138 Dr. W. J. Walker on Fluid Discharges 



Summary. 



On the assumption that interionic forces in solutions of 

 electrolytes are inverse-square functions of the distances 

 apart of dissimilar ions, and that the forces causing dis- 

 sociation of molecules may be regarded as inverse higher- 

 poAer functions of the distance, a quantitative theoretical 

 interpretation is given to the Rudolphi relation and a 

 qualitative one to the van't Hoff relation, connecting the 

 dilution and the degree of dissociation of an electrolyte. 



Bedford Modern School, 

 7 February, 1921. ■ 



X. Fluid Discharges as affected by Resistance to Flow. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



I TRUST you will allow me to add the following to my 

 note on " Fluid Discharges as affected by Resistance to 

 Flow," which appeared in your February number. 



In that note it appears that the abnormal values of G 

 obtained are due to the total resistance to flow becoming 

 negative below a certain velocity. That argument I cannot, 

 of course, for a moment uphold. What I set out to show 

 was that it is possible for the total fluid resistance to be 

 positive and yet to yield, by analysis, values of C greater 

 than unity. In my note, the values given to the constants 

 " a " and " b " were not taken from experimental results, 

 but were chosen merely to illustrate the analytical results. 

 These results appeared to me when I arrived at them to 

 yield analytical curves, the similarity of which to the ex- 

 perimental curves was so striking that, unfortunately, I did 

 not sufficiently emphasize the fact that the total resistance R 

 must be positive before such results can have any analytical 

 value. Such an analysis, explaining genuine experimental 

 discharges greater than would be obtained with a perfect 

 fluid under the same manometer head, need not imply any 

 violation of the conservation of energy if it is the result of 

 the inclusion of some hitherto neglected effect upon the 

 manometer head readings. 



To render the equation 



R = av + bv 2 



more general when "a" is negative, so that R will always 

 be positive, it may be written 



R, = & + at?4- bv 2 . 



