VII 



OF THE BEE'S CELL 531 



helped notably to spread these and other errors, and his writings 

 on the bee's cell contain, according to Glaisher, "as striking 

 examples of bad reasoning as are often to be met with in writings 

 relating to mathematical subjects." The fact is that, were the 

 angles and facets of the honevcomb as sharp and smooth, and as 

 constant and uniform, as those of a quartz-crystal, it would still be 

 a dehcate matter to measure the angles within a minute or two of 

 arc, and a technique unknown in Maraldi's day would be required 

 to do it. The minute-hand of a clock (if it move continuously) 

 moves through one degree of arc in ten seconds of time, and through 

 an angle of two minutes m one-third of a second; — and this last is 

 the angle which Maraldi is supposed to have measured. It was 

 eighty years after Maraldi had told Reaumur what the angle was 

 that Boscovich pointed out for the first time that to ascertain the 

 angle to the nearest minute by direct admeasurement of the waxen 

 cell was utterly impossible. Yet Reaumur had certainly beheved, 

 and apparently had persuaded Koenig, that Maraldi's determina- 

 tions, first and last, were the result of measurement ; and Fontenelle, 

 the historian of the Academy, epitomising Koenig's paper, speaks 

 of "les mesures actuelles de M. Maraldi," of the bees being in 

 error to the trifling extent of 2', and of the grande merveille of their 

 so nearly solving a problem belonging to the higher geometry. 

 Boscovich, in a long-forgotten note, rediscovered by Glaisher, puts 

 the case in a nutshell: "Mirum sane si Maraldus ex observatione 

 angulum aestimasset intra minuta, quod in tarn exigua mole fieri 

 utique non poterat. At is (ut satis patet ex ipsa ejus determina- 

 tione) affirmat se invenisse angulos circiter 110° et 70°, nee minuta 

 emit ex observatione sed ex equahtate angulorum pertinentium ad 

 rhombos et ad trapezia ; ad quam habendam Geometria ipsa docuit 

 requiri ilia minuta*." Indeed he goes on to say the wonder is that 

 the angles could be measured even within a few degrees, variable 

 and irregular as they are seen to be, and as even Reaumur f knew 



* In his note De apium cellulis, appended to the philosophical poem of Benedict 

 Stay, II, pp. 498-504, Romae, 1792. 



t Op. cit. V, p. 382. Several authors recognised that the cells are far from 

 identical, and do no more than approximate to an average or ideal angle: e.g. 

 Swammerdam in the Biblia Naturae, u, p. 379; G. S. Klugel, Grosstes u. Kleinstes, 

 in Mathem. Worterb. 1803, Castillon, op. cit.; and especially Jeffries Wyman, 

 Notes on the cells of the bee, Proc. Amer. Acad. Sci. and Arts, vn, 1868. 



