Mr. J. W. L. Glaisber on the Form of the Cells of Bees. 109 



Bees deposit their Honey ," appears in the Philosophical Transac- 

 tions for 1743, pp. 565-571 *. After an accurate f history of the 

 question, he gives a geometrical proof of Kcenig's proposition to 

 disprove the assertion that any "higher geometry than was 

 known to the Antients" was necessary, and correctly finds the 

 angles to be 109° 28' 16" and 72° 31' 44". He proceeds, 

 " Though Monsieur Maraldi had found by his mensuration these 

 obtuse angles to be of about 110 degrees, the small difference 

 between this and the 109° 28' 16", just found by calculation, 

 seems to have been either accidental, or owing to the difficulty 

 of measuring such angles with exactness. Besides that he 

 seems to admit the real equality of the several plane angles, that 

 form as well the apex, as the other solid ones we have been treat- 

 ing of. And, as to the small difference between our angle and 

 that determined by Mr. Koenig, who first considered this pro- 

 blem, but has not yet published his demonstration of it, that 

 can only be owing to his not carrying on his computation so far, 

 and would scarcely have been worth the mentioning, were it not 

 yet in favour of the practice of these industrious little insects." 

 The whole of the above passage has been quoted, because other- 

 wise the concluding words " were it not in favour &c." might 

 give an erroneous impression of Maclaurin's meaning, which 

 from the context is seen to be that the correct answer is 2' 16" 

 nearer to the observed angle (110°) than was Koenig' s angle, a 

 correction favourable to the bees. To a not very careful reader 

 the words might at first sight seem to imply that the writer had 

 vindicated the bees from their supposed error of two minutes. 

 Maclaurin calculates the saving as "almost one fourth part 



j= of the pains and expense of wax they bestow above 



what what was necessary for completing the parallel sides of the 

 cells." This is quite correct ; the amount mentioned is equal 



to 7^ ="183 ... of the wax required for a plane hexa- 

 gonal floor. It is strange that Maclaurin did not so express it, 

 and thus point out the important error made by Koenig in 

 stating it as equal to the whole floor. 



Boscovich's investigations occur in the notes to Stay's poem J. 



* The paper appears in full also in the Abridgement by Hutton, Shaw, 

 and Pearson, vol. viii. pp. 709-713 (1809). 



f " Monsieur Maraldi had found by mensuration that the obtuse angles 

 of the rhombus's were of 110 degrees nearly; upon which he observed that 

 if the three obtuse angles which formed the solid angles above mentioned 

 were supposed equal to each other, they must each be 109° 28'; from 

 whence it has been inferred that this last was really the true and just mea- 

 sure of them" (p. 566). 



\ Philosophise recentioris a Benedicto Stay .... versibus traditse 



