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Mr. W. N. Shaw. On a Pneumatic [Apr. 24, 



April 24, 1890. 



Sir G. GABRIEL STOKES, Bart., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : — 



I. " On a Pneumatic Analogue of the Wheatstone Bridge." 

 By W. N. Shaw, M.A., Lecturer in Physics in the University 

 of Cambridge. Communicated by Lord Rayleigh, Sec. R.S. 

 Received March 31, 1890. 



When fluid flows steadily through an orifice in a thin plate, the 

 relation between the rate of flow, V, measured in units of volume of 

 fluid per second, and the head H (the work done on unit mass of the 

 fluid during its passage) may be expressed by the equation : — 



H = RV 2 , 



where R is a constant depending upon the area of the orifice, If the 

 head be measured in gravitation units, R is equal to l/2^^ 3 a 2 , where 

 g is the acceleration of gravity, a the area of the orifice, and h the 

 coefficient of contraction of the vein of fluid, a factor which is 

 independent of the rate of flow. 



Let us suppose a current of incompressible fluid to be drawn in suc- 

 cession through two orifices, a v o 2 , arranged one at each end of a 

 closed space, B, so large that there is no appreciable difference of head 

 between different parts of it and that the kinetic energy of the flow 

 through the one orifice does not affect the flow through the other. 

 By the principle of continuity, the flow V will be the same through 

 each of the orifices, and we have for the head H x between the 

 two sides of the orifice of entry, JL l = R,V 2 , and for the head H 2 

 between the two sides of the orifice of exit, H 2 = R 2 V 2 , where R x and 

 R 2 are corresponding constants for the two orifices. From the defini- 

 tion of the term " head," it follows that H 1 + H 2 (=^) is the total head 

 between the outside of the second orifice and the outside of the 

 first. We may therefore regard Hj and H 2 as partial heads which 

 make up the total head Ij. We may suppose that the head Jj is due 

 to a constant manometric depression maintained in a second large 

 closed space, A, communicating with the first space, B 1? by means of 



