98 



Mr. 0. Reynolds. 



[Mar. 15, 



by the difference of the logarithm of — for the two tubes, the 

 vertical shifts by the difference of the logarithm of 



The temperatures at which the experiment had been made were 

 nearly the same, but not quite, so that the effect of the variations of ju. 

 showed themselves. 



15. Comparison with Darcy's Experiments. — The definiteness of these 

 results, their agreement with Poiseuille's law, and the new form which 

 they more than indicated for the law of resistance above the critical 

 velocity, led me to compare them with the well-known experiments of 

 Darcy on pipes ranging from 0*014 to 0*5 metre. Taking no notice 

 of the empirical laws by which Darcy had endeavoured to represent 

 his results, T had the logarithmic homologues plotted from his pub- 

 lished experiments. If my law was general then these log curves, 

 together with mine, should all shift into coincidence if each were 

 shifted horizontally through 



In calculating these shifts there were some doubtful points. Darcy's 

 pipes were not uniform between the gauge points, the sections varying 

 as much as 20 per cent., and the temperature was only casually given. 

 These matters rendered a close agreement unlikely ; it was rather a 

 question of seeing if there was any systematic disagreement. When 

 the curves came to be shifted the agreement was remarkable ; in only 

 one respect was there any systematic disagreement, and this only 

 raised another point ; it was only in the slopes of the higher portions 

 of the curves. In both my tubes the slopes were as 1*722 to 1 ; in 

 Darcy's they varied according to the nature of the material, from 

 the lead pipes, which were the same as mine, to 1*92 to 1 with the 

 cast iron. This seems to show that the nature of the surface of the 

 pipe has an effect on the law of resistance above the critical velocity. 



16. The Critical Velocities. — All the experiments agreed in giving 



D 



5! 



P 2 



and vertically through — 



P 



as the critical velocity, to which correspond as the critical pressure 



__1__P2 



47700000 D 3 ' 



