jo. 1331. DRAGON-FLY WING VENATION— NEEDHAM. 751 



I V. DYNAMIC CONTROL IN VEIN EVOLUTION. 



\ So numerous are the evidences that veins are largely controlled in 

 heir development by purely mechanical causes, it would be impossible, 

 ^ere it not also undesirable, to enumerate them here. We have come 

 Ipon parallelisms at every turn. We have seen essentially the same 

 iiechanical feature of efficient wings made out of homologically dif- 

 ferent things repeatedly. But the adult wing is only a machine, and 

 his was to have been expected. It remains now for us to notice a few 

 |eatures which indicate the operation in these wings of far-reaching 

 nechanical principles. 



It is not at all surprising that we should Hnd the first regular form 

 liken on by the areoles of the wing to l)e hexagonal. The hexagon is 

 [lature's favorite plane figure, and there is a good mathematical reason 

 yhy it should be so: economy is a good biological reason. We have 



fiG. 39.— Diagram illustrating a typical (hypothetical) arrangement of the aeroles in 



I ONE OF the wider SPACES OF THE WING. 



r 

 f 



ilready shown that bordering, straight veins eliminate certain angles 

 |»f the hexagons, converting them into pentagons and rectangles. We 

 )ass now to notice the arrangement of the areoles in the wider areas 

 >f the wing, where least influenced by the veins. The spaces between 

 ')rincipal veins or branches of veins, widening distally, are filled prox- 

 mally by a single row of rectangles or b}" a double row of alternating 

 )entagons. Actual hexagons are present onl}^ when there are three or 

 laore rows of areoles included. The first cell in each added row is 

 ypically a pentagon, which presents an angle to the cleft between the 

 eparating rows of areoles and a straight side to meet succeeding hexa- 

 gons. A triangle or a heptagon would of course do the same, but 

 lot with so little disturbance of surrounding hexagons. Opposite the 

 nitial pentagon an areole in one of the preexisting rows acquires an 

 idditional side, becoming a heptagon (or a hexagon, of course, if it 

 v^ere first a pentagon). Thus pentagon and heptagon arc complemcntal, 

 nd together initiate new rows of cells with the least possible disturb- 



