Eriggs.] Oi-i [Nov. 3, 



orifice in a thin plate, from a conical adjutage either protruding or re- 

 entrant, has a section, where the stream flows out in sensibly parallel lines, 

 of more than half the area of the orifice, and that this condition only 

 ceases for a re-entrant nozzle, in the form of a parallel tube as treated of in 

 Mr. Froude's paper. The conclusions of Professer Thomson do not seem 

 to the writer as warranted by the conditions to which he limits liis propo- 

 sition. The value of the assumed force which he denotes hy P is by no 

 means satisfactorily exhibited. As the purpose of this paper is to discuss 

 other points, further notice of Professor Thomson's article may be omitted, 

 only it will be assumed that the reader of this refers to the Glasgow So- 

 ciety's proceedings to see for himself what is set forth by the Professor. 



The fourth paper is an abstract of remarks by R. D. Napier, Esq., who 

 gave some consideration of this subject, which was published in 1866, in a 

 pamphlet " On the Velocity of Steam, ^c," in which he made the general 

 assertion, with some qualifications, that the area of the true theoretical vena 

 contracta is half that of the orifice. He says, "I have proved in the 

 pamphlet referred to, that the pressure in the plane of the orifice is nearly 

 half the pressure due to the head, and that from thence to the vena con- 

 tracta [the words are here used in the sense of the section of least area] it 

 gradually diminishes to zero. This diminishing pressure causes increasing 

 velocity, and is thus the direct cause of the vena contracta. * * * 

 "About three-eighths of the ultimate velocity and five eighths of the 

 vis viva is imparted to the water outside of the plane of the orifice, and it 

 is absurd to attribute these eflFects either to what I maj' call the converging 

 momentum being transferred from one side of the orifice to the other, or 

 to the converging particles preventing the free egress of the stream through 

 the orifice, which are the only views hitherto offered to explain the cause 

 of the vena contracta." 



This question of the vena contracta is a very pretty one in physics, and 

 deserves a more c >mplcte and general discussion than it receives in the 

 pages of the Glasgow Society. It should be recognized however, that it 

 does not admit of the simplicity of investigation, either mathematically or 

 experimentally, which the papers of Mr. Froude and Professor Thomson 

 assume. It is impossible to divest the consideration from the fluid friction 

 against the contiguous sides, surfaces, or the edges of the aperture, nor 

 from the fluid friction of the liquid within itself which constitutes viscosity; 

 nor yet further, from the frictional resistance to discharge into another 

 medium (the atmosphere in this case); while the absolute strength of 

 water is brought into action in the emerging column to the extent of pres- 

 . sure of the atmosphere. Values for these various elements can be accepted, 

 and the mathematical investigation proceeding from them, would enable 

 a thorough solution of the problem, in place of the extremely partial one 

 essayed in the proceedings of the Glasgow Philo. Soc. Even the eftVct of 

 dimension of vessel or volume of water with relation to the aperture 

 might be made a part of the investigation and appear in the result. 

 In such an attempt to find a general solution of the theorem it would at 



