Instinct and its Lessons 109 



following problem : " To find the construction of a 

 hexagonal prism terminated by a pyramid composed of 

 three equal and similar rhombs, such that the solid may 

 be made of the least quantity of materials." 1 This 

 problem resolves itself into another, namely, what should 

 be the angles of the rhombs that cut the hexagonal 

 prism, so as to form with it the figure of least possible 

 surface. The value of the angles as found by the Bees, 

 and correctly found, are 109 28' and 70 32'. Also the 

 working Bee must have the power, by whatever process 

 acquired, of striking perfect circles from centres, the 

 distance of which from each other must be accurately 

 adjusted, and the centre of the circle drawn on one side 

 of the comb must be equi-distant from the centres of the 

 three adjacent circles on the other side: a problem 

 which man would find not altogether easy, even though 

 armed with compass and rule. It has been confidently 

 argued, against the obvious inference to be drawn from 

 these facts, that the form and arrangement of the Bees' 

 cells naturally result from the manner in which they set 

 about their work. But the answer is obvious; how 

 did they learn so to set about it? On the whole it 

 is not, I think, an unfair statement of the case, that, 

 either a most delicate mathematical problem is solved 

 by every Bee that makes a cell, or the problem has 

 been solved, once for all, for every Bee before it was 

 born. 



Bees and Wasps perform from their own resources the 

 various operations necessary for the public weal, wax- 

 working, honey-storing, cell-construction, and nursing of 

 the larvae. It is not so with all social insects. Some 

 Ants have another instinct that prompts them to engage 

 in the slave-trade. One of our English species (Formica 

 sanguined) does this at the expense of another (Formica 



1 The problem was proposed in this form by Reaumur to Konig, 

 who calculated the angles as 109 26' and 70 34'. Further calcu- 

 lation has shown that the trifling error was on the side of the mathe- 

 matician, or rather on the table of logarithms he used. See the 

 Encyclopaedia Britannica (last editioi ), article " Bees." 

 VI.* 



