SECTION 22.OBSERVA TION. 321 



been remarked that a skilful workman with fitting tools and measures, 

 would find it very difficult to make cells of wax of the true form, though 

 this is effected by a crowd of bees working in a dark hive. Granting 

 whatever instincts you please, it seems at first quite inconceivable how 

 they can make all the necessary angles and planes, or even perceive when 

 they are correctly made. But the difficulty is not nearly so great as it 

 at first appears : all this beautiful work can be shown, I think, to follow 

 from a few simple instincts. 



"I was led to investigate this subject by Mr. Waterhouse, who has 

 shown that the form of the cell stands in close relation to the presence 

 of adjoining cells; and the following view may, perhaps, be considered 

 only as a modification of his theory. Let us look to the great principle 

 of gradation, and see whether Nature does not reveal to us her method 

 of work. At one end of a short series we have humble-bees, which use 

 their old cocoons to hold honey, sometimes adding to them short tubes 

 of wax; and likewise making separate and very irregular rounded cells 

 of wax. At the other end of the series we have the cells of the hive- 

 bee, placed in a double layer: each cell, as is well known, is an hexagonal 

 prism, with the basal edges of its six sides bevelled so as to join an in- 

 verted pyramid of three rhombs. These rhombs have certain angles, and 

 the three which form the pyramidal base of a single cell on one side of 

 the comb enter into the composition of the bases of three adjoining cells 

 on the opposite side. In the series between the extreme perfection of 

 the cells of the hive-bee and the simplicity of those of the humble-bee 

 we have the cells of the Mexican Melipona domestica carefully described 

 and figured by Pierre Huber. The Melipona itself is intermediate in struc- 

 ture between the hive- and humble-bee, but more nearly related to the 

 latter; it forms a nearly regular waxen comb of cylindrical cells, in which 

 the young are hatched, and, in addition, some large cells of wax for hold- 

 ing honey. These latter cells are nearly spherical and of nearly equal 

 sizes, and are aggregated into an irregular mass. But the important point 

 to notice is, that these cells are always made at that degree of nearness 

 to each other that they would have intersected or broken into each other 

 if the spheres had been completed ; but this is never permitted, the bees 

 building perfectly flat walls of wax between the spheres which thus tend 

 to intersect. Hence, each cell consists of an outer spherical portion, and 

 of two, three, or more flat surfaces, according as the cell adjoins two, 

 three, or more other cells. When one cell rests on three other cells, 

 which, from the spheres being nearly of the same size, is very frequently 

 and necessarily the case, the three flat surfaces are united into a pyramid ; 

 and this pyramid, as Huber has remarked, is manifestly a gross imitation 

 of the three-sided pyramidal base of the cell of the hive-bee. As in the 

 cells of the hive-bee, so here, the three plane surfaces in any one cell 

 necessarily enter into the construction of three adjoining cells. It is 

 obvious that the Melipona saves wax, and what is more important, labour, 

 by this manner of building; for the flat walls between the adjoining cells 

 are not double, but are of the same thickness as the outer spherical por- 

 tions, and yet each flat portion forms a part of two cells. 



"Reflecting on this case, it occurred to me that if the Melipona had 

 made its spheres at some given distance from each other, and had made 

 them of equal sizes and had arranged them symmetrically 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 j/2, or radius X 1.41421 (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 



21 



