CHAP. VIII.] CELL-MAKING INSTINCT. 207 



in a double layer, the resulting structure would have been as 

 perfect as the comb of the hive-bee. Accordingly I wrote to 

 Professor 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 V 2, or radius x I'4i421 (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 measurements which 

 have been made of the cells of the hive-bee. But I hear from 

 Prof. Wyman, who has made numerous cireful measurements, 

 that the accuracy of the workmanship of the bee has been greatly 

 exaggerated ; so much so, that whatever the typical form of the 

 cell may be, it is rarely, if ever, realised. 



Hence we may safely conclude that, if we 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 suppose the Melipona 

 to have the power of forming her cells truly spherical, and of 

 equal sizes ; and this would not be very surprising, seeing that she 

 already does so to a certain extent, and seeing what perfectly 

 cylindrical burrows many insects make in wood, apparently by 

 turning round on a fixed point. We must suppose the Melipona 

 to arrange her cells in level layers, as she already does her 

 cylindrical cells; and we must further suppose, and this is the 

 greatest difficulty, that she can somehow judge accurately at what 

 distance to stand from her fellow-labourers when several are 

 making their spheres ; but she is already so far enabled to judge 

 of distance, that she always describes her spheres so as to intersect 

 to a certain extent ; and then she unites the points of intersection 

 by perfectly flat surfaces. By such modifications of instincts 

 which in themselves are not very wonderful, hardly more 

 wonderful than those which guide a bird to make its nest, I 

 believe that the hive-bee has acquired, through natural selection, 

 her inimitable architectural powers. 



But this theory can be tested by experiment. Following the 

 example of Mr. Tegetmeier, I separated two combs, and put 

 between them a long, thick, rectangular strip of wax: the bees 

 instantly began to excavate minute circular pits in it; and aa 



