XVI] THE STRUCTURE OF BONE 677 



The I or the H-girder or rail is designed to resist bending in one 

 particular direction, but if, as in a tall pillar, it be necessary to 

 resist bending in all directions alike, it is obvious that the tubular 

 or cylindrical construction best meets the case ; for it is plain 

 that this hollow tubular pillar is but the I-girder turned round 

 every way, in a "solid of revolution," so that on any two opposite 

 sides compression and tension are equally met and resisted, and 

 there is now no need for any substance at all in the way of web 

 or " filling" within the hollow core of the tube. And it is not only 

 in the supporting pillar that such a construction is useful ; it is 

 appropriate in every case where stiffness is required, where bending 

 has to be resisted. The long bone of a bird's wing has little or 

 no weight to carry, but it has to withstand powerful bending 

 moments ; and in the arm-bone of a long- winged bird, such as 

 an albatross, we see the tubular construction manifested in its 

 perfection, the bony substance being reduced to a thin, perfectly 

 cylindrical, and almost empty shell. The quill of the bird's 

 feather, the hollow shaft of a reed, the thin tube of the wheat- 

 straw bearing its heavy burden in the ear, are all illustrations 

 which Galileo used in his account of this mechanical principle*. 



Two points, both of considerable importance, present themselves 

 here, and we may deal with them before we go further. In the 

 first place, it is not difficult to see that, in our bending beam, the 

 strain is greatest at its middle ; if we press our walking-stick hard 

 against the ground, it will tend to snap midway. Hence, if our 

 cyHndrical column be exposed to strong bending stresses, it will 

 be prudent and economical to make its walls thickest in the middle 

 and thinning off gradually towards the ends; and if we look at 

 a longitudinal section of a thigh-bone, we shall see that this is 

 just what nature has done. ■ The thickness of the walls is nothing 

 less than a diagram, or "graph," of the " bending-moments " 

 from one point to another along the length of the bone. ' 



The second point requires a little more explanation. If we 



* Galileo, Dialogues concerning Two Netv Sciences (1638), Crew and Salvio's 

 translation, New York, 1914, p. 150; Opere, ed. Favaro, viii, p. 186. Cf. Borelli, 

 De Motu Animalium, i, prop. CLXXX, 1685. Cf. also Camper, P., La structure des 

 OS dans les oiseaux, 0pp. iii, p. 459, ed. 1803; Rauber, A., Galileo iiber Knochen- 

 formen, Morphol. Jahrb. vii, pp. 327. 328, 1881 ; Paolo Enriques, Delia economia 

 di sostanza nelle esse cave, Arch. f. Ent. Mech. xx, pp. 427-465, 1906. 



