XIII] A NOTE UPON TORSION 627 



of torsion, so manifest in the former case, will be absent in the 

 latter. 



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 in 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 cylinder, that is to say, it is still in section every- 

 where circular. But if it be of any other shape than cylindrical 

 the case is quite different, for now the sectional shape tends to 

 alter under the strain of torsion. Thus, if our rod be elliptical 

 in 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-pointed 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 greatly increasing its strength in 

 the way of 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 



40—2 



