les mesures que nous avons prises, ont les deux angles obtus chacun de 110 degrûˋs, et par consûˋquent les deux aigus chacun de 70ô¯.ã He also stated that the angles of the trapeziums which form the sides of the body of the cell were identical angles, of 110ô¯ and 70ô¯; but in the same paper he speaks of the angles as being, respectively, 109ô¯ã₤28ÿ£¢ãý and 70ô¯ã₤32ÿ£¢ãý. Here a singular confusion at once arose, and has been perpetuated in the books27. ãUnfortunately Rûˋaumur chose to look upon this second determination of Maraldiãs as being, as well as the first, a direct result of measurement, whereas it is in reality theoretical. He speaks of it as Maraldiãs more precise measurement, and this error has been repeated in spite of its absurdity to the present day; nobody {330} appears to have thought of the impossibility of measuring such a thing as the end of a beeãs cell to the nearest minute.ã At any rate, it now occurred to Rûˋaumur (as curiously enough, it had not done to Maraldi) that, just as the closely packed hexagons gave the minimal extent of boundary in a plane, so the actual solid figure, as determined by Maraldi, might be that which, for a given solid content, gives the minimum of surface: or which, in other words, would hold the most honey for the least wax. He set this problem before Koenig, and the geometer confirmed his conjecture, the result of his calculations agreeing within two minutes (109ô¯ã₤26ÿ£¢ãý and 70ô¯ã₤34ÿ£¢ãý) with Maraldiãs determination. But again, Maclaurin28 and Lhuilier29, by different methods, obtained a result identical with Maraldiãs; and were able to shew that the discrepancy of 2ÿ£¢ãý was due
Table of Contents
CHAPTER VII THE FORMS OF TISSUES OR CELL-AGGREGATES
319