344 Profs. H. T. Barnes and E. G. Coker. [Nov. 4, 



l-7th power, the intersection of the logarithmic homologues gave a 

 method of determining it. Eeynolds remarks that for a short distance 

 above and below the critical velocity the gauges became unsteady and 

 no readings could be made. 



By means of his experiments Eeynolds was able to verify his 

 mathematical deductions, and he showed from three different pipes, 

 together with a comparison with the experiments of D'Arcy for large 

 pipes and with Poiseuille's for small tubes, that the critical velocity 

 varied inversely as the diameter of the pipe. He further showed that 

 the critical velocity followed the viscosity temperature law as deduced 

 by Poiseuille, and, therefore, varied as the viscosity over the density. 

 Similar experiments with three different pipes by the method of 

 colour bands showed that the upper limit followed the same laws 

 approximately. The theoretical equations, however, had to do with 

 the lower limit. 



In our experiments on the upper limit of critical velocity with 

 absolutely quiet water, we found that stream-lines were preserved in 

 many cases to very much higher velocities than would be expected 

 from the inverse-diameter law, and that the upper limit falls off slightly 

 more rapidly with rise in temperature than the law of Poiseuille. We 

 do not wish to lay stress on these points, or intimate in any way that 

 we think they question the validity of the theoretical laws which have 

 been so completely worked out by Reynolds. We think, however, 

 that they show the instability of the upper limit of stream-line flow, 

 and how much it depends on forms of disturbance. We have, more- 

 over, made independent determinations of the temperature variation of 

 the lower limit, and find by two different methods that over a wide 

 range in temperature the critical velocity follows the viscosity 

 temperature law accurately.* 



The slight deviation from the theoretical law for the variation with 

 temperature of the upper limit which we have observed in the case of 

 two pipes of different diameters is, we think, due to the fact that it 

 becomes more and more difficult, as the temperature rises, to maintain 

 stream-line flow in the unstable region. This would result in the 

 upper limit apparently falling off more rapidly than the temperature 

 formula would allow for. 



The question has suggested itself to us that some form of initial 

 disturbance in our tank may have come in as the temperature was 

 raised to cause a greater falling-off in the upper limit than the 

 theoretical. Convection currents might have supplied such a form 

 of disturbance, but the size of our tank and the fact that the mouth 

 of our pipes was always placed at or near the middle, together with 



* E. GK Coker and S. B. Clement, ' Phil. Trans./ A, vol. 201, p. 45 (1903) ; 

 H. T. Barnes, B. A. Report,' Belfast (1902). 



