42 THE PLASTIC STATE. 



At the other limit perfect plasticity we have the 

 shearing stress uniform over the whole area of the cross 

 section. 



Thus, /= constant. 

 The resistance of each elemental ring of the section is 



/2?r x8x 



and its moment f2wu?8x. 



So that the total resistance, 



r 



T = 2 vf f 



(XXX.) 



For hollow shafts 



T = |-/7r(R 3 - r') . . (XXXI.) 



o 



= ^/^(D 3 - d 3 ) 



17. The Flow of fletals. It would seem strange at 

 first sight to talk about flow taking place in a substance 

 whose normal condition is that of a solid. But a little 

 thought will no doubt bring to mind familiar instances of 

 phenomena in solid bodies which are in themselves very 

 similar to many of those which are found to manifest them- 

 selves in the more palpably fluid substances. We can 

 proceed by easy stages from the flow of liquids to the flow 

 of solids. Thus we are quite familiar w r ith the flow of 

 water, the more viscous flow of oils, and the still more 

 viscous flow of wet clay and mud. When a wax candle is 

 placed in an unsupported horizontal or inclined position, 

 it will be observed that after a time it will be found to have 

 assumed a curved shape, and if the conditions are favourable 

 may ultimately collapse altogether. This is undoubtedly a 

 case of a movement of the particles, or flow, taking place 

 in a substance which we usually look upon as solict A 

 similar case is that of a rod of sealing w r ax left for a time 

 under precisely similar conditions. It will be found 

 that the weight of the wax generally looked upon 

 as a brittle substance when cold has been sufficient to 



