386 Scientific Proceedings, Roi/at Dublin Society. 



have already remarked that this tube was in a single unbroken length, some 

 400 centimetres. Now in the liglit of the previous discussion this would 

 mean that tlie critical velocity shown was probablj' really that corresponding 

 to the diameter, inasmuch as there were no constrictions of tlie bore. Another 

 explanation of the discrepancy would be that the part of the tube used for 

 experimental purposes (between A and B) was wider than tlie mean diameter 

 This was not the case. A third possibility — one which I think at least as 

 probable as any of the others — is that the tube being long and very uniform, 

 the point where the linear flow became sufficiently unstable to give place to 

 turbulent motion was at a somewhat higher velocity. With shorter tubes, 

 small eddies produced at entering have not time to die away ; with uneven 

 bores, eddies are produced, which, as the critical point is approached, 

 naturally lielp to precipitate the destruction of the linear flow. This 

 behaviour resembles results obtained by Barnes and Coker {loc. cit.). 



We may then summarize Table I as follows : — The mean value of 

 the constant K for all the glass tubes (excepting that of smallest bore, 

 1-1 cms.) is 2481. 



That is to say, Reynolds' equation would become, for air in these glass 

 tubes : — 



while for copper tubes (or possibly for all tubes sufficiently long and uniform ) 

 the constant K is 3120, and the equation : — 



V. = ^i^^ ... (E) 



pa 



The value of the constants in each ease is higher than Reynolds gives for 



water ; but it is remarkable that the difference is only, at most, about fifty 



per cent. ; the order of the number is the same both for air and water. 



P.ARI IV. 



Verification of the laic of dependence of the critical velocity on Density and 



Viscosity. 



The first attempt to examine how the critical velocitj' depended on the 

 densitv and viscosity was made by comparing the results obtained by 

 working at widely different temperatiu-es. Two lengths of hard glass tube 

 were employed for the tubes AB and AG, the latter one being selected as 

 long as possible. They were fitted through corks in two large copper tubes 

 (7 cms. diameter) which enclosed each of tliem for the greater part of their 

 length. The copper tubes served as steam-jackets for the experimental 

 tubes, and steam inlet and outlet tubes were inserted through the corks 

 at either end. Curves were plotted (1) at room-temperature, and subsequently 



