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The National Geographic Magazine 



obvious that if we make our structure 

 large enough it will be too heavy to fly — 

 even by itself — far less be the means of 

 supporting an additional load like a man 

 and an engine for motive power. This 

 conclusion is undoubtedly correct in the 

 case of structures that are "exactly alike 

 excepting in their dimensions," but it is 

 not true as a general proposition. 



EVADING AN OLD LAW 



A small bird could not sustain a heavy 

 load in the air ; and while it is true that a 

 similar bird of double the dimensions 

 would be able to carry a less proportion- 

 ate weight, because it is itself heavier in 

 proportion to its wing surface than the 

 smaller bird — eight times as heav}', in 

 fact, with only four times the wing sur- 

 face — still it is conceivable that a flock of 

 small birds could sustain 

 a heavy load divided 

 equally among them ; 

 and it is obvious that in 

 this case the ratio of 

 Unit cell having weight to wing surface 

 the form of the would be the same for 

 hedrlTn ^^^'^' the whole flock as for the 

 individual bird. If, then, 

 we build our large structure by combin- 

 ing together a number of small structures 

 each light enough to fly, instead of sim- 

 ply copying the small structure upon a 

 larger scale, we arrive at a compound or 

 cellular structure in which the ratio of 

 weight to supporting surface is the same 

 as that of the individual units of which 

 it is composed, thus overcoming entirely 

 the really valid objections of Professor 

 Newcomb to the construction of large 

 flying-machines. 



In my paper upon the tetrahedral prin- 

 ciple in kite structure I have shown that 

 a framework having the form of a tetra- 

 hedron possesses in a remarkable degree 

 the properties of strength and lightness. 

 This is specially the case when we adopt 

 as our unit structure the form of the 

 regular tetrahedron, in which the skeleton 

 frame is composed of six rods of equal 

 length, as this form seems to give the 

 maximum of strength with the minimum 



of material. When these tetrahedral 

 frames or cells are connected together by 

 their corners they compose a structure of 

 remarkable rigidity, even when made of 

 light and fragile material, the whole 

 structure possessing the same properties 

 of strength and lightness inherent in the 

 individual cells themselves (page 12). 



The unit tetrahedral cell yields the 

 skeleton form of a solid, and it is bounded 

 by four equal triangular faces. By cov- 

 ering two adjoining faces with silk, or 

 other material suitable for use in kites, 

 we arrive at the unit ''winged cell" of the 

 compound kite, the two triangular sur- 

 faces in their flying position re.= .;mbling a 

 pair of wings raised with theii points up- 

 ward, the surfaces forming a dihedral 

 angle (Fig. A, p. 13). 



Four of these unit cells, connected 

 together at their corners, form a four- 

 celled structure having itself the form of 

 a tetrahedron containing in the n iddle an 

 empty space of octahedral form equal in 

 volume to the four tetralied "al cells them- 

 selves (Fig. B, p. 13). 



In my paper I showed that four of 

 these four-celled structures connected at 

 their corners resulted in a sixteen-celled 

 structure of tetrahedral form containing, 

 in addition to the octahedral spaces be- 

 tween the unit cells, a large central spare 

 equivalent in volume to four of the four- 

 celled structures (Fig. C, p. 13). 



In a similar manner four of the sixteen- 

 celled structures connected together at 

 their corners form a sixty-four-celled 

 structure (Fig. D, p. 13). 



Four of the sixty-four-celled structures 

 form a two hundred and fifty-six-celled 

 structui-e, etc., and in each of these cases 

 an empty space exists in the center equiv- 

 alent to half of the cubical contents of the 

 whole structure, in addition to spaces be- 

 tween the individual cells and minor 

 groups of cells. 



Kites so formed exhibit remarkable 

 stability in the air under varying condi- 

 tions of wind, and I stated in my paper 

 that the kites which had the largest cen- 

 tral spaces seemed to be the most stable 

 in the air. Of course, these were the 



