The Principles of Biology, Volume 2 (of 2)

by Herbert Spencer

§ 254. When an elongated mass of any substance is transversely strained, different parts of the mass are exposed to forces of opposite kinds. If, for example, a bar of metal or wood is supported at its two ends, as shown in Fig. [281], and has to bear a weight on its centre, its lower part is thrown into a state of tension, while its upper part is thrown into a state of compression. As will be manifest to any one who observes what happens on breaking a stick across his knee, the greatest degree of tension falls on the fibres forming the convex surface, while the fibres forming the concave surface are subject to the greatest degree of compression. Between these extremes the fibres at different depths are subject to different forces. Progressing upwards from the under surface of the bar shown in Fig. [281], the tension of the fibres becomes less; and progressing downwards from the upper surface, the compression of the fibres becomes less; until, at a certain distance between the two surfaces, there is a place at which the fibres are neither extended nor compressed. This, shown by the dotted line in the figure, is called in mechanical language the “neutral axis.” It varies in position with the nature of the substance strained: being, in common pine-wood, at a distance of about five-eighths of the depth from the upper surface, or three-eighths from the under surface. Clearly, if such a piece of wood, instead of being subject to a downward force, is secured at its ends and subject to an upward force, the distribution of the compressions and tensions will be reversed, and the neutral axis will be nearest to the upper surface. Fig. [282] represents these opposite attitudes of the bar and the changed position of its neutral axis: the arrow indicating the direction of the force producing the upward bend, and the faint dotted line a, showing the previous position of the neutral axis. Between the two neutral axes will be seen a central space; and it is obvious that when the bar has its strain from time to time reversed, the repeated changes of its molecular condition must affect the central space in a way different from that in which they affect the two outer spaces. Fig. [283] is a diagram conveying some idea of these contrasts in molecular condition. If A B C D be the middle part of a bar thus treated, while G H and K L are the alternating neutral axes; then the forces to which the bar is in each case subject, may be readily shown. Supposing the deflecting force to be acting in the direction of the arrow E, then the tensions to which the fibres between G and F are exposed, will be represented by a series of lines increasing in length as the distance from G increases; so that the triangle G F M, will express the amount and distribution of all the molecular tensions. But the molecular compressions throughout the space from G to E, must balance the molecular tensions; and hence, if the triangle G E N be made equal to the triangle G F M, the parallel lines of which it is composed (here dotted for the sake of distinction) will express the amount and distribution of the compressions between E and G. Similarly, when the deflecting force is in the direction of the arrow F, the compressions and tensions will be quantitatively symbolized by the triangles K F O, and K E P. And thus the several spaces occupied by full lines and by dotted lines and by the two together, will represent the different actions to which different parts of the transverse section are subject by alternating transverse strains. Here, then, it is made manifest to the eye that the central space between G and K, is differently conditioned from the spaces above and below it; and that the difference of condition is sharply marked off. The fibres forming the outer surface C D, are subject to violent tensions and violent compressions. Progressing inwards the tensions and compressions decrease—the tensions the more rapidly. As we approach the point G, the tensions to which the fibres are alternately subject, bear smaller and smaller ratios to the compressions, and disappear at the point G. Thence to the centre occur compressions only, of alternating intensities, becoming at the centre small and equal; and from the centre we advance, through a reverse series of changes, to the other side.

Fig. 281.

Fig. 282.

Fig. 283.

Thus it is demonstrable that any substance in which the power of resisting compression is unequal to the power of resisting tension, cannot be subject to alternating transverse strains, without having a central portion differentiated in its conditions from the outer portions, and consequently differentiated in its structure. This conclusion may easily be verified by experiment. If something having a certain toughness but not difficult to break, as a thick piece of sheet lead, be bent from side to side till it is broken, the surface of fracture will exhibit an unlikeness of texture between the inner and outer parts.

§ 255. And now for the application of this seemingly-irrelevant truth. Though it has no obvious connection with the interpretation of vertebral structure, we shall soon see that it fundamentally concerns us.