Brlggs.J ^1^ [Nov. 3, 



one-half inch, and that of r,j as five inches (or ten times r), the velocity 



of flow towards the aperture at r^,, would be only one tenth of that at r ; 

 the head riMinircd to produce the velocity at r^ would only he one-one- 

 hundredth of that corresponding to the velocity at r; and the pressure of 

 the head remaining on the plate or bottom at t^q, would be ninefy-nine- 

 one-hundredths of the total head. 



These two pressures on the plate and the bottom would be equal and 

 opposite pressures, and if the plate were removed, the unbalanced pressure 

 on the bottom would represent the force P, to which Professor Thomson 

 gives an undefined value. Its total, is of course the sum of the head upon 

 the area of half the opening, and continuing the supposition of removal 

 of the plate, it is encountered and balanced by the moinentum of the descend- 

 ing tnass, so that the bottom would now be in equilil)rium of pressure, and 

 the force P, as an unbalanced one, would disappear. 



Returning to the examination of the proposition as shown in Fig. 5 : 

 the static resistance of the under surface of the conoid Z in a vertical di- 

 rection against the fiow of water in its radial movement towards the centre 

 of the orifice, and while following the path of the under surface of the 

 conoid, is represented in total by the divergence at right angles of the en- 

 tire effluent stream ; = to ^ D of superfice, under the head which has 

 produced the eiflux. The reaction of the flow of liquid downwnrds is also 

 equal to another statical resistance of the same value, and in the same di- 

 rection ; and as the total pressure on the conoid Z from above, is its entire 

 upper surface, under the head of liquid above it; the one pressure above 

 balances the two pressures below, and the conoid itself is in equilibrium. 



If it is now assumed that there exists no frictional adhesion of the liquid 

 to the surfaces of the supposed plate, and of the bottom of the vessel, and 

 the vessel is of indefinite extent, .so that the velocity of entry at E E is re- 

 duced to an inappreciable rate of flow, then the condition of the formation 

 of a perfect vena contracta will have been exhibited. The removal of the 

 guide plate E E, and the removal of the bottom of the vessel, and substi- 

 tution of a re-entrant tube, would replace the supposed frictionless surfaces 

 by liquid mass, which if it is still continued to be supposed devoid of vis- 

 cosity, would enter the peripheral surfixce C A with the same force, and in 

 t]\o same direction, and would slill preserve the same perfect vena contrncta. 

 The removal of the conoid Z would provide a fluid conoid of the same 

 shape, or a distribution of internal strains productive of the same resist- 

 ance, and (still assuming tlie perfect liquid i the same perfect vena contracta 

 would follow. If however there is admitted to exist a certain adhesion to 

 the bottom of the vessel, or to the surface or edges A A .so that the velocity 

 of a particle on A B is less than that fully due to the head; the surface (d) 

 would then become larger than J D, tiie dimension C A would be properly 

 increased to give the corresponding area of cfHux, and the conoid Z would 

 also have sucli a contour as would permit the uniformity of flow of each 

 and every particle of tlie liquid at unchanged velocity, in any section of 

 the vena contracta transverse to the direction of the flow. This increase 



