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



In the space of six pages and a quarter he has treated the matter 

 very ably and in a manner worthy of his high reputation. He has 

 clearly read with care all that had been previously published on 

 the question, except Maclaurin's memoir, which heknewof and had 

 in vain endeavoured to procure; he therefore does not know what 

 method Maclaurin used, or whether any of his own remarks had 

 been anticipated by him • but he thinks it likely that such may 

 have happened, " cum in tanto Geometra nihil desiderari unquam 

 possit, quod aut ad simplicitatem solutionum, aut ad penetra- 

 tionem, et combinationes consectariorum pertineat," a well- 

 deserved compliment to the Scotch mathematician. 



Boscovich points out distinctly that Maraldi's values 109° 28' 

 and 70° 32' were not the result of measurement ; and he even 

 goes further and expresses a doubt whether, without the know- 

 ledge of the solution of the mathematical problem^ he would even 

 have been able to measure them to the nearest degree. His own 

 words are worth quoting : — " Mirum sane esset, si Maraldus ex 

 observation e, angulum sestimasset intra minuta, quod in tarn 

 exigua mole fieri utique non poterat. At is ut satis patet ex ipsa 

 ejus dissertatione, affirmat se invenisse angulos circiter graduum 

 110 et 70, nee minuta eruit ex observatione, sed ex sequalitate 

 angulorum pertinentium ad rhombos, et ad trapezia ; ad quam 

 habendam Geometria ipsum docuit requiri ilia minuta. Quin 

 immo satis vereor, ne hsec ipsa, aut aliquaejusmodi consideratio 

 dederit ipsum graduum numerum ilium tarn proximum ; nam 

 observatio intra plures gradus incerta esse debuit in mole adeo 

 exigua, nee ita accurate efformata; cum plures irregularitates, 

 et in hisce rhombis, et in omni reliqua constructione alveolorum 

 observari passim affirmet ipse Reaumurius. 



" Verum quidquid sit de graduum numero, certe numerum mi- 

 nutorum Maraldus non proponit tanquam observatione immediata 

 definitum, sed ex ilia sequalitatis consideratione, quam diximus, 

 adeoque si Koenigii solutio rite procederet, determinatio minimi 

 non ab angulo observato per ilia duo minuta discederet, sed ab 

 angulo requisito ad ejusmodi sequalitatem, cum observato tamen 

 congrueret adhuc intra limites admodum arctos, et qui in ejus- 

 modi argumento omnem superant observatoris industriam." 



Reaumur himself (t. v. p. 382) says that some of the rhombs 

 appear square, but that generally they are " lozanges ou rhombes 

 plus ou moins allonges -" and any one who remarks how greatly 



libri x. cum adnotationibus, et supplementis P. Rogerii Josephi Boscovich, 

 S.J. vol. ii. Rome, 1760, 8vo. The note De Apium Cellulis refers to 

 verse 2306 of hook vi., and is the last note in the second volume (pp. 498- 

 504). The first volume was published in 1 755, and, according to the Bio- 

 graphie Universelle (Michaud), the third in 1792, the publication having 

 been retarded by Boscovich's delay in the preparation of the notes. 



