324 Prof. L. Vessot King on 



fluid and not on the relative velocity of adjacent layers, 

 the general solution of (2) is 



U=A + B,y+(l/2^ . (dp/-d.v) .f , . . (4) 



A and B being constants of integration. Experimental 

 evidence 7 is consistent with the condition U = at the 

 boundary y= +b ; under these conditions 



u= - (i/2/o (p-j^.Gp/a*). • • • (5) 



so that the velocity at the centre U is given by 



Uo=-(6 , /2/.).( ft -p I )/J .... (6) 

 The total flow per unit breadth is given by the expressions 



P J_ s Ud - 3//. 9« 3 /. I -3 ,U °' (7j 

 and the mean velocity is thus given by 



U = -i(&»-(9i>/B*)=fU . ... (8) 



This simple case of steady motion has been made the 

 starting point of some of the various theoretical treatments 

 of the stability of laminar motion briefly reviewed in Part II. 

 As far as the writer is aware, no experiments have been 

 carried out with a disposition of apparatus corresponding to 

 this solution. As the linear hot-wire anemometer developed 

 by the writer and described in detail in a previous paper 8 

 is especially suited to the study of this distribution of 

 velocities, the present solution was made the basis of a 

 detailed experimental investigation of gaseous viscosity by 

 studying not only the variation of the total flow with 

 pressure-gradient, lengths and breadths of channels, &c, 

 but by an actual examination of the gradients of velocities 

 themselves. The high resolving-power and sensitiveness to 

 low velocities of the linear hot-wire anemometer make this 

 instrument exceptionally useful for this type of work. The 

 results obtained by this means (which will be fully illustrated 



7 See Lamb, ' Hydrodynamics,' p. 544. In the case of gases, recent 

 experimental work by Knudsen (' La Theorie du Rayonnement et les 

 Quanta,' G authier-Villars, Paris, 1912, p. 133 et see/.) and by Dunoyer 

 ('Les Idees Modernes sur la Constitution de la Matiere,' Gauthier- 

 Villars, Paris, 1913, p. 215 et seq.) on ultra-rarefied gases indicates that 

 molecules actually embed themselves in the material of the boundary, to 

 return into the gas at some later time with a velocity whose direction is- 

 entirely independent of the previous collision with the walls. 



8 King, L. V., " On the Precision Measurement of Air Velocity by 

 means of the Linear Hot-Wire Anemometer/' Phil. Mag. vol. xxix„ 

 April 1915, pp. 556-572. 



