528 THE FORMS OF TISSUES [ch. 



instance, in the Garden of Cyrus: "And the Combes themselves 

 so regularly contrived that their mutual intersections make three 

 Lozenges at the bottom of every Cell* which severally regarded 

 make three Rows of neat Rhomboidall Figures, connected at the 

 angles, and so continue three several chains throughout the whole 

 comb " Or as Reaumur put it, a little later on: "trois cellules 

 accolees laissent un vuide pyramidal, precisement semblable a celui 

 de la base d'une autre cellule tourn^e en sens contraire." 



Kepler had deduced from the space-filling symmetry of the honey- 

 comb that its angles must be those of the rhombic dodecahedron; 

 and Swammerdam also recognised the same geometrical figure in 

 the base of the cell*. But Kepler's discovery passed unnoticed, 

 and Maraldi the astronomer, Cassini's nephew, has the credit of 

 ascertaining for the first time the shape of the rhombs and of the 

 sohd angle which they bound, while watching the bees in "les ruches 

 vitrees dans le jardin de M. Cassini attenant I'Observatoire de 

 Paris -f." The angles of the rhomb, he tells us, are 110° and 70°: 

 "Chaque base d'alveole est formee de trois rombes presque toujours 

 egaux et semblables, qui, suivant les mesures que nous avons 2^rises, 

 ont les deux angles obtus chacun de 110 degres, et par consequent 

 les deux aigus chacun de 70 degres." Further on (p. 312), he 

 observes that on the magnitude of the angles of the three rhombs 

 at the base of the cell depends that of the basal angles of the six 

 trapezia which form its sides; and it occurs to him to ask what 

 must these angles be, if those of the floor and those of the sides be 

 equal one to another. The solution of this problem is that "les 

 angles aigus des rombes etant de 70 degres 32 minutes, et les obtus 

 de 109 degres 28 minutes, ceux des trapezes qui leur sont contigus 

 doivent etre aussi de la meme grandeur." And lastly: "II resulte 

 de cette grandeur d' angle non seulement une plus grande facilite et 

 simpHcite dans la construction, a cause que par cette maniere les 

 abeilles n'employent que deux sortes d'angles, mais il en resulte 

 encore une plus belle simetrie dans la disposition et dans la figure 



* Kepleri Opera omnia, ed. Fritsch, v, pp. 115, 122, 178, vii, p. 719, 1864; 

 Swammerdam, Tractatus de apibus (observations made in 1673). 



t Obs. sur les abeilles, Mem. Acad. R. Sciences (1712), 1731, pp. 297-331. 

 Sir C. Wren had used "transparent bee-hives" long before; see his Letter concerning 

 that pleasant and profitable invention, etc., in S. Hartlib's Reformed Common- 

 Wealth of Bees, 1655. 



