96 



Mr. 0. Reynolds. 



[Mar. 15, 



been ascertained, and the relation between the four leading features 

 and the circumstances on which they depend traced, for the case of 

 water in parallel flow. But as it appeared that the critical velocity 

 in the case of motion in one direction did not depend on the cause of 

 instability with a view to which it was investigated, it followed that 

 there must be another critical velocity which would be the velocity at 

 which previously existing eddies would die out, and the motion become 

 steady as the water proceeded along the tube. This conclusion has 

 been verified. 



14. Results of Experiments on the Law of Resistance in Tubes. — The 

 existence of the critical velocity described in the previous article 

 could only be tested by allowing water in a high state of disturbance 

 to enter a tube, and after flowing a sufficient distance for the eddies 

 to die out, if they were going to die out, to test the motion. As it 

 seemed impossible" to apply the method of colour bands, the test 

 applied was that of the law of resistance as indicated in questions (1) 

 and (2) in § 8. The result was very happy. Two straight lead pipes, 

 No. 4 and No. 5, each 16 feet long, and having diameters of a quarter 

 and half inch respectively, were used. 



The water was allowed to flow through rather more than 10 feet 

 before coming to the first gauge-hole, the second gauge-hole being 

 5 feet further along the pipe. 



The results were very definite, and are partly shown in fig. 8. 



Fia. 8. 



(1.) At the lower velocities the pressure was proportional to the 

 velocity, and the velocities at which a deviation from this law first 

 occurred were in the exact inverse ratio of the diameters of the 

 pipes. 



(2.) Up to these critical velocities the discharges from the pipes 

 agreed exactly with those given by Poiseuille's formula for capillary 

 tubes. 



(3.) For some little distance after passing the critical velocity no 

 very simple relations appeared to hold between the pressures and 

 velocities ; but by the time the velocity reached 1*3 (critical velocity) 

 the relation became again simple. The pressure did not vary as the 

 square of the velocity, but as 1*722 power of the velocity; this law 



