532 



THE FORMS OF TISSUES 



[CH. 



well they were. The old misunderstanding was at last explained 

 and corrected by Leslie Ellis; and better still by Glaislier, in a 

 Uttle-known but very beautiful paper*. For these two mathe- 

 maticians shewed that, though Maraldi's account of his "measure- 

 ments" led to misunderstanding, yet he had really done well and 

 scientifically when he eked out a rough observation by finer theory, 

 and deemed himself entitled thereby to discuss the cell and its angles 

 in the same precise terms that he would use as a mathematician in 

 speaking of its geometrical prototype f. 



y Many diverse proofs { have been 



given of the minimal character of the 

 bee's cell, some few, hke Maclaurin's, 

 purely geometrical, others arrived at by 

 help of the calculus. The following 

 seems as simple as any: 



ABCDEF, abcdef, is a right prism 

 upon a regular hexagonal base. The 

 corners B, D, F are cut oif by planes 

 through the fines AC, CE, EA, meeting 

 in a point V on the axis VN of the 

 prism, and intersecting Bb, Dd, Ff, in 

 Z, Y, Z. The volume of the figure thus 

 formed is the same as that of the 

 L original prism with its hexagonal ends : 

 for, if the axis cut the hexagon ABCDEF 

 in N, the volumes ACVN, ACBX are 

 equal. 

 pjg 205. It is required to find the inchnation 



to the axis of the faces forming the 



/ 



L.eslie Ellis, On the form of bees' cells, in Mathematical and other Writings, 

 1863, p. 353; J. W. L. Glaisher, do., Phil. Mag. (4), xlvi, pp. 103-122, 1873. 



t The learned and original Kieser, in his Memoire sur Vorganisation des plantes, 

 1812, p. iv, gives advice to the same effect: "II est indispensable de se former, 

 avant de dessiner, une idee de Tobjet dans sa plus grande perfection, et de dessiner 

 selon cette idee, et non pas I'objet plus ou moins imparfait, plus ou moins altere 

 par le scalpel.. Voila la methode qu'ont suivi Haller, Albinus et tous les autres 

 grands anatomistes. . . . Mais il faut employer pour cela la plus grande precaution, 

 la circonspection la plus tranquille pour I'observation, etc." 



I Cf. Koenig, Lhuiller and Boscovich, opp. cit. ; H. Hennessy, Proc. E.S. xxxix, 

 p. 253, 1885; XLi, pp. 4^2, 443, 1886; XLii. pp. 176, 177, 1887. 



