74 



The Right Hon. Lord Rayleigh 



[March 20, 



extreme cusewhen the diameter of a previously uniform tube suddenly 

 becomes infinite ? (Fig. 3 without card.) Ordinary experience 

 teaches that in such a case the flow does not follow the walls round 

 tbe corner, but shoots across as a jet, which for a time preserves its in- 

 dividuality and something Hke its original section. Since the velocity 

 is not lost, the pressure which would replace it is not developed. 

 It is instructive to compare this case with another, experimented on 

 by Savart * and W. Froude,t in which a free jet is projected through 

 a short cone, or a mere hole in a thin wall, into a vessel under a 

 higher pressure. The apparatus consists of two precisely similar 

 vessels with apertures, in which the fluid (water) may be at different 

 levels (Fig. 7, copied from Froude). Savart found that not a single 

 drop of liquid was spilt so long as the pressure in the recipient vessel 

 did not exceed one-sixth of that under which the jet issues. And 

 Froude reports that so long as the head in the discharge cistern is 



maintained at a moderate height above that in the recipient cistern, 

 the whole of the stream enters the recipient orifice, and there is " no 

 waste, except the small sprinkling ^'hich is occasioned by inexactness 

 of aim, and by want of exact circularity in the orifices." 1 am dis- 

 posed to attach more importance to the small spill, at any rate when 

 the conoids are absent or very short. For if there is no spill, the jet 

 (it would seem) might as well be completely enclosed : and then it 

 would propagate itself into the recipient cistern without sudden ex- 

 pansion and consequent recovery of pressure. In fact, the pressure 

 at the narrows would never fall below that of the recipient cistern, 

 and the discharge would be correspondingly lessened. When a de- 

 cided spill occurs. Froude explains it as due to the retardation by 

 friction of the outer layers, which are thus unable to force themselves 

 against tbe pressure in front. 



Evidently it is the behaviour of these outer layers, especially at 



* Ann. de Chimie, Iv. p. 257, 1833. 

 t Nature, vol. iii. p. 93, 1875. 



