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Show 226 INSTINCT. CHAP. VII. which thus tend to I. ntersect. H en ce eafc ht cellt hcro nsists of an outer spherical porti·O n and . o wtoh ' elel ' odr more perfectly flat surf aces, a ccording Was h e ce a 11- . . t three or more ot he r ce lls . en one ce JOlUS W. O, ' t .t h three other ce 11 s., wh "l Ch ' f rom comes Into cont.ac Wlearly of the same size, is very the spheres bdmng nsarily the case, the three flat sur-frequently an neces · "d faces are un1" t ed I.n t ° a pyramid ; and th1s ·p yr·a m1· , asf Huber h as remark ed' is manifestly a gross rm1tatwhni o t h e thr ee-s1' de d pyramidal basis of the cell of the hrv e- bee. A s m. the cells of the hive-bee, s·o here, th· e t hee plane sur f:a ces I·n any one cell necessarily. enter. 1nto t e construe t1. on of three adJ'oining cells. It IS ob.v w. us th£a t the Melipona saves wax by thi~ ~anner of building ; or the flat walls between the adjoirnng cells are not dou?le, but are of the same thickness as the outer sphencal po rt1. ons, and yet each flat portion forms a part of two 00~ htifth Reflecting on this case, it occurred to m~ t a . e Melipona had made its spheres at some g1ven .distance from each other, and had made them of equal s1zes and had arranged them symmetrically in a double layer, the resulting structure would probably hav~ been as perfect as the comb of the hive-bee. Accordingly I wrote to Professor Miller, of Cambridge, and this geometer has kindly read over the following sta~e~ent,.drawn up fr~m his information, and tells me that It 1s stnctly correct·-: If a number of equal spheres be described with thmr centres placed in two parallel layers; with the centre of each sphere at the distance of rad i us X "'' 2,, or radius x 1·41421 (or at some lesser distance), from the centres of the six surrounding spheres in the sa~e layer. and at the same distance from the centres oft e adJ"oi~ing spheres in the other and parallel layer; the~, if planes of I. ntersecti.o n b etween the sever al spheres 1ll CHAP. VII. CELLS OF THE HIVE-BEE. 227 both layers b~ formed,. there will result a double layer of hexagonal pr1sms united together by pyramidal bas'es formed of three rhombs ; and the rhombs and the sides of the hexagonal prisms will have every angle identically the same with the best measurements which have been made of the cells of the hive-bee. Hence we may safely conclude that if we could slightly modify the instincts already possessed by the Melipona, and in themselves not very wonderful, this bee would make a structure as wonderfully perfect as that of the hive-bee. We must suppose the Melipona to make her cells truly spherical, and of equal sizes; and this would not be very surprising, seeing that she already does so to a certain extent, and seeing what perfectly cylindrical burrows in wood many insects can make, apparently by turning round on a fixed point. We must suppose the Melipona to arrange her cells in level layers, as she already does her cylindrical cells; a~d we must further suppose, and this is the greatest difficulty, that she can somehow judge accurately at what distance to stand from her fellow-labourers when several are making their spheres ; but she is already so fa~ enabled to judge of distance, that she always descr1bes her spheres so as to intersect largely; and then she unites the points of intersection by perfectly flat s~rfaces. We have further to suppose, but this is no difficulty, that after hexagonal prisms have been formed by the intersection of adjoining spheres in the sam~ ~ayer, she :can prolong the hexagon to any length reqms1te to hold the stock of honey ; in the same way as the. rude humble-bee adds cylinders of wax to t~e circular mouths of her old cocoons. By such modifications of instincts in themselves not very wonder~ ul,-hardly more wonderful than those which guide a bud to make its nest,-I believe that the hive-bee |