390 REPORT— 1886. 



portant. The bases of it are liis own experiments on conductivity, and 

 those of Hittorf on ' migration ' or unequal concentration. 



Up to the present time the numbers given by KoUrauscb for the 

 absolute velocity of different ions in centimetres per second have been 

 deduced from theoretical grounds only, and the sole verification to v^hich 

 they have been subjected bas been by showing that from them the 

 observed conductivities and migration coefficients of a considerable 

 number of solutions can be calculated (see, for instance, page 337 

 above). In a paper published last year' I indicated reasons for doubting 

 the complete truth of the Koblrausch theory as it stood, i.e., for supposing 

 it deficient in generality, and also initially suggested an experimental 

 method suitable for examining the question, and for giving a direct 

 determination of the absolute velocity of various ions, in a form apparently 

 free from any hypothesis. 



The method consisted in passing a current through an electrolyte con- 

 tained in a uniform glass tube, and arranging some form of test substance 

 to detect the position to which the ions had at any instant attained in 

 their journey along the tube. The speed of any ion which lent itself to 

 this mode of chemical detection could thus obviously be measured, 

 provided disturbing causes could be excluded. 



The experiments I have made on this plan hitherto, though numerous, 

 can hardly be regarded as more than preliminary — a good many diffi- 

 culties, some expected, some unexpected, having turned up in the course 

 of the investigation, as usual. Nevertheless, a fair approach to a satis- 

 factory and accurate result has been in some of the later instances 

 obtained, and, besides the experience, some of the results themselves are 

 worth having. 



Let me first rapidly obtain the theoretical values of ionic velocity, in 

 a complete manner, in order to distinguish the parts of the theory which 

 are manifestly true from the parts which may require modification and 

 development. 



Consider a unit cube of electrolyte, containing ?i^ active molecules, 

 i.e., v? molecules actually engaged in conveying a current, and ignoring 

 any inert molecules such as those of the solvent have (perhaps without 

 reason) usually been supposed to be. Let q be the total charge of each 

 kind of electricity possessed by the constituent ions of each active mole- 

 cule, and let U be the velocity with which the two oppositely charged 

 ions are being sheared past one another by the applied slope of potential 



dv 



—~. Then, if A: is the conductivity of the unit cube, we have the foUow- 



dx 



ing couple of expressions for the intensity of current {i.e., quantity of 



electricity conveyed per second through unit area normal to the flow) : — 



First n'-q * riU, from simple notions of convection ; 



d'v 

 second k —- , from Ohm's law. 



ax 



Writing N for the number of monad gramme-equivalents of the active 

 substance present in the unit cube, and jj for the E.C.E. of hydrogen (that 

 is, 1 ji] for the quantity of electricity corresponding to any monad gramme- 

 equivalent), it is plain that 



N. -=«■%. 



V 



' Aberdeen Eejfort, p. 754. 



