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.