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ish¡¡F¡£¡¡sanguinea£»¡¡which£»¡¡as¡¡we¡¡have¡¡seen£»¡¡is¡¡less¡¡aided¡¡by¡¡its¡¡slaves¡¡than¡¡the¡¡same¡¡species¡¡in¡¡Switzerland£»¡¡I¡¡can¡¡see¡¡no¡¡difficulty¡¡in¡¡natural¡¡selection¡¡increasing¡¡and¡¡modifying¡¡the¡¡instinct¡¡always¡¡supposing¡¡each¡¡modification¡¡to¡¡be¡¡of¡¡use¡¡to¡¡the¡¡species¡¡until¡¡an¡¡ant¡¡was¡¡formed¡¡as¡¡abjectly¡¡dependent¡¡on¡¡its¡¡slaves¡¡as¡¡is¡¡the¡¡Formica¡¡rufescens¡£¡¡
Cell¡­making¡¡instinct¡¡of¡¡the¡¡Hive¡­Bee¡£¡¡I¡¡will¡¡not¡¡here¡¡enter¡¡on¡¡minute¡¡details¡¡on¡¡this¡¡subject£»¡¡but¡¡will¡¡merely¡¡give¡¡an¡¡outline¡¡of¡¡the¡¡conclusions¡¡at¡¡which¡¡I¡¡have¡¡arrived¡£¡¡He¡¡must¡¡be¡¡a¡¡dull¡¡man¡¡who¡¡can¡¡examine¡¡the¡¡exquisite¡¡structure¡¡of¡¡a¡¡comb£»¡¡so¡¡beautifully¡¡adapted¡¡to¡¡its¡¡end£»¡¡without¡¡enthusiastic¡¡admiration¡£¡¡We¡¡hear¡¡from¡¡mathematicians¡¡that¡¡bees¡¡have¡¡practically¡¡solved¡¡a¡¡recondite¡¡problem£»¡¡and¡¡have¡¡made¡¡their¡¡cells¡¡of¡¡the¡¡proper¡¡shape¡¡to¡¡hold¡¡the¡¡greatest¡¡possible¡¡amount¡¡of¡¡honey£»¡¡with¡¡the¡¡least¡¡possible¡¡consumption¡¡of¡¡previous¡¡wax¡¡in¡¡their¡¡construction¡£¡¡It¡¡has¡¡been¡¡remarked¡¡that¡¡a¡¡skilful¡¡workman£»¡¡with¡¡fitting¡¡tools¡¡and¡¡measures£»¡¡would¡¡find¡¡it¡¡very¡¡difficult¡¡to¡¡make¡¡cells¡¡of¡¡wax¡¡of¡¡the¡¡true¡¡form£»¡¡though¡¡this¡¡is¡¡perfectly¡¡effected¡¡by¡¡a¡¡crowd¡¡of¡¡bees¡¡working¡¡in¡¡a¡¡dark¡¡hive¡£¡¡Grant¡¡whatever¡¡instincts¡¡you¡¡please£»¡¡and¡¡it¡¡seems¡¡at¡¡first¡¡quite¡¡inconceivable¡¡how¡¡they¡¡can¡¡make¡¡all¡¡the¡¡necessary¡¡angles¡¡and¡¡planes£»¡¡or¡¡even¡¡perceive¡¡when¡¡they¡¡are¡¡correctly¡¡made¡£¡¡But¡¡the¡¡difficulty¡¡is¡¡not¡¡nearly¡¡so¡¡great¡¡as¡¡it¡¡at¡¡first¡¡appears£º¡¡all¡¡this¡¡beautiful¡¡work¡¡can¡¡be¡¡shown£»¡¡I¡¡think£»¡¡to¡¡follow¡¡from¡¡a¡¡few¡¡very¡¡simple¡¡instincts¡£¡¡
I¡¡was¡¡led¡¡to¡¡investigate¡¡this¡¡subject¡¡by¡¡Mr¡£¡¡Waterhouse£»¡¡who¡¡has¡¡shown¡¡that¡¡the¡¡form¡¡of¡¡the¡¡cell¡¡stands¡¡in¡¡close¡¡relation¡¡to¡¡the¡¡presence¡¡of¡¡adjoining¡¡cells£»¡¡and¡¡the¡¡following¡¡view¡¡may£»¡¡perhaps£»¡¡be¡¡considered¡¡only¡¡as¡¡a¡¡modification¡¡of¡¡this¡¡theory¡£¡¡Let¡¡us¡¡look¡¡to¡¡the¡¡great¡¡principle¡¡of¡¡gradation£»¡¡and¡¡see¡¡whether¡¡Nature¡¡does¡¡not¡¡reveal¡¡to¡¡us¡¡her¡¡method¡¡of¡¡work¡£¡¡At¡¡one¡¡end¡¡of¡¡a¡¡short¡¡series¡¡we¡¡have¡¡humble¡­bees£»¡¡which¡¡use¡¡their¡¡old¡¡cocoons¡¡to¡¡hold¡¡honey£»¡¡sometimes¡¡adding¡¡to¡¡them¡¡short¡¡tubes¡¡of¡¡wax£»¡¡and¡¡likewise¡¡making¡¡separate¡¡and¡¡very¡¡irregular¡¡rounded¡¡cells¡¡of¡¡wax¡£¡¡At¡¡the¡¡other¡¡end¡¡of¡¡the¡¡series¡¡we¡¡have¡¡the¡¡cells¡¡of¡¡the¡¡hive¡­bee£»¡¡placed¡¡in¡¡a¡¡double¡¡layer£º¡¡each¡¡cell£»¡¡as¡¡is¡¡well¡¡know£»¡¡is¡¡an¡¡hexagonal¡¡prism£»¡¡with¡¡the¡¡basal¡¡edges¡¡of¡¡its¡¡six¡¡sides¡¡bevelled¡¡so¡¡as¡¡to¡¡join¡¡on¡¡to¡¡a¡¡pyramid£»¡¡formed¡¡of¡¡three¡¡rhombs¡£¡¡These¡¡rhombs¡¡have¡¡certain¡¡angles£»¡¡and¡¡the¡¡three¡¡which¡¡form¡¡the¡¡pyramidal¡¡base¡¡of¡¡a¡¡single¡¡cell¡¡on¡¡one¡¡side¡¡of¡¡the¡¡comb£»¡¡enter¡¡into¡¡the¡¡composition¡¡of¡¡the¡¡bases¡¡of¡¡three¡¡adjoining¡¡cells¡¡on¡¡the¡¡opposite¡¡side¡£¡¡In¡¡the¡¡series¡¡between¡¡the¡¡extreme¡¡perfection¡¡of¡¡the¡¡cells¡¡of¡¡the¡¡hive¡­bee¡¡and¡¡the¡¡simplicity¡¡of¡¡those¡¡of¡¡the¡¡humble¡­bee£»¡¡we¡¡have¡¡the¡¡cells¡¡of¡¡the¡¡Mexican¡¡Melipona¡¡domestica£»¡¡carefully¡¡described¡¡and¡¡figured¡¡by¡¡Pierre¡¡Huber¡£¡¡The¡¡Melipona¡¡itself¡¡is¡¡intermediate¡¡in¡¡structure¡¡between¡¡the¡¡hive¡¡and¡¡humble¡¡bee£»¡¡but¡¡more¡¡nearly¡¡related¡¡to¡¡the¡¡latter£º¡¡it¡¡forms¡¡a¡¡nearly¡¡regular¡¡waxen¡¡comb¡¡of¡¡cylindrical¡¡cells£»¡¡in¡¡which¡¡the¡¡young¡¡are¡¡hatched£»¡¡and£»¡¡in¡¡addition£»¡¡some¡¡large¡¡cells¡¡of¡¡wax¡¡for¡¡holding¡¡honey¡£¡¡These¡¡latter¡¡cells¡¡are¡¡nearly¡¡spherical¡¡and¡¡of¡¡nearly¡¡equal¡¡sizes£»¡¡and¡¡are¡¡aggregated¡¡into¡¡an¡¡irregular¡¡mass¡£¡¡But¡¡the¡¡important¡¡point¡¡to¡¡notice£»¡¡is¡¡that¡¡these¡¡cells¡¡are¡¡always¡¡made¡¡at¡¡that¡¡degree¡¡of¡¡nearness¡¡to¡¡each¡¡other£»¡¡that¡¡they¡¡would¡¡have¡¡intersected¡¡or¡¡broken¡¡into¡¡each¡¡other£»¡¡if¡¡the¡¡spheres¡¡had¡¡been¡¡completed£»¡¡but¡¡this¡¡is¡¡never¡¡permitted£»¡¡the¡¡bees¡¡building¡¡perfectly¡¡flat¡¡walls¡¡of¡¡wax¡¡between¡¡the¡¡spheres¡¡which¡¡thus¡¡tend¡¡to¡¡intersect¡£¡¡Hence¡¡each¡¡cell¡¡consists¡¡of¡¡an¡¡outer¡¡spherical¡¡portion¡¡and¡¡of¡¡two£»¡¡three£»¡¡or¡¡more¡¡perfectly¡¡flat¡¡surfaces£»¡¡according¡¡as¡¡the¡¡cell¡¡adjoins¡¡two£»¡¡three¡¡or¡¡more¡¡other¡¡cells¡£¡¡When¡¡one¡¡cell¡¡comes¡¡into¡¡contact¡¡with¡¡three¡¡other¡¡cells£»¡¡which£»¡¡from¡¡the¡¡spheres¡¡being¡¡nearly¡¡of¡¡the¡¡same¡¡size£»¡¡is¡¡very¡¡frequently¡¡and¡¡necessarily¡¡the¡¡case£»¡¡the¡¡three¡¡flat¡¡surfaces¡¡are¡¡united¡¡into¡¡a¡¡pyramid£»¡¡and¡¡this¡¡pyramid£»¡¡as¡¡Huber¡¡has¡¡remarked£»¡¡is¡¡manifestly¡¡a¡¡gross¡¡imitation¡¡of¡¡the¡¡three¡­sided¡¡pyramidal¡¡basis¡¡of¡¡the¡¡cell¡¡of¡¡the¡¡hive¡­bee¡£¡¡As¡¡in¡¡the¡¡cells¡¡of¡¡the¡¡hive¡­bee£»¡¡so¡¡here£»¡¡the¡¡three¡¡plane¡¡surfaces¡¡in¡¡any¡¡one¡¡cell¡¡necessarily¡¡enter¡¡into¡¡the¡¡construction¡¡of¡¡three¡¡adjoining¡¡cells¡£¡¡It¡¡is¡¡obvious¡¡that¡¡the¡¡Melipona¡¡saves¡¡wax¡¡by¡¡this¡¡manner¡¡of¡¡building£»¡¡for¡¡the¡¡flat¡¡walls¡¡between¡¡the¡¡adjoining¡¡cells¡¡are¡¡not¡¡double£»¡¡but¡¡are¡¡of¡¡the¡¡same¡¡thickness¡¡as¡¡the¡¡outer¡¡spherical¡¡portions£»¡¡and¡¡yet¡¡each¡¡flat¡¡portion¡¡forms¡¡a¡¡part¡¡of¡¡two¡¡cells¡£¡¡
Reflecting¡¡on¡¡this¡¡case£»¡¡it¡¡occurred¡¡to¡¡me¡¡that¡¡if¡¡the¡¡Melipona¡¡had¡¡made¡¡its¡¡spheres¡¡at¡¡some¡¡given¡¡distance¡¡from¡¡each¡¡other£»¡¡and¡¡had¡¡made¡¡them¡¡of¡¡equal¡¡sizes¡¡and¡¡had¡¡arranged¡¡them¡¡symmetrically¡¡in¡¡a¡¡double¡¡layer£»¡¡the¡¡resulting¡¡structure¡¡would¡¡probably¡¡have¡¡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¡¡statement£»¡¡drawn¡¡up¡¡from¡¡his¡¡information£»¡¡and¡¡tells¡¡me¡¡that¡¡it¡¡is¡¡strictly¡¡correct£º¡­¡¡
If¡¡a¡¡number¡¡of¡¡equal¡¡spheres¡¡be¡¡described¡¡with¡¡their¡¡centres¡¡placed¡¡in¡¡two¡¡parallel¡¡layers£»¡¡with¡¡the¡¡centre¡¡of¡¡each¡¡sphere¡¡at¡¡the¡¡distance¡¡of¡¡radius¡¡X¡¡/sqrt£§2£§¡¡or¡¡radius¡¡X¡¡1¡£41421¡¡£¨or¡¡at¡¡some¡¡lesser¡¡distance£©£»¡¡from¡¡the¡¡centres¡¡of¡¡the¡¡six¡¡surrounding¡¡spheres¡¡in¡¡the¡¡same¡¡layer£»¡¡and¡¡at¡¡the¡¡same¡¡distance¡¡from¡¡the¡¡centres¡¡of¡¡the¡¡adjoining¡¡spheres¡¡in¡¡the¡¡other¡¡and¡¡parallel¡¡layer£»¡¡then£»¡¡if¡¡planes¡¡of¡¡intersection¡¡between¡¡the¡¡several¡¡spheres¡¡in¡¡both¡¡layers¡¡be¡¡formed£»¡¡there¡¡will¡¡result¡¡a¡¡double¡¡layer¡¡of¡¡hexagonal¡¡prisms¡¡united¡¡together¡¡by¡¡pyramidal¡¡bases¡¡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£»¡¡and¡¡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¡¡far¡¡enabled¡¡to¡¡judge¡¡of¡¡distance£»¡¡that¡¡she¡¡always¡¡describes¡¡her¡¡spheres¡¡so¡¡as¡¡to¡¡intersect¡¡largely£»¡¡and¡¡then¡¡she¡¡unites¡¡the¡¡points¡¡of¡¡intersection¡¡by¡¡perfectly¡¡flat¡¡surfaces¡£¡¡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¡¡same¡¡layer£»¡¡she¡¡can¡¡prolong¡¡the¡¡hexagon¡¡to¡¡any¡¡length¡¡requisite¡¡to¡¡hold¡¡the¡¡stock¡¡of¡¡honey£»¡¡in¡¡the¡¡same¡¡way¡¡as¡¡the¡¡rude¡¡humble¡­bee¡¡adds¡¡cylinders¡¡of¡¡wax¡¡to¡¡the¡¡circular¡¡mouths¡¡of¡¡her¡¡old¡¡cocoons¡£¡¡By¡¡such¡¡modifications¡¡of¡¡instincts¡¡in¡¡themselves¡¡not¡¡very¡¡wonderful£»¡¡hardly¡¡more¡¡wonderful¡¡than¡¡those¡¡which¡¡guide¡¡a¡¡bird¡¡to¡¡make¡¡its¡¡nest£»¡¡I¡¡believe¡¡that¡¡the¡¡hive¡­bee¡¡has¡¡acquired£»¡¡through¡¡natural¡¡selection£»¡¡her¡¡inimitable¡¡architectural¡¡powers¡£¡¡
But¡¡this¡¡theory¡¡can¡¡be¡¡tested¡¡by¡¡experiment¡£¡¡Following¡¡the¡¡example¡¡of¡¡Mr¡¡Tegetmeier£»¡¡I¡¡separated¡¡two¡¡combs£»¡¡and¡¡put¡¡between¡¡them¡¡a¡¡long£»¡¡thick£»¡¡square¡¡strip¡¡of¡¡wax£º¡¡the¡¡bees¡¡instantly¡¡began¡¡to¡¡excavate¡¡minute¡¡circular¡¡pits¡¡in¡¡it£»¡¡and¡¡as¡¡they¡¡deepened¡¡these¡¡little¡¡pits£»¡¡they¡¡made¡¡them¡¡wider¡¡and¡¡wider¡¡until¡¡they¡¡were¡¡converted¡¡into¡¡shallow¡¡basins£»¡¡appearing¡¡to¡¡the¡¡eye¡¡perfectly¡¡true¡¡or¡¡parts¡¡of¡¡a¡¡sphere£»¡¡and¡¡of¡¡about¡¡the¡¡diameter¡¡of¡¡a¡¡cell¡£¡¡It¡¡was¡¡most¡¡interesting¡¡to¡¡me¡¡to¡¡observe¡¡that¡¡wherever¡¡several¡¡bees¡¡had¡¡begun¡¡to¡¡excavate¡¡these¡¡basins¡¡near¡¡together£»¡¡they¡¡had¡¡begun¡¡their¡¡work¡¡at¡¡such¡¡a¡¡distance¡¡from¡¡each¡¡other£»¡¡that¡¡by¡¡the¡¡time¡¡the¡¡basins¡¡had¡¡acquired¡¡the¡¡above¡¡stated¡¡width¡¡£¨i¡£e¡£¡¡about¡¡the¡¡width¡¡of¡¡an¡¡ordinary¡¡cell£©£»¡¡and¡¡were¡¡in¡¡depth¡¡about¡¡one¡¡sixth¡¡of¡¡the¡¡diameter¡¡of¡¡the¡¡sphere¡¡of¡¡which¡¡they¡¡formed¡¡a¡¡part£»¡¡the¡¡rims¡¡of¡¡the¡¡basins¡¡intersected¡¡or¡¡broke¡¡into¡¡each¡¡other¡£¡¡As¡¡soon¡¡as¡¡this¡¡occurred£»¡¡the¡¡bees¡¡ceased¡¡to¡¡excavate£»¡¡and¡¡began¡¡to¡¡build¡¡up¡¡flat¡¡walls¡¡of¡¡wax¡¡on¡¡the¡¡lines¡¡of¡¡intersection¡¡between¡¡the¡¡basins£»¡¡so¡¡that¡¡each¡¡hexagonal¡¡prism¡¡was¡¡built¡¡upon¡¡the¡¡festooned¡¡edge¡¡of¡¡a¡¡smooth¡¡basin£»¡¡instead¡¡of¡¡on¡¡the¡¡straight¡¡edges¡¡of¡¡a¡¡three¡­sided¡¡pyramid¡¡as¡¡in¡¡the¡¡case¡¡of¡¡ordinary¡¡cells¡£¡¡
I¡¡then¡¡put¡¡into¡¡the¡¡hive£»¡¡instead¡¡of¡¡a¡¡thick£»¡¡square¡¡piece¡¡of¡¡wax£»¡¡a¡¡thin¡¡and¡¡narrow£»¡¡knife¡­edged¡¡ridge£»¡¡coloured¡¡with¡¡vermilion¡£¡¡The¡¡bees¡¡instantly¡¡began¡¡on¡¡both¡¡sides¡¡to¡¡excavate¡¡little¡¡basins¡¡near¡¡to¡¡each¡¡other£»¡¡in¡¡the¡¡same¡¡way¡¡as¡¡before£»¡¡but¡¡the¡¡ridge¡¡of¡¡wax¡¡was¡¡so¡¡thin£»¡¡that¡¡the¡¡bottoms¡¡of¡¡the¡¡basins£»¡¡if¡¡they¡¡had¡¡been¡¡excavated¡¡to¡¡the¡¡same¡¡depth¡¡as¡¡in¡¡the¡¡former¡¡experiment£»¡¡would¡¡have¡¡broken¡¡into¡¡each¡¡other¡¡from¡¡the¡¡opposite¡¡sides¡£¡¡The¡¡bees£»¡¡however£»¡¡did¡¡not¡¡suffer¡¡this¡¡to¡¡happen£»¡¡and¡¡they¡¡stopped¡¡their¡¡excavations¡¡in¡¡due¡¡time£»¡¡so¡¡that¡¡the¡¡basins£»¡¡as¡¡soon¡¡as¡¡they¡¡had¡¡been¡¡a¡¡little¡¡deepened£»¡¡came¡¡to¡¡have¡¡flat¡¡bottoms£»¡¡and¡¡these¡¡flat¡¡bottoms£»¡¡formed¡¡by¡¡thin¡¡little¡¡plates¡¡of¡¡the¡¡vermilion¡¡wax¡¡having¡¡been¡¡left¡¡ungnawed£»¡¡were¡¡situated£»¡¡as¡¡far¡¡as¡¡the¡¡eye¡¡could¡¡judge£»¡¡exactly¡¡along¡¡the¡¡planes¡¡of¡¡imaginary¡¡intersection¡¡between¡¡the¡¡basins¡¡on¡¡the¡¡opposite¡¡sides¡¡of¡¡the¡¡ridge¡¡of¡¡wax¡£¡¡In¡¡par

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