concerning Voltas Contact Force, 457 



velocities under the above forces can easily be written down. 

 But the actual velocities in the steady state will be equal ; 

 therefore, as the condition of steadiness, 



e \n dx dx J e \n dx dx J 



which simplifies to 



^V v. — Mi dp 



tie — -— — * - J — • 



dx Vi + ?/! dx 



At this stage it is customary to introduce the osmotic 

 pressure gas-analogy, writing the characteristic equation of 

 a mass M and volume V, 



^Y = MRT, 



where R is a characteristic constant, viz. the specific heat of 

 expansion per gramme of perfect gas, which for hydrogen is 

 accidentally almost equal to J, the specific heat of water. 



M 



Writing ^- =pz=nm, and considering the gas pressure p 



to be the osmotic pressure, 



dp = mHT dn, 



at constant temperature. 



And so finally the steady difference of potential due to 

 diffusion between two solutions which differ only in concen- 

 tration, one containing n the other n' active atoms to the 

 litre, is 



V-V'=™RT^=^log^. 



e Vi -f- u ± ° n 



I have written this out fully because it is usually somewhat 

 slurred over, the electrochemical equivalent m/e omitted, 

 the argument rendered obscure, and the dimensions wrong. 



It follows that although usually the E.M.F. thus set up 

 is very small, yet by having one of the solutions extremely 

 weak (n' nearly =0), the E.M.F. generated may be made 

 surprisingly high, that is a large fraction of a volt, provided 

 the anions and cations concerned do not diffuse at nearly the 

 same rate under the same circumstances. 



For instance, if silver is placed in a liquid containing some 

 chloride, no molecules of silver can accumulate in any quantity 

 in the solution, and accordingly the concentration will be almost 

 infinitesimal, and the E.M.F. comparatively high ; thus Ost- 

 wald gives the following as a cell which has, and ought on 



