Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 117 



tables, has been developed into it by persons not very careful 

 about the truth. The story given by Lord Brougham was suf- 

 ficiently romantic ; but the person who added the climax, and 

 gave it point by the sensational allusion to the ship, certainly 

 deserves to have his services remembered. 



Maclaurin suggested that Koenig did not carry his approxi- 

 mations far enough ; but I imagine that he either felt a delicacy 

 about saying in so many words that Kcenig had made a blunder, 

 or that he had in his mind (like Boscovich) the probability of 

 his having obtained a complicated equation and solved it by ap- 

 proximation. But Lord Brougham could not have felt this 

 delicacy a century later ; and he certainly did not attach Bos- 

 covich/s meaning to the word approximations. 



Lord Brougham objects most strongly to the results obtained 

 by Lhuillier ; and his arguments are of so remarkable a charac- 

 ter that I hope 1 shall be excused for quoting his exact words, 

 and the more so as the reasoning certainly must have appeared 

 to its author to carry weight, as it is reproduced (although 

 somewhat more briefly) in the French memoir. 



He denies that Lhuillier is right in calculating the saving of 

 wax as only ^ T ) ne writes (p. 291) : — " It is extremely erroneous 

 to represent the saving as only jj part. . . . The proportion 5 } T 

 is obtained by comparing the saving upon the base with the 

 whole wax of the cell, including the walls, and supposing the 

 height of the wall to be to the sides as 5 to 1 *387. But why is 

 the wax of the wall to be imported into the calculation, with 

 which it has nothing to do ? The question is between two 

 forms of the bottom, not of the whole cell. Suppose two 

 kinds of roof for a house were to be compared in order to 

 choose the one that required least timber ; though the whole 

 house might be made of wood, we should only compare the 

 expense of the roofs, and leave out the walls that would be 

 common to both plans ; otherwise the relative amount of the 

 saving would depend on the height of the house as well as the 

 shape of the roof. This becomes the more evident in the case 

 of the cells from the circumstance of their depth varying in the 

 same comb, and for the same bee, according to many accidental 

 circumstances. . . . [The author then states the great variations 

 that occur in the depth of cells.] The saving therefore is some- 

 where about a ninth, and not somewhat less than a fifty-first 

 part." 



" But there is another consideration which shows still more 

 strikingly the fallacy of the argument derived from taking the 

 whole walls of the cell into calculation. The thickness of the 

 wax is very different in different parts of the cell, being much 

 greater in the base, that is, in the rhomboidal plates, and the 



