218 SPECIAL INSTINCTS. Chap. VII. 



hive-bee, so licre, the three plane surfaces in anyone cell neces- 

 sarily enter into the construction of three adjoining cells. It 

 is obvious that the Meli])ona saves wax, and, what is more im- 

 portant, lal)or, by this manner of buildinjr; for the Hat walls 

 between the adjoining cells are not double, but are of the Siune 

 thickness as the outer spherical portions, and yet each flat por- 

 tion forms a part of two cells. 



Rc^flecting on this case, it occurred to me that if the Meli- 

 pona had made its spheres at some given distance from each 

 other, and had made them of erjnal sizes, and had arranged 

 them s^-nnnetrically in a double layer, the resulting structure 

 would probably have been as perfect as the comb of the hive- 

 bee. Accordingly, I wrote to Prof. Miller, of Cambridge, and 

 this geometer has kindly read over the following statement, 

 drawn up from his information, and tells me that it is strictly 

 correct : 



If a number of equal spheres be described with their centres 

 placed in two parallel layers, with the centre of each sphere at 

 the distance of radius X 1^ 2, or radius X 1.414:'21 (or at some 

 lesser distance), from the centres of the six surrounding spheres 

 in the same layer; and at the same distance from the centres 

 of the adjoining spheres in the other and parallel layer ; then, 

 if planes of intersection between the several spheres in both 

 layers be formed, there will result a double layer of hexagonal 

 prisms united together by pyramidal bases formed of three 

 rhombs ; and the rhombs and the sides of the hexagonal prisms 

 will have every angle identically the same with the best meas- 

 urements Avhich have been made of the cells of the hive-bee. 

 But I hear from Prof. Wyman, who has made numerous care- 

 ful measurements, that the accuracy of the workmanship of the 

 bee has been greatly exaggerated ; so much so, that, as he adds, 

 whatever the typical form of the cell may be, it is rarely, if 

 ever, realized. 



Hence, we may safely conclude that, if Ave could slightly 

 modify the instincts already possessed by the Melipona, and in 

 themselves not very wonderful, this bee would make a structure 

 as wonderfully perfect as that of the hive-bee. "We must sup- 

 pose the Melipona to have the power of forming her cells truly 

 spherical, and of equal sizes ; and this would not be very sur- 

 prising, seeing that she already does so to a certain extent, and 

 seeing what perfectly cvlindrical burrows in wood many insects 

 can make, apparently by turning round on a fixed jioint. AVc 

 must suppose the Melipona (o arrange her cells in level layers, 



