106 Scientific Proceedings, Royal Dublin Society. 



of the current and on the form and size of the portion of the tube 

 between these points, or 



Pi-p 2 = F 12 (C), 



where the form of the function F n depends on the linear dimen- 

 sions of the tube only ; the density and viscosity of the liquid and 

 the character of the motion between the points considered being 

 assumed to be independent of the absolute pressure. 



If now the pressure-difference pi-p-i corresponding to a certain 

 value of the current C be determined from an observation in 

 which the absolute values of both pressures are determinable, then, 

 when C has the same value again, and the absolute value of p x can 

 be measured, that of p 2 may be at once deduced. 



Now in the case of liquid flowing through a tube of varying 

 section (as shown in fig. 1) the pressures in the large-bore portions 

 of the tube as at the point marked (1) or (3) are easily measurable 

 by manometers connected to the tube; but in the small-bore portion 

 as at the point (2) the difficulty of inserting a manometer connec- 

 tion would be great: the readings of the manometer might not give 

 a true indication of the pressure in the flowing liquid (as, owing to 

 the high velocity of flow, the effect of the eddies formed at the 

 junction of the manometer tube with the tube in which the liquid 

 was flowing would be large and uncertain), and finally, as soon as 

 the pressure became negative, rupture would occur in the stationary 

 liquid within the manometer tube. So that negative pressures, if 

 produced, cannot be measured directly, but must be deduced from 

 observations on measurable positive pressures. 



But in order that negative pressures at the narrow portion of 

 the tube may be deduced from observed values of the current, and 

 of the pressure in the large-bore portion of the tube by the use of 

 the relation 



p x -Pi = F u {C) t 



it is necessary that some special determination of values of p 1 and 

 p 2 be made for each value of C. For p { the determination is easily 

 made by a manometer, and for p 2 advantage is taken of the fact 

 that a special value of p % , viz. a value very nearly equal to the 

 the vapour pressure of the liquid is produced and maintained when 

 the flow of liquid just below the point (2) is discontinuous, for 

 then the pressure in the space not occupied by liquid can only be 



