1883.3 
Origin of the Cells of the Hive Bee . 
643 
IV. ON THE ORIGIN OF THE CELLS OF 
THE HIVE BEE. 
S HE cell of the hive bee has for many centuries called 
forth the wonder of naturalists, and indeed of all 
observers. Why should, or how should, so compa- 
ratively humble a creature in the construction of its comb 
seleCt that precise form which offers the greatest economy 
of form and material ? Granting that the bee possesses no 
inconsiderable share of intelligence, we can scarcely con- 
ceive of her having made sufficient progress in the higher 
mathematics to seleCt knowingly the precise angles which 
are best adapted to the object in view. Hence not a few 
writers, even to the present day, maintain that we have here 
a typical case of “ instinCt ” in the old acceptation of the 
word, — that is, of blind, unconscious, untaught aCtion, pro- 
ducing results which man can only reach by dint of highly 
cultivated reason. So many of these so-called instincts 
have lately found a scientific explanation that naturalists 
of the Old School have recognised the cell of the bee as one 
of their last entrenchments. 
It is therefore very satisfactory that Herr K. Miillenhoff* 
has found a quite simple and satisfactory solution of the 
question, which neither admits of any mysterious instinCt 
nor — on the other hand — credits the bee with the knowledge 
of the differential calculus. 
Taking first a preliminary view of the case, we find that 
Pappus, fifteen hundred years ago, noted that bees con- 
structed their cells in the form of regular six-sided columns, 
and proved mathematically the superiority of this shape to 
any other. In the last century Maraldi, and after him 
Reaumur, examined the form of the middle plate of the 
entire comb, — i.e., the bottoms of the cells formed each of 
three rhombs. At the instigation of Reaumur the mathe- 
matician Konig, in 1739, found by calculation the most 
suitable — i.e., the most economical — of all possible forms 
for the middle plate, and ascertained that it must consist of 
pyramids formed by three rhombs having at the apex the 
angle 109° 28'. Maraldi had found this as the very angle 
actually employed by the bees. 
* Naturforsgher und Berlin Entomolog. Zeitschrift, 
