578 



SCIENCE. 



[N. S. Vol. XX. No. 514. 



studied this subject primarily from an em- 

 pirical standpoint, and that it will be my 

 aim to present to you a series of general- 

 ized statements of the experimental results, 

 formulated in such a way as to show their 

 relation to the important hypotheses con- 

 nected with the ionic theory. ■ Unfortu- 

 nately, it will not be possible in this ad- 

 dress to reproduce, or even fully refer to, 

 the data upon which these conclusions are 

 based— a defect serious in a work of this 

 kind, which will be remedied in a subse- 

 quent publication. I shall, however, try 

 to show the general character of the evi- 

 dence for each conclusion, and the degree 

 of accuracy within which it has been con- 

 firmed. I wish to add that I have been 

 most ably assisted in the preparation of 

 the material upon which paper is based, 

 by Dr. J. W. Brown and Dr. M. S. Sher- 

 rill, of the Massachusetts Institute of Tech- 

 nology. 



The principles to be first presented have 

 reference to two of the main hypotheses 

 which are commonly employed in quanti- 

 tative applications of the ionic theory. 

 One of these hypotheses is that the migra- 

 tion-velocities of the ions of a salt do not 

 vary appreciably ivith Us concentration, at 

 least up to a moderate concentration; and 

 consequently, that the degree of ionization 

 is equal to the ratio of the equivalent con- 

 ductivity at the concentration in question 

 to the limiting value of the equivalent con- 

 ductivity at zero concentration — a ratio 

 which I will hereafter call simply the con- 

 ductivity-ratio. The other hypothesis is 

 that ioiis, and also the un-ionized molecules 

 accompanying them, produce an osmotic 

 pressure substantially equal to the pressure 

 exerted iy the same number of gaseous 

 molecides at the same temperature, at least 

 up to a moderate concentration; a hypoth- 

 esis which may be more briefly expressed 

 by the statement that the osmotic-pressure 

 constant for dissolved electrolytes is iden- 



tical with the gas-constant. It is evident 

 that with the help of this hypothesis we can 

 calculate, either from measurements of os- 

 motic pressure or from those of any other 

 property which is thermodynamically re- 

 lated to osmotic pressure, the number of 

 mols in the solution resulting from one 

 formula weight of salt, that is, the quan- 

 tity which van't Hofi: has represented by 

 the letter i. From the latter, provided the 

 ionization is not complicated by the forma- 

 tion of complex molecules or ions, the de- 

 gree of ionization is readily derived. 



The first of these hypotheses can not be 

 independently tested, because no direct 

 method of determining the change of mi- 

 gration-velocity with the concentration, is 

 known. But the following principle, which 

 has an important significance with refer- 

 ence to the relative influence of concentra- 

 tion- on the velocities of different ions, has 

 been established by measurements of the 

 concentration-changes at the electrodes at- 

 tending the electrolysis of salt solutions. 



TJi,e transf errence numier, or ratio of 

 the conductivity of one ion to the sum of 

 the conductivities of ioth ions, is constant 

 ivithin one per cent., between the concen- 

 trations of 1/200 and 1/10 normal, for all 

 salts thus far accurately investigated, ex- 

 cept lithium chloride, the halides of bi- 

 valent metals and cadmium sidphate. 



This principle holds true, according to 

 the results of various investigators, in the 

 case of potassium and sodium chlorides, 

 hydrochloric and nitric acids, silver nitrate, 

 barium nitrate, potassium sulphate and 

 copper sulphate— -thus in the case of salts 

 of the three different ionic types, which I 

 will speak of as the uni-univalent, the uni- 

 bivalent and the bi-bivalent types, in cor- 

 respondence with the valences of the two 

 ions composing the salt. 



Two conclusions are to be drawn from 

 this result. The first is that complex ions 

 are not present in important quantity in 



