ON PASSIVE STRENGTH AND FRICTION. 107 



tain the specific gravity of such a substance in different states of tension 

 and compression, and some light might he thrown by the comparison, on 

 the nature and operation of the forces which are concerned. It has indeed 

 been asserted that the specific gravity of elastic gum is even diminished by 

 tension, so that the actual distances of the particles cannot, in this case, be 

 supposed to be materially increased. 



It is difficult to compare the lateral adhesion, or the force which resists 

 the detrusion of the parts of a solid, with any form of direct cohesion. This 

 force constitutes the rigidity or hardness of a solid body, and is wholly 

 absent from liquids, although their immediate cohesion appears to be nearly 

 equal to that of solids. Some experiments have been made on the fracture 

 of bodies by means of detrusion, but it does not appear that the force 

 necessary to produce a temporary derangement of this kind has ever been 

 examined : it may be inferred, however, from the properties of twisted 

 substances, that the force varies in the simple ratio of the distance of the 

 particles from their natural position, and it must also be simply propor- 

 tional to the magnitude of the surface to which it is applied. 



The most usual, as well as the most important effect produced by the 

 application of force, is flexure. When a force acts on a straight column in 

 the direction of its axis, it can only compress or extend it equally through 

 its whole substance ; but if the direction of the force be only parallel to 

 the axis, and applied to some point more or less remote from it, the com- 

 pression or extension will obviously be partial : it may be shown that in 

 a rectangular column, when the compressing force is applied to a point 

 more distant from the axis than one sixth of the depth, the remoter surface 

 will no longer be compressed but extended ; and it may be demonstrated 

 that the distance of the neutral point from the axis is inversely as that of 

 the point to which the force is applied. From the effect of this partial 

 compression, the column must necessarily become curved : and the curva- 

 ture of the axis at any point will always be proportional to its dis- 

 tance from the line of direction of the force, not only while the column 

 remains nearly straight, but also when it is bent in any degree that the 

 nature of the substance will allow. If the column was originally bent, 

 any force, however small, applied to the extremities of the axis will 

 increase the curvature according to the same law, but if the column was 

 originally straight, it cannot be kept in a state of flexure by any lon- 

 gitudinal force acting precisely on the axis, unless it be greater than a 

 certain determinate force which varies according to the dimensions of the 

 column. It is not however true, as some authors have asserted, that every 

 column pressed by such a force must necessarily be bent ; its state when it 

 is straight and submitted to the operation of such a force will resemble a 

 tottering equilibrium, in which a body may remain at rest until some 

 external cause disturbs it. The figure of a cplumn naturally straight, 

 but bent a little by a longitudinal force, will coincide with that of the 

 harmonic curve, in which the curvature is as the distance from the basis. 

 (Plate IX. Fig. 117... 121.) 



Considerable irregularities may be observed in all the experiments 

 which have been made on the flexure of columns and rafters exposed to 



