336 Prof. L. Vessot King on 



curve connecting the pressure-gradient and the total flow is 

 one of nearly continuous curvature, so that a " critical 

 velocity" in the usual sense is not sharply defined unless 

 the velocities and pressure-gradients are large and the 

 diameters of the tubes small. An elaborate series of experi- 

 ments under these conditions was carried out by Ruckes 37 , 

 who employed capillary tubes of internal diameters between 

 0*1 and 2'2 mm. at pressures from a fraction of an atmo- 

 sphere to about 50 atmospheres ; Reynolds's Constant, as 

 determined from the curves connecting total flow and 

 pressure-gradient, had values in the neighbourhood of 

 K = 2000 ; in several cases stability continued until velocities 

 corresponding to values of K between 3000 and 8000 were 

 reached, resembling in this respect the observations of Barnes 

 and Ooker 30 already discussed. For metal capillaries K 

 had values as low as 400 and 500, a somewhat surprising- 

 result, probably due, as has already been mentioned, to the 

 degree of mechanical finish of the interior of the capillaries. 



Experiments by Grindley and Gibson 38 on the flow of air 

 through a long lead pipe (108*2 feet long and diameter 

 0*125 inch) gave a value K = 2200. 



Among the earliest observations on the distribution of 

 velocity over the cross-section of tubes may be mentioned 

 those of Becker 39 , the velocity-measuring device involving 

 the aerodynamic resistance of small aluminium spheres. 



Experiments by Fry and Tyndall 40 were carried out 

 by the use of Pitot tubes, and very sensitive manometers 

 specially designed for the purpose ; the curves of velocity- 

 distribution differed markedly from the paraboloidal distri- 

 bution required by the viscous theory, and, as in Morrow's 

 observations 32 , the transition to distributions above the 

 critical velocity was gradual ; the change took place most 

 rapidly in the neighbourhood of a velocity corresponding to 

 a value of Reynolds's Constant K = 2500. 



Very elaborate observations along these lines haverecently 

 been published by Kohlrausch 41 and are worth careful study. 

 Five glass tubes were employed of diameters between 0'76 

 and 3*6 cm. Several series of curves connecting the total 

 flow and the pressure-gradient are given ; a careful inspection 

 of these curves shows that, while they exhibit a decided 



37 Ruckes, W., Ann. d. Phys. vol. xxv. p. 983 (1908). 



38 Grindley & Gibson, Proc. Roy. Soc. vol. lxxx. p. 114 (1908). 



39 Becker, Ann. d. Phys. vol. xxiv. p. 863 (1907). 



40 Fry & Tvndall, Phil. Mag. March 1911, p. 348. 



41 Kohlrausch, K. W. F., Ann. d. Phys. vol. xliv. p. 297 (1914). 



