THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
95 7 
the tank, or arising from irregularities in the tube, were necessary to the existence of 
a state of instability. 
But whatever these peculiarities may mean as to the way in which eddies present 
themselves, the broad fact of there being a critical value for the velocity at which the 
steady motion becomes unstable, which critical value is proportional to 
a 
P c 
where c is the diameter of the pipe and - the viscosity by the density, is abundantly 
P 
established. And cylindrical glass pipes for approximately steady water have for the 
critical value 
P 
V B,D 
where in metres B J =43 , 79 about. ' 
Section III. 
Experiments to determine the critical velocity by means of resistance in the pipes. 
24. Although at first sight such experiments may appear to be simple enough, 
yet when one began to consider actual ways and means, so many uncertainties and 
difficulties presented themselves that the necessary courage for undertaking them was 
only acquired after two years’ further study of the hydrodynamical aspect of the 
subject by the light thrown upon it by the previous experiment with the colour bands. 
This has been already explained in Art. 13. Those experiments had shown definitely 
that there was a critical value of the velocity at which eddies began if the water were 
approximately steady when drawn into the tube, but they had also shown definitely 
that at such critical velocity the water in the tube was in a highly unstable condition, 
any considerable disturbance in the water causing the break down to occur at velocities 
much below the highest that could be attained when the water was at its steadiest; 
suggesting that if there were a critical velocity at which, for any disturbance what¬ 
ever, the water became stable, this velocity was much less than that at which it would 
become unstable for infinitely small disturbances; or, in other words, suggesting that 
there were two critical values for the velocity in the tube, the one at which steady 
motion changed into eddies, the other at which eddies changed into steady motion. 
Although the law for the critical value of the velocity had been suggested by the 
equations of motion, it was, as already explained, only at the beginning of this year 
that I succeeded in dealing with these equations so as to obtain any theoretical expla¬ 
nation of the dual criteria; but having at last found this, it became clear to me that 
if in a tube of sufficient length the water were at first admitted in a high state of 
disturbance, then as the water proceeded along the tube the disturbance would settle 
down into a steady condition, which condition would be one of eddies or steady 
MDCCCLXXXIII. 6 G 
