xviii INTRODUCTORY DISCOURSE OF THE 



Mine weight than they would be if thinner and 8olid. Now the bones of animals are all more or less 

 hollow, and are therefore stronger with the same weight and quantity of mutter, than they otherwise would 

 be. But birds have the largest bones in proportion to their weight ; their bones are more hollow than 

 those of animals which do not fly; and therefore they have the needful strength, without having to carry 

 more weight than is absolutely necessary. Their quills derive strength from the same construction. 

 They possess another peculiarity to help their flight. No other animals have any communication between 

 the air-vessela of the lungs and the hollow parts of their bodies; but birds have it; and by this means 

 they can blow out their bodies as we do a bladder, and thus become lighter when they would either 

 make their flight towards the ground slower, or rise more swiftly, or float more easily in the air ; while, by 

 lessening their bulk and closing their wings, they can drop more speedily if they wish to chase or to 

 escape. Fishes possess a power of tho same kind, though not by the same means. They have air-bladder* 

 in their bodies, and can puff them out, or press them closer, at pleasure : when they want to rise in the 

 water, they fill out the bladder, and this lightens them ; when they would sink, they squeeze the bladder, 

 pressing the air into a smaller space, and this makes them heavier. If the bladder break, the fish remains 

 at the bottom, and can be held up only by the most laborious exertions of the fins and tail. Accordingly, 

 flat fish, such as skaits and flounders, which have no air-bladders, seldom rise from the bottom, but are found 

 lying on banks in the sea, or at the bottom of rivers. 



If you have a certain space, as a room, to fill up with closets or little cells, all of the same size and 

 shape, there are only three figures which will answer, and enable you to fill the room without losing any 

 space between the cells ; they must either be squares, or figures of three equal sides, or figures of six equal 

 sides. With any other figures whatever, space would be lost between the cells. This is evident upon 

 considering the matter; and it is proved by mathematical reasoning. The six-sided figure is by far the most 

 convenient of those three shapes, because its corners are flatter, and any round body placed in it has 

 therefore more space, less room being lost in the corners. This figure, too, is the strongest of the 

 three ; any pressure from without or from within will hurt it least, as it has something of the strength of 

 an arch. A round figure would be still stronger, but then room would be lost between the circles, whereas 

 with the six-sided figure none is lost. Now, it is a most remarkable fact, that Sees build their cells exactly 

 in this shape, and thereby save both room and materials beyond what they could save if they built them 

 iu any other shape whatever. They build in the very best possible shape for their purpose, which is to 

 save all the room and all the wax they can. So far as to the shape of the walls of each cell ; but the roof 

 and floor, or top and bottom, are built on equally true principles. It is proved by mathematicians, that, 

 to give the greatest strength, and save the most room, the roof and floor must be made of three square 

 planes meeting in a point ; and they have further proved, by a demonstration belonging to the highest parts 

 of Algebra, that there is one particular angle or inclination of those planes to each other where they meet, 

 which makes a greater saving of materials and of work than any other inclination whatever could possibly 

 do. Now, the Bees actually make the tops and bottoms of their cells of three planes meeting in a point ; 

 and the inclinations or angles at which they meet are precisely those found out by the mathematician to 

 be the best possible for saving wax and work.* Who would dream of the bee knowing the highest 

 branch of the Mathematics the fruit of Newton's most wonderful discovery a result, too, of which he was 

 himself ignorant, one of his most celebrated followers having found it out in a later age ? This little insect 

 Works with a truth and correctness which are perfect, and according to the principles at which man has 

 arrived only after ages of slow improvement in the most difficult branch of the most difficult science. 

 But the Mighty and All- wise Creator, who made the insect and the philosopher, bestowing reason on the 

 latter, and giving the former to work without it to Him all truths are known to all eternity, with an 

 intuition that mocks even the conceptions of the sagest of human kind. 



It may be recollected, that when the air is exhausted or sucked out of any vessel, there is no longer 

 the force necessary to resist the pressure of the air on the outside ; and the sides of the vessels are 

 therefore pressed inwards with violence : a flat glass would thus be broken, unless it were very thick ; 

 a round one, having the strength of an arch, would resist better; but any soft substance, as leather or skin, 

 would be crushed or squeezed together at once. If the air were only sucked out slowly, the squeezing 

 would be gradual; or, if it were only half sucked out, the skin would only be partly squeezed together. 

 This is the process by which Bees reach the fine du.-t and juices of hollow flowers, like the honeysuckle, 

 and some kinds of long fox-glove, which are too narrow for them to enter. They fill up the mouth of tho 

 flower with their bodies, and suck out the air, or at least a largo part of it ; this makes the soft sides ot 

 the flower close, and squeezes the dust and juice towards the insect, as well as a hand could do, if applied 

 to the outside. 



We may remember this pressure or weight of the atmosphere as shown by the barometer and tho 



* Ko?ni K , pupil of Bernoulli, and Maclaurin, proved by very refined investigations, carried on with the aid of the fluxional 

 ralcului, that the obtuse angle must be 109 28', and the arute 70 32', to save the most wax and work possible. Mar 

 by actual measurement, that the angles arc about 110 and 70. These angles never vary in any pla<-c ; and it is scarcely I, 

 in.nilar, that the bre.icith of all Ix-es' cells is everywhere precisely the same, the drone or male cells being 5-18ths, and t 

 or female cells 13-GOtlis of an inch in breadth, and this in all countries and times. 



