XVI] OF TUBULAR STRUCTURES 971 



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 

 Gahleo used in his account of this mechanical principle f; and the 

 working of his practical mind is exemplified by this catalogue of 

 varied instances w^hich one demonstration suffices to explain. 



The same principle is beautifully shewn in the hollow body and 

 tubular limbs of an insect or a crustacean ; and these complicated 

 and elaborately jointed structures have doubtless many constructional 

 lessons to teach us. We know, for instance, that a thin cylindrical 

 tube, under bending stress, tends to flatten before it buckles, and 

 also to become "lobed" on the compression side of the bend; and 

 we often recognise both of these phenomena in the joints of a 

 crab's legj. 



Two points, both of considerable importance, present themselves 

 here, and w^e may deal with them before we go further on. In the 

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

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

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

 cylindrical 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 presence of a "danger-point" has been 

 avoided, and the thickness of the walls becomes nothing less than 



* Marsigli (op. cit.) was acquainted with the hollow wfng-bones of the pelican; 

 and Bulfon deals with the whole subject in his Discours sur la nature des oiseaux. 



f Galileo, Dialogues concerning Two New Sciences (1638). Crew and Salvio's 

 translation. New York, 1914, p. 150; Opere, ed. Favaro, viii, p. 186. (According 

 to R, A. Millikan, "we owe crur present day civilisation to Galileo.") Cf. Borelli, 

 De Motu Animaliiim, i, prop, clxxx, 168.5. Cf. also P. Camper. La structure des 

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

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

 di sostanza nelle osse cave, Arch. f. Entw. Mech. xx, pp. 427-465, 1906. Galileo's 

 views on the mechanism of the human body are also discussed by 0. Fischer, in his 

 article on Physiologische Mechanik, in the Encycl. d. mathem. Wissenschaften, 1904. 



X Cf. L: G. Brazier, On the flexure of thin cylindrical shells, etc., Proc. R.S. (A), 

 cx^^, p. 104, 1927. 



