186 Prof. Osborne Reynolds on 



With smaller pressures in the discharging vessel the times 

 occupied by the pressure in falling a proportional distance 

 are nearly the same until the pressure in the receiving vessel 

 reaches about the same relative height. 



What the exact relation between the two pressures is when 

 the change in rate of flow occurs is not determined in these 

 experiments. For as the change comes on slowly, it is at first 

 too small to be appreciable in such short intervals as 7*5 and 

 8 seconds. But an examination of Mr. Wilde's table vi. 

 shows that it lies between *5 and '53. 



This very remarkable fact, to which Mr. Wilde has recalled 

 attention, excited considerable interest fifteen or twenty years 

 ago. Graham does not appear to have noticed it, although 

 on reference to Graham's experiments it appears that these 

 also show it in the most conclusive manner (see table iv., 

 Phil. Trans. 1846, vol. iv. pp. 573-632; also Reprint, p. 106). 

 These experiments also show that the change comes on when 

 the ratio of the pressures is between '483 and *531. 



R. D. Napier appears to have been the first to make the 

 discovery*. He found, by his own experiments on steam, that 

 the change came on when the ratio of pressures fell to *5 

 (see Encyc. Brit. vol. xii. p. 481). Zeuner, Fliegner, and Hirn 

 have also investigated the subject. 



At the time when Graham wrote, a theory of gaseous 

 motion did not exist. But after the discovery of the mecha- 

 nical equivalent of heat and thermodynamics, a theory became 

 possible, and was given with apparent mathematical com- 

 pleteness in 1856. This theory appeared to agree well with 

 experiments until the particular fact under discussion was dis- 

 covered. This fact, however, directly controverts the theory. 

 For on applying the equations giving the rate of flow through 

 an orifice to such experiments as Mr. Wilde's, it appears that 

 there is a marked disagreement between the calculated and 

 experimental results. The calculated results are even more 

 remarkable than the experimental; for while the experiments 

 only show that diminishing the pressure in the receiving 

 vessel below a certain limit does not increase the flow, the 

 equations show that by such diminution of pressure the flow 

 is actually reduced and eventually stopped altogether. 



In one important respect, however, the equations agree 



* The account of R. D. Napier's experiments is contained in letters in 

 the ' Engineer,' 1867, vol. xxiii. January 4 and 25. They were made with 

 steam generated in the boiler of a small screw-steamer and discharged 

 into an iron bucket, the results being calculated from the heat imparted 

 to a constant volume of water in the bucket in which the steam was 

 condensed. 



