68 PROCEEDINGS OF THE AMERICAN ACADEMY 



Hereafter steam-power can be sold by the thousand or million foot- 

 pounds. 



Mr. Ruggles does not patent his valuable invention. 



Dr. Jeffries Wyman presented the following paper : — 



Notes on the Cells of the Bee. 



It is more than a century and a half since Maraldi studied the form 

 of the cells of the hive bee, and described them as hexagonal prisms 

 with trihedral bases, each face of the base being a rhomb, the greater 

 angles of which were 109° 28', and the lesser 70° 32'.* Twenty-five 

 years later, Reaumer, the most admirable of the observers of insect 

 life, with the view of ascertaining how far such a form was an econom- 

 ical one, proposed to Koenig the following problem, — " Of all hexago- 

 nal cells, having a pyramidal base composed of three equal and similar 

 rhombs, to determine that which can be constructed with the least 

 amount of material." f It is a part of the history of this subject, that 

 Koenig's results differed from those of Maraldi by two minutes in each 

 of the angles, the former having made them 109° 26' and 70° 34'. 

 It has recently been stated that the table of logarithms used by 

 Koenig had an error which would exactly account for the difference. 



Admitting an error of two minutes in each of the angles, still the 

 close correspondence between the results of Koenig and the measure- 

 ments of Maraldi was well fitted to excite the wonder and admiration 

 of all, and from that time to this the belief has prevailed, that the in- 

 stinct of the bee enables it to construct such a cell as that sought in 

 Reaumer's problem, if not in all cases, at least in the larger portion 

 of them, without sensible error. It were unjust to keep out of sight 

 the fact, that, however correct the measurements of Maraldi may have 

 been, he has left no record of his method of making them, and further- 

 more, the possibility of measuring the angles of such a structure as the 

 cell of the bee, without liability to an error of one or two degrees in 

 each angle, is denied by competent authorities, since the angles of the cell 

 are nowhere sharply defined and the surfaces are not strictly planes. % 



* Mem. Acad, des Sciences, 1712. 



t Memoires pour servir aVHistoire des Insectes, Tom. V. p. 389. Paris, 1740. 



J The first person who appears to have called Maraldi's measurements in ques- 

 tion was Father Boscovich, "who had supposed that the admeasurement of the 

 angles was too nice to be accurately performed, and that the coincidence of M. 



