t)owLiNG — Steady and Turbulent Motion in Gases. 386 



lias been calculated for each curve, and the result is given in 



column 9 of the table. With two exceptions the numbers lie close 

 together. The two exceptions are for curves No. 3 and No. 13. No. 3 

 curve represents the results for the narrowest tubes, and, as we shall see, 

 there are reasons for believing that this number might very well be too low. 

 The conditions in the tube in the case of No. 13 are also different. This 

 was a copper tube, thirteen feet long, and very straight and uniform, and 

 there was no joining throughout its whole length.^ It will be as well to 

 consider here the possible effect that a constriction in the tube would have 

 on the results. Let us consider the tube I'l cms. diameter. It is very 

 probable that at best the paper tube was narrower by a millimetre (indeed, 

 it might very well be more different) . If F is the mean velocity in the 



glass tube, tlie velocity in the paper one would be <' = ( ~t" j V- Now 



T) 



the critical velocity will be reached in the narrowest part first. The 

 condition fulfilled by the critical velocity V, is that 



Vf y. d = constant, 



/1'1\' 

 but y = ( — j- ) ^ a-nd the ratio of the diameters being only 1 : 14, the 



product V y. d for the narrow part will be reached when VxD for the 

 wide glass tube is still only — - of its value for the critical velocity. That 



is equivalent to saying that the velocity is — — of the critical velocity, or 



10 per cent, short of the critical. If turbulence sets in in the paper tube, 

 its effects will be probably identical with those produced by turbulence in the 

 glass tube, and consequently the electrometer readings will indicate the passing 

 of the critical point when the velocity in the glass tube is still 10 per cent, 

 short of its critical value. If the joining tube differs by more than 1 mm. 

 for a I'l cm. tube — the effects will be correspondingly greater. The net result 

 is that the product V x d is too small, and so also the expression for K. 

 This investigation shows us that even the other glass tubes may all give a 

 result a little too low. However, the other values of K vary irregularly and 

 do not show any progressive diminution with decreasing diameter, such as 

 would be expected if the effect we are considering were important, except 

 for the ease we have considered. 



The other case where there was a radical difference between the tubes 

 was that of the copper tube (Curve No. 13). 



In this case the resulting value of the constant Z" is much higher. We 



' A smull place on the tube wall was filed thin to allow the radium rays to enter. 



3 M 2 



