80 The Right Hon. Lord Rayleigh [March 20, 



the product of diameter and velocity be given. Thus, if we know 

 the motion for a particular diameter and velocity of the sphere, we 

 can infer what it will be when the velocity is halved and the diameter 

 doubled. The fluid velocities also will everywhere be halved at the 

 corresponding places. M. Eiffel found that for any sphere there is a 

 velocity which may be regarded as critical, i.e. a velocity at which 

 the law of resisUmce changes its character somewhat suddenly. It 

 follows from the rule that these critical velocities should l)e inversely 

 proportional to the diameters of the spheres, a conclusion in pretty 

 good agreement with M. Eiffel's observations.* But the principle is 

 at leasf equally important in effecting a comparison between different 

 fluids. If we'know what happens on a certain scale and at a certain 

 velocity in water, we can infer what will happen in air on any other 

 scale, provided the velocity is chosen suitably. It is assumed here 

 that the compressibility of the air does not come into account, an 

 assumption which is admissible so long as the velocities are small in 

 comparison with that of sound. 



But although the principle of similarity is well established on the 

 theoretical side and has met Avith some confirmation in experiment, 

 there has been much hesitation in applying it, due perhaps to certain 

 discrepancies with observation which stand recorded. And there is 

 another reason. It is rather difficult to understand how viscosity 

 can play so large a part as it seems to do, especially when we intro- 

 duce numbers, which make it appear that the viscosity of air, or 

 water, is very small in relation to the other data occurring in 

 practice. In order to remove these doubts it is very desirable to 

 experiment with different viscosities, but this is not easy to do on a 

 moderately large scale, as in the wind channels used for aeronautical 

 purposes. I am therefore desirous of bringing before you some 

 observations that I have I'ecently made with very simple apparatus. 



When liquid flows from one reservoir to another through a 

 channel in which there is a contracted place, we can compare what 

 we may call the head or driving pressure, i.e. the difference of the 

 pressures in the two reservoirs, with the suction, i.e. the difference 

 between the pressure in the recipient vessel and that lesser pressure 

 to be found at the narrow place. The ratio of head to suction is a 

 purely numerical quantity, and according to the principle of similarity 

 it should for a given channel remain unchanged, provided the 

 velocity be taken proportional to the kinematic viscosity of the 

 fluid. The use of the same material channel throughout' has the 

 advantcige that no question can arise as to geometrical similarity, 

 which in principle should extend to any roughnesses upon the surface, 

 while the necessary changes of velocity are easily attained by altering 

 the head and those of viscosity by altering the temperature.' 



* Comptes Rendus, Dec. 30, 1912 ; Jan. 13, 1913. 



