1880.] Strained Material, Ley den Jars, and Voltameters. 421 



where n varies from 2 to 2*28, but as motions in water become slower 

 and slower, n becomes more and more nearly equal to unity. In the 

 following investigation, we assume that the rates of deformation of the 

 materials, after the first instant, are so slow, that n always equals 

 unity. Our hypothesis is exactly analogous with Ohm's law in 

 electricity ; and just as Ohm's law has only been proved for metallic 

 conductors of electricity, so our hypothesis is only known to be true 

 for gases and liquids. All the analogies which we have observed 

 cannot be discussed in this short paper, but they are such that we are 

 led to believe that if our hypothesis proves to be untrue for materials 

 subjected to small strains, then Ohm's law will prove untrue for 

 currents of electricity in bad conductors. It will be seen that it leads 

 to the conclusion that just as there are no perfect insulators of elec- 

 tricity, so no material, however rigid it may appear to be to us, can for 

 an infinite time resist the effect of even small forces tending to change 

 its form. 



Let MNOP be a large prism of unit square section, formed of 

 blocks of different materials of lengths, a^, a 2 , &c. Let them be sub- 

 jected to shear stress by the action of tangential force v distributed 

 over the surface MIST, and an equal and opposite tangential force 

 distributed over the parallel plane OP. Let the compound prism 

 be so long that we need not speak of the terminal couple which is 

 required to produce equilibrium. Let/ ls / 2 , &c, be the strains exist- 

 ing in the blocks which would be instantaneously destroyed if the 

 stress disappeared, so that if the shear stresses in the blocks are re- 

 spectively X l5 X 2 , &c, then — 



*i=Vi (8), 



where \, k 2 , &c, are the moduli of elasticity of the separate blocks. 

 The distributed external force acting on either of the upper or lower 

 sides of the block being of course a 1 X 1 . 



If the velocity of OP with regard to MN is u, then u is the rate at 

 which each block is gaining strain, because the motion of OP with 

 regard to MN is the measure of the common strain which exists in 

 all the blocks. Consequently, by our hypothesis for any block, we 

 have — 



x K-f) 



VOL. XXX. 2 H 



