Dowj.iNG — Stead// and Turhdent 3Iotion in Gases. 391 



For the copper tubes we now have two numbers for K, the mean of 

 which is 3073 ; and for tliis tube Reynolds' equation now becomes 

 approximately 



Also for glass tubes, taking tlie mean of all tlie results in Table I (excepting 

 Nos. 3, 10, 13), and those for CO2 in glass tubes in Table IV., we obtain 

 the mean value 2500 for K, giving the equation for glass tubes 



pn 

 These results, of course, are subject to the same remarks as to steadiness, 

 &e., which were made in discussing Table I. 



We have now shown that Reynolds' equation applies to gases, as well as to 

 liquids — but that the constant K, while of the same order, is greater for gases 



We will now consider the significanee of the second discontinuity in the 

 curves, which clearly indicates a second critical stage in the flow. 



Part V. 



Investigation of the second critical stage. 



The existence of the second critical stage was not suspected. There were 

 no a priori I'easons for supposing the existence of such an effect in a tube of 

 uniform bore. The effect we now consider was first noticed on one of the 

 widest tubes (5-03 ems.), and was there so well marked that it was mistaken 

 for the ' Reynolds ' effect. This caused some surprise, for the product V x d 

 was about twice too great. This experiment was the first performed with the 

 gasometer arrangement, The next tube was the 3-centimetre tube, and 

 this gave only one discontinuity in the curve, .at a velocity which made 

 V X d - 369, or of the order expected.' The next tube used gave the clue 

 to these discrepancies. Tioo ' discontinuities ' were found on the curve (No. 4, 

 Plate XXXIl.), for one of which the product V x d = 359. This we have 

 already identified (Table I) with the ' Reynolds ' effect. It was noticed that 

 the other, together with that for the 3-cm. tube (Curve No. 5), and that 

 found for the 5*03-cm. tube, were roughly proportional to the radius of the 

 tube. Fresh experiments with the large tube revealed the fact that this also 

 gave tico well-marked ' discontinuities ' — that for the lower velocity giving 

 the product F x rf = 327, not very different from the other ' Reynolds ' critical 

 points. In subsequent experiments both discontinuities were sought for, and, 



1 Cf. Part I, A & B, Part III, C. 

 SCIBNT. PEOC. R.D.S., VOL. XHI., NO. XXVI. 3 N 



