330 Prof. L. Vessot King on 



Sommerfeld 24 , tends to confirm the original conclusions of 

 Kelvin and Rayleigh as to the stability of a state of steady 

 motion. The unsatisfactory state of knowledge at the present 

 time on the subject is clearly shown from the Table given at 

 the end of this paper, from which it is seen that the 

 theoretical estimates of Reynolds's Constant K differ very 

 markedly from each other, and very greatly from the 

 generally accepted values obtained for liquids and gases. 



It may be noted that all experimental data refer to tubes 

 of circular cross-section, whereas the simplest theoretical case 

 refers to the flow of fluid between parallel planes ; in the 

 latter case observations have not hitherto been available. 

 The deficiency is now made up by the writer's own experi- 

 ments on the flow of air to be described in detail in 

 Part III. ; the results indicate the existence of hitherto 

 unsuspected conditions of laminar flow, both at extremely 

 low velocities as well as at velocities considerably higher 

 than those which are taken to represent, according to the 

 usual interpretation, critical velocities. 



By means of the linear hot-wire anemometer developed 

 by the writer 8 , the velocity-distribution over the cross- 

 section of a two-dimensional channel (section 0'45 cm. x 5'08 

 cm.) was measured for various pressure-differences. Owing 

 to the high resolving power of the instrument, it was found 

 possible to measure velocities at intervals of 0*05 mm. over 

 the cross-section, and in this way a velocity-distribution 

 curve representing as many as 100 observations couM be 

 obtained, the pressure-difference under which the flow took 

 place being maintained constant to 1/10 of one per cent. 

 Even at velocities considerably below the "critical velocity/' 

 as usually defined, the distribution curves showed consistent 

 and interesting deviations from the parabolic form demanded 

 by theory. 



(i.) The experimental curves developed well-marked 

 "humps" in the neighbourhood of planes midway between 

 those dividing the distance between the walls of the channel 

 in equidistant parts ; these appeared at very low velocities 

 (maximum velocity 20 cm. per sec), and, with increasing- 

 velocities, the number of " humps " increased, as many as 

 nine being easily discernible in the carve corresponding to a 

 maximum velocity of 650 cm. per second. 



(ii.) Although the general shape of these distribution 

 curves is parabolic, the maximum falls very much below 

 that demanded by the theoretical viscous-flow theory, as 



24 Sommerfeld, Proc. Int. Congress of Mathematicians, Rome, 1908. 



