xiii] A NOTE UPON TORSION 891 



There is one other phenomenon which meets us in the twining 

 and twisted stem, and which is doubtless illustrated also, though 

 not so well, in the antelope's horn; it is a phenomenon which forms 

 the subject of a second chapter of St Venant's researches on the 

 effects of torsional strain in elastic bodies. We have already seen 

 how one effect of torsion, in for instance a prism, is to produce 

 strains parallel to the axis, elevating parts and depressing other 

 parts of each transverse section. But m addition to this, the same 

 torsion has the effect of materially altering the form of the section 

 itself, as we may easily see by twisting a square or oblong piece of 

 india-rubber. If we start with a cylinder, such as a round piece 

 of catapult india-rubber, and twist it on its own long axis, we have 

 already seen that it suffers no other distortion; it still remains 

 a cyhnder, that is to say, it is still in section everywhere circular. 

 But if.it be of any other shape than cylindrical the case is different, 

 for now the sectional shape tends to alter under the strain of torsion. 

 Thus, if our rod be eUiptical m section to begin with, it will, under 

 torsion, become a more elongated ellipse ; if it be square, its angles 

 will become more prominent and its sides will curve inwards, till at 

 length the square assumes the appearance of a four-pomted star 

 with rounded angles. Furthermore, looking at the results of this 

 process of modification, we find experimentally that the resultant 

 figures are more easily twisted, less resistant to torsion, than were 

 those from which we evolved them; and this is a very curious 

 physical or mathematical fact. So a cylinder, which is especially 

 resistant to torsion, is very easily bent or flexed; while projecting 

 ribs or angles, such as an engineer makes in a bar or pillar of iron 

 for the purpose of increasing its resistance to bending, actually make 

 it much weaker than before (for the same amount of metal per unit 

 length) in the way of resistance to torsion. 



In the hop itself, and in a very considerable number of other 

 twining and twisting stems, the ribbed or channelled form of the 

 stem is a conspicuous feature. We may safely take it, (1) that such 

 stems are especially susceptible of torsion; and (2) that the effect 

 of torsion will be to intensify any such peculiarities of sectional 

 outline which they may possess, though not to initiate them in an 

 originally cylindrical structure. In the leaf-climbers the case does 

 not present itself, for there, as we have seen, torsion itself is not, 



