out that Huygens, unlike Descartes, had extensive experience both in grinding lenses, and using them for discovery (for instance his discovery of the moon and rings of Saturn in 1656 is epic), yet the overall point of this tendency in conception holds. And likely it is to this that Spinoza is in some degree responding.

To better conceive of the contrast between whatever state the Huygens machine may have exhibited (in this spectrum of automatizations), and the simple lathe Spinoza may have employed, a juxtaposition of one of Huygens’s drawings a reproduction of a possible Spinoza lathe will serve:

 

 Oeuvres Complètes, XVII (p.302)

From the Middelburg 400th Anniversary of the Telescope Exhibit, design from Manzini’s “L’occhiale all’occhio, dioptrica pratica”  (1660), circa 1614.

From Manzini

One can immediately see the kind of condensed block mechanism that Huygens would like to have built, and to some degree had built, and the kind of traditional lathe that Spinoza may have used. In fact I have come to strongly suspect that in addition to the simple hand driven lathe depicted above, he likely also used a spring-pole lathe (such as the one in the Rijnsburg museum [here], though this museum piece is not of the period, nor a lens grinding lathe), most likely of the kind Hevelius used (pictured below) the hypothesis discussed here:

Spinoza’s lathe emphasized personal skill, the sensitive hand-eye-machine interface that drew not only on experience and a patient, attentive eye, but also on the particular passed on abrasive recipes and techniques of individual masters. Huygens’s ambition, as was Descartes’ was to transcend the event of crafting, mathematically. That is, with a mathematics that was embodied by the mechanism itself he hoped to simply machine the accuracy. Spinoza’s doubts to whatever fabrica he saw at the Huygens Estate were doubts about removing the “free hand” from the technology. And there is something to this that goes beyond whether this machine or that is at any one moment in history the better machine.

Speculatively: What Spinoza has in mind with the “free hand” is that the human element must be included in any epistemological assemblage. He would no more refuse the mechanized advances in contemporary technology than he would refuse more and more adequate ideas, but he would still look for the “free hand”, the touching point that circulates that knowledge back down to the user, and other men. Technical knowledge still must be human knowledge. The causes of things related to the causes of men. This is what I believe he meant by the fourth stimulation of the “means necessary to attain our end” in the Emendation of the Intellect:

4. To compare this result [the extent to which things can and cannot be acted upon] with the nature and power of man.

There is no doubt that Huygens was on the right track. His mentality was to lead him to a wave theory of light to complement Newton’s spectrum discoveries of the same. In fact, Huygens’s scientific discoveries and inventions are prodigious for the age, but it is good to note that Spinoza in the year of 1665 was fairly close to Huygens, and in many ways Spinoza’s optical and practical knowledge circulated with that of Huygens. That latter would affirm as late as 1668 that Spinoza was in fact right all along about the superiority of small objectives in microscopes, and had marveled at the lens polish that Spinoza was able to achieve through rather craftsman-like means. In reading the objection that Spinoza makes to Huygens’ machine one should understand it at two levels. The first is simply the pragmatic matter of an experienced craftsman who is not intoxicated by technical marvels in their own right. The turning of shiny gears does not make his heart sing. Taking his hand off the lens seems to him one of the last things one would want to do, and it would take a striking result to convince him otherwise, a result which Huygens would not be able to provide. The second level is as vast as the first is earthbound. Spinoza’s notion is that no matter how intricate the device (or the mathematical figure), the meaning of its products, the degrees to which their ideas set us free or not, must relate back to the human being itself, as it finds itself in history. In a sense, Spinoza is looking microscopically beneath, and macroscopically beyond Huygens’s improvements in his letter 32, as a craftsman and a metaphysican.

Some Personal Thoughts on a Possible Spinoza Lathe

Some discussion has been going on over at the Practical Machinist forum, where I have sought any views about the real world workings of any of the devices Spinoza may have used at grind lenses. I have come to the thought that it might very well be a rather simple device that Spinoza used, not much differnt than the one Manzini depicts for the start of the 17th century:

In response to my query someone was kind enough to relate some of his own, unique experiences with a machine not unlike the one illustrated. I post them here because they serve to vivify the elementary nature of these technical movements, in the manner of which a 20th century workman and a 17th century philosopher might share an experience of material and design effects.

Joe writes:

When I was in my 20s I worked for a couple of years at the Peerless Optical Co in Providence, Rhode Island, making lenses for glasses. While much of the work was automated to a degree there was still a little corner of the shop where very special lenses were ground. Because I was actually interested in the work, that became my department.

The lenses were ground against iron forms, called “laps” (either convex or concave) using a variety of progressively finer abrasives. The final polish was achieved by gluing a thick disc of felt to the lap and using a much finer polishing media. The lap spun in a bucket-like contraption that worked very much like a potters wheel. The lens was kept in contact with the lap by means of a hinged arm with an adjustable pin. The arm was held in place with the left hand, the pin pushing against the lens, while you added abrasive to the lap with the right hand. To secure the lens without damaging it, a small flat piece of metal with a center hole was “glued” to it using thick green pitch, exactly like the “sealing wax” used before the invention of gummed envelopes. We melted the pitch onto the lens with a bunsen burner. It was removed by chilling the whole piece, at which point the pitch would harden and fall off the glass.
Other than the motor that spun the lap, there isn’t a thing about this whole process that any 17th century mechanic would find surprising. Also, with particularly difficult lenses, I would have to forgo the hinged arm and hold the lens against the lap with my hand.

In our case, a special purpose-built machine re-cut the laps when they wore…I had a beautiful engraved set of brass gauges which I used to check them (by holding the gauge and lap up to a window) and which must have been 100 years old or more when I was using them. I can see where a lathe of some sort would be essential for making the laps, a primative lathe would suffice, but I can’t see it being used to actually make the lens itself.

The machine illustrated in the post above this one is very much like what I am describing. In fact, other than the hand operation it would be instantly recognizable to anyone who was making lenses in the manner I was. I actually made a couple of lenses for an antique telescope on this equipment…they worked perfectly.

In coincidence to this, Rijk-Jan Koppejan sent me a photograph of a reproduction of just this illustrated device, built by his team and part of their exposition on the invention of the telescope, organized around the 400th year Middelburg anniversary. There is to be a symposium of speakers in September, which I just may have to find a way of attending. He says he may be able to take new, more revealing photographs and send them. I will post them as he might.

Joe mentions that the curvature of this grinding “dish” may be too extreme, but that Manzini’s illustrator may not have thought this a significant factor (also, we cannot see the internal curavature of the reproduction). I don’t know enough about the optics of the time to comment.

He mentions as few more interesting details of his memory of lens grinding with such a lathe, in particular the method he had to use to correct the wear on the “laps” (as he calls them) – Spinoza calls them patinas or scutellae, plates or dishes – and thoughts about processes by which a spherical lens is checked for its optical quality:

I suspect that the drawback to using male/female laps against each other is that both pieces will wear. I am guessing that if the lens maker had a set of gages like I used, which are simply used to check the curve, the lap could be spun in any lathe-like machine and the surface selectively filed or ground to return it to true. As I’ve said, I held the lap and the gage up to a window and looked for a streak of light between them…a very accurate way of measuring once you have some practice and know what to look for.

…Another memory just came back…I think that the felt was attached to the lap with fish or hide glue. The lens was checked by holding it up to a light bulb with a single filiment. You held it in such a way that the light from the filiment reflected off the surface. If there were no breaks or nicks in the reflection, the lens was perfectly true. This could also be done by stretching a hair across a window and picking up the shadow. You could never see the imperfections with the naked eye..

…The lens was finished in what we called an “edger” which was nothing more than a lathe-like spindle that gripped the little metal piece glued to the lens and spun it against a grinding wheel. These were not the modern clay-based wheels but slow turning natural stone wheels that ran in water, the grinding wheel turning one way and the lens in the opposite direction. In this way the outer edge was gradually reduced in a manner perfectly concentric with the optical center. Even if the metal attachment was slightly off center on the original lump of glass, this process insured that it would be perfectly concentric when finished. You could only remove the metal piece after this was done and you could not replace it perfectly so it was a once-chance-only affair.

Althought at this point it is only a collective intution that Spinoza did not use a large, spring-pole lathe such as the one shown at the Rijnsburg, there are some facts that lead to me this thought. First is that when Huygens writes of the superior polish of Spinoza’s lenses, he describes them as “little lenses”:

“the Jew of Voorburg finishes his little lenses by means of the instrument and this renders them very excellent” (Complete Works, 6:155).

I do not have the original word from which “instrument” is translated, but at least at this point it strikes me that this is a small device. And these lenses are small. I am unsure if Huygens is talking about telescope lenses or microscope lenses, but there is the implication of very fine work. This also coincides with Spinoza’s own light criticism of Huygens’ very complex machine, in letter 32 to Oldenburg. (See some of my thoughts on this here.) It is of course possible that Spinoza had a spring-pole lathe much like the Rijnsburg and Hevelius lathes, but the contrast between his own approaches and Huygens’s seems more at home with a simpler device. There are other factors that cause me to think that this is so, but for now this is enough to discuss.