1890.] 



Analogue of the Wheatstone Bridge, 



463 



the second orifice. If now we have a third closed space, B 2 , likewise 

 provided with two orifices, a 3 , a 4 , one of which, a 4 , communicates 

 with the space A where the constant manometric depression is main- 

 tained, while the other, a 3 , is open to the same supply of fluid as that 

 which feeds a v we get a second flow, V, which we may speak of as 

 being in multiple arc with the first, and to which the following 

 equations apply : — 



H 3 = R 8 V'2, 



H 3 and H 4 are the partial heads for the second flow, and R 3 , R 4 the 

 constants for the orifices a 3 , a± respectively. 



We have, therefore, an arrangement for the flow of fluid analogous 

 to the arrangement of the Wheatstone quadrilateral for the flow 

 of electricity, the galvanometer circuit being supposed open. The 

 head jj corresponds to the electromotive force of the battery, V 2 and 

 V' 2 , correspond to the electric currents in the two branches ; 



R 2 , R/ 3 , R 4 , to the four electrical resistances ; the spaces A, B x , B 2 , 

 take the places of the brass connecting blocks of a Post Office box or 

 the copper connexion pieces of a metre bridge. The partial heads, 

 H l5 H. 2 , H 3 , H 4 , correspond to the electromotive forces between the 

 ends of the four several wires. Making contact with a key in the 

 galvanometer circuit would correspond to opening a tube of commu- 

 nication between the spaces B l5 B 2 , above mentioned, and the hydro- 

 dynamic condition corresponding to no current through the galvano- 

 meter would evidently be the condition of no flow of fluid through 

 the tube, and the galvanometer must be represented by some appa- 

 ratus for detecting a flow of fluid ; the detector need not, however, be 

 designed to measure a flow any more than the galvanometer need be 

 suitable for measuring a current. The condition for no flow in the 

 " galvanometer " tube is that there should be no head between its 

 ends ; this condition is satisfied if H x = H 3 or H 2 = H 4 ; from which 

 it follows that the condition is entirely independent of the total head, 

 Ij, and depends only on the constants of the four orifices ; we have, in 

 fact, the ordinary Wheatstone-bridge relation : — 



Ri _ Rs 

 R 2 R 4 



If the coefficients of contraction may be assumed to be independent 

 of the shape of the orifice, we get the condition for no flow through 

 the " galvanometer " tube : — 



_ H 



a 2 a 4 



