THE FOUNDATION OF THE CITY 105 



to make the greatest possible saving, or the least expense of 

 material and labour. This is one of the problems which 

 belong to the higher parts of mathematics. It has accordingly 

 been resolved by some mathematicians, particularly by the 

 ingenious Maclaurin, by a fluctionary calculation, which is 

 to be found in the Transactions of the Royal Society of 

 London. He has determined precisely the angle required, 

 and he found, by the most exact mensuration the subject would 

 admit, that it is the very angle in which the three planes at the 

 bottom of the cell of a honeycomb do actually meet." 



I myself do not believe that the bees indulge in these 

 abstruse calculations ; but, on the other hand, it seems equally 

 impossible to me that such astounding results can be due to 

 chance alone, or to the mere force of circumstance. The 

 wasps, for instance, also build combs with hexagonal cells, so 

 that for them the problem was identical, and they have solved 

 it in a far less ingenious fashion. Their combs have only one 

 layer of cells, thus lacking the common base that serves the 

 bees for their two opposite layers. The wasps' comb, there- 

 fore, is not only less regular, but also less substantial ; and 

 so wastefully constructed that, besides loss of material, they 

 must sacrifice about a third of their space, and a quarter of 

 the energy they put forth. Again, we find that the trigons 

 and meliponas, which are veritable and domesticated bees, 

 though of less advanced civilisation, erect only one row of 

 rearing-cells, and support their horizontal, superposed combs 

 on shapeless and costly columns of wax. Their provision-cells 



