1876.] *^J-* [Brlggs. 



of dimension of tlie cross section d, and the effect of the descending pencil 

 in accelerating the flow through it, can be taken as sufficient to account for 

 Weisbach's observed value of = 0.8D, and position of least section at =z 

 I D, as has been before quoted. 



It must not be taken for granted that the writer is arguing that the 

 conoid Z actually exists in the water, but it is here assumed for the purpose 

 of showing that all the phenomena of the i^ena contracta are consistent 

 with the supposition. Mr. Froude's "tangential" direction for the fluid 

 in Fig. 3, which lie says appears if closely studied, is a portion of the pro- 

 position, and this discussion exhibits "the imparting of velocity and »?s 

 viva outside of the plane of the orifice," as alluded to by Mr. Napier 



There is one other point worthy of notice in this radial flow of currents 

 towards an orifice, and the radial direction at the edges of the opening. 

 With or without the assumed central, neutral conoid, this flow is in ex- 

 ceedingly unstable equilibrium, especially when in contact with a bottom 

 plate, (the friction or adiiesion to which retards the flow), the radial direc- 

 tion may be diverted to a small extent, so that the particle of water where 

 it curves at the point A, or at any other point on the line C A may possess 

 absolute momentum out of the line towards the central axis of the pencil. 



The radius of the opening calls for a very slight deviation of entering 

 horizontal current, when its dimension is compared to the area from which 

 this current is derived ; and there is really but the slightest cause for the 

 currents to direct themselves to the exact centre of the orifice. In point 

 of fact the permanency of the vena contracta of downward discharge is 

 derived in great degree from the pressure of the atmosphere, which is 

 brought into action, by the descending pencil below it. The eftect of a 

 tangential afflux at the peripheral circle C A is to give a rotation to the 

 pencil, which at once accelerates, to some limit of discharge, and obliterates 

 the vena contracta The motion of the particles will yet remain limited 

 in any direction by the head, but as the stream emerges with a rotary mo- 

 tion, the path of any particle becomes a spiral one, and the whole pencil 

 advances, or is discharged, at a slower rate than is due to the particle 

 velocity. In the case of the re-entrant tube, where the pencil is dives* ed 

 from the eftect of gravity, by exhaustion of the air by the effluent stream 

 passing from the tube, it is very difficult to get a vena contracta, as Mr. 

 Froude testifies. This action of the tangential afflux is not confined to the 

 emerging stream, but shows itself in the vessel as well, where a whirl is 

 established which involves the entire mass of water enclosed. In the case 

 where the bottom of the vessel has a funnel shape, this whirl sets up with 

 great vehemence, and the centrifugal force of the established current may 

 be sufficient, under fovorable circumstances of form, head and dimension 

 of vessel, to displace the entire central portion of the liquid, and the i)encil 

 of emergence will become a tube, whose core will be filled by an induced 

 current of air. These phenomena of efflux are only noticed to embrace in 

 ray remarks some of the influences which efffect the vena contracta where 

 the conditions of formation are varied by adjutages, and to make it evi- 



PROC. AMER. PHILOS. SOC. XVI. 98. 3N 



