2Z4

Mechanics

PlateXI.Fi g- 5-

Fig. 6.

with less Force than with two of thoseWheels, and two of a lesser Size. (4.)If the Load be laid on the Axle of thelarger Wheels, it will be drawn with less

Force

17. I cannot conclude this Speculation of the Maximaand Minima of Quantities, without observing to theReader, that though the Method of discovering themby Fluxions is a Part of Knowledge which the Mathe-maticians have but lately acquired, and which theyesteem the Sublimity of human Science, yet this veryThing was imparted to the Inj'eSi Tribe at the first Cre-ation of Things; for by this very Method it is thatBees construct the Cells of their Combs in which theydeposit their Honey.

18. Each Cell consists of six plain Sides, which areall Trapeziums , but equal to each other. The Bottomof the Cell is contrived with three Rhombus’s H K D I,D E F I, and F I H G, so disposed as to constitute aSolid Angle at I, under the three equal Angles D I H,D I F, and HIE; each of which is double the Maxi-mum Angle of 54 0 — 44' = D I K a: D K 1 . Henceit comes to pass, that a less Quantity of Surface is suf-ficient to contain a given Quantity of Honey, than ifthe Bottom had been flat, in the Proportion of 4658 to5550, as I have found by Calculation ; that is, -^st,or j- Part of the Whole, so far as the Figure of the Endsof the Cells extends in each, which fifth Part of Waxand Labour saved amounts to a vast deal in the wholeStructure of the Comb. And if those Creatures knewtheir Advantage, they could not more nicely keep up tothe Rules of this sublime Geometry.

19. The last Thing among the Maxima, that I shallmention, is, that if a Chain A B C be suspended by itstwo Ends, it will sink down in such a Manner, by itsGravity, as to form the Curve ABC, called the Cate-narian which if inverted, would exhibit the best Formfor an Arch of any other whatsoever. For the Demon-stration of this, we must refer the Reader to the Inven-tor Dr. Gregory, in Philos. Trans. N 9 231.