132 DUBLIN NATTIEAL HISTORY SOCIETY. 



of Konig, to calculate the angle of the lozenge which should gi^^e the 

 least surface with a given volume. Konig determined this angle at 

 109° 26', agreeing with Maraldi within two minutes. 



Mac Laurin published in the "Philosophical Transactions," 1743, 

 p. 565, an elaborate geometrical paper on the subject, in which he 

 proves that the tangent of the angle in question is the square root of 2, 

 and that it is therefore equal to 109° 28' 16"; and he computes the 

 saving of wax as " almost one fourth part of the pains and expense of 

 wax they bestow, above what was necessary for completing the paral- 

 lelogram side of the cells." 



Lluilier, in 1781, published in the "Berlin Memoirs," p. 277, an 

 elaborate discussion of the entire problem, in which he arrived at the 

 following results, already found by Mac Laurin' s geometrical method: — 



a. That the economy of wax is less than one-fifth of what would 

 make a flat base. 



h. That the economy of wax, referred to the total expenditure, is 

 jyth, so that the bees can make fifty-one cells, instead of fifty, by the 

 adoption of the rhombic dodecahedron. 



He does not share, however, in the enthusiasm of the naturalists, 

 but maintains, and proves, that mathematicians could make cells, of the 

 same form as those of the bees, which, instead of using only a minimum 

 of wax, would use the minimum minimorum, so that five cells could be 

 made of less wax than that which noAv makes only four, instead of 

 fifty- one out of fifty. 



Notwithstanding this conclusive decision in favour of the mathe- 

 maticians, the advocates of final cause, and those who maintain that 

 economy of wax can create a new species, have both persisted in using 

 the bees' cell in illustration of their respective theories, with a pertina- 

 city that proves the persistent vitality of an exploded theory. In 

 illustration of this remarkable tendency of false theories to reproduce 

 themselves, I shall here add, as an appendix to my account of the form 

 of the wasps' and bees' cells, some remarks on the Origin of Species, the 

 substance of which originally appeared in the "ITatural History Ee- 

 view" of 1860. 



Appendix on the Oeigin of Species. 



The active and restless mind of man has never been content with 

 the knowledge of the present, but has always sought to know the 

 future and the past. The guesses of the ancients as to the future . of 

 man are amongst the most interesting, and, at the same time, the most 

 puerile of their philosophical speculations. The reader of the Tusculan 

 Disputations rises from his task, charmed by the style of the writer, 

 but thankful that a certain revelation of the future renders him immea- 

 surably superior in knowledge to the weavers of these pleasant webs of 

 fiction, and though he admires the skill of the ingenious sophists who 

 live again and dispute in the pages of Cicero, he would not for an 

 instant exchange his own position for theirs. 



