X793*' "" theinsl'tnct of animals, 151 



of several planes, meeting in a solid angle in the middle 

 point. It is only in one of these two ways that all the 

 cells can be similar without losing room. And, for the 

 same intention, the planes of which the bottom is com- 

 posed, if there be more than one, must be three in number, 

 and neither more nor fewer. 



It has been demonstrated, that, by making the bot- 

 toms of the cells to consist of three planes meeting in a 

 point, there is a saving of material and labour no way 

 inconsiderable. The bees, as if acquainted with these 

 principles of solid geometry, follow^ them most accurately j 

 the bottom of each cell being composed ef three planes 

 which make obtuse angles with the side partitions, and 

 with one another, and meet in a point in the middle of 

 the bottom 5 the three angles of this bottom being sup- 

 ported by three partitions on the other side of the comb, 

 and the point of it by the common intersection of those 

 three partitions. 



One instance more of the mathematical ikill displayed 

 in the structure of a honey -comb, deserves to be men- 

 tioned. 



it is a curious mathematical problem, at what precise 

 angle the three planes, which compose the bottom of a 

 cell, ought to meet, in order to make the greatest pofsible 

 saving, or the least expence of material and labour. 



This is one of those problems, belonging to the higher 

 parts of mathematics, which are called problems of maxima 

 and minima. It has been resolved by some mathematicians, 

 particularly by the ingenious Mr Maclaurin, by a fluxiona-. 

 ry calculation, which is to be found in the transactions of 

 the royal society of London. He has determined pre- 

 cisely the angle required j and he found by the most ex- 

 act mensuration the subject could admit, that it is the vc- 



