Tracing Snowflakes

December 20th, 2018

Unseasonably warm temperatures here in Madison have recently melted what little snow we have received this season. By way of what we’re missing, we turn first to Robert Hooke’s Micrographia, with its attention to “Observables in figur’d snow,” beginning on page 91: “Exposing a piece of black Cloth, or a black Hatt to the falling Snow, I have often with great pleasure, observ’d such an infinite variety of curiously figur’d Snow, that it would be as impossible to draw the Figure and shape of every one of them, as to imitate exactly the curious and Geometrical Mechanisme of Nature in any one.” Hooke referred the reader to examples in the engraved plate labeled Schem. VIII, and noted that “they were always branched out with six principal branches, all of equal length, shape, and make, from the center, being each of them inclin’d to either of the next branches on either side of it, by an angle of sixty degrees.”

Schema VIII, in Robert Hooke, Micrographia: Or some physiological descriptions of minute bodies made by magnifying glasses (London: Printed for John Martyn, 1667). Thordarson Collection, Department of Special Collections, Memorial Library, University of Wisconsin-Madison.

For more, see “Observ. XIV. Of several kindes of frozen figures,” pages 88-93, in the Thordarson copy of Micrographia available in UW Digital Collections.

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Snowflakes received more attention in volume 6 (1740) of the Miscellanea berolinensia — in full, the Miscellanea berolinensia ad incrementum scientiarum ex scriptis Societati Regiae Scientiarum exhibitis edita, cum figuris aeneis et indice materiarum, call number: AS182 B382 A3, principal publication of the 18th-century Berlin Academy of Sciences — which contained a short article by Johannes Lulofs (1711-1768) on the shape of snow (num. XIV, pp. 83-89).

The snowflakes comprising Tab. I, engraved by F. H. Frisch, began with a simple six-pointed figure with radii separated by 60 degrees, as explained on page 84, but quickly increased in complexity, as the successive figures suggest. Miscellanea berolinensia, vol. 6.

Lulofs, one of numerous 18th-century Dutch natural philosophers of a Newtonian stripe, was closely associated with another, Petrus van Musschenbroek (1692-1761), whose textbook, Elementa physicæ: Conscripta in usus academicos, editio altera (Leiden: Apud Samuelem Luchtmans, 1741), included a similar array of snowflakes, and pointed back to Hooke’s elegant depictions (page 539). 

Tab. XXIV in Musschenbroek’s Elementa physicæ. 

The Elementa physicæ (call number: Tank LH M98) is part of the Tank Collection, which contains thousands of titles from the library of the Reverend R.J. van der Meulen, minister of the Dutch Reformed Church, as donated to the Wisconsin Historical Society by his daughter, Mrs. N. O. Tank; the Society subsequently transferred the collection to the UW-Madison Library. Though best known for its theological holdings, the Tank Collection is also rich in works by Dutch natural philosophers. For more on the complicated publishing history of Musschenbroek’s textbooks, see Kees de Pater, ” ‘The Wisest Man to Whom this Earth Has as Yet Given Birth’: Petrus van Musschenbroek and the limits of Newtonian natural philosophy,” in Newton and the Netherlands: How Isaac Newton was fashioned in the Dutch republic, ed. Eric Jorink and Ad Maas (Amsterdam: Leiden University Press, 2012), on p. 143.

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As we noted in a previous December, one of the plates for Physique in the Encyclopédie of Diderot and d’Alembert also included an array of snowflake diagrams

Plate 2 of 5 for Physique, from Recueil de planches, sur les sciences sciences, les arts libéraux, et les arts méchaniques avec leur explication, vol. 5 (Paris: Chez Briasson, David, Le Breton, 1767), from our full set of the Encyclopédie.

and the description of the plate hearkened back to the discussion in the Berlin Academy’s Miscellanea. We have ourselves borrowed a detail from the plate for the Special Collections web site.

— Robin Rider