278 



Prof. A. Gray on the Steady Flow of 



long) makes it certain that if water be given at rest between 

 two infinite planes both at rest, and if one of the planes 

 be suddenly, or not too gradually, set in motion, and kept 

 moving uniformly, the motion of the water will be at first 

 turbulent, and the ultimate condition of uniform shearing will 

 be approached by gradual redaction and ultimate annulment 

 of the turbulence. I hope to make a communication on this 

 subject to Section A of the British Association in Manchester, 

 and to have it published in the October number of the Philo- 

 sophical Magazine. Corresponding questions must be ex- 

 amined with reference to the corresponding tubular problem, 

 of an infinitely long, straight, solid bar kept moving in water 

 within an infinitely long fixed tube. It is to be hoped that 

 the 1888 Adams Prize will bring out important investiga- 

 tions on this subject. 



[To be continued.] 



XXXV. Note on an Elementary Proof of certain Theorems 

 regarding the Steady Floiv of Elecfricity in a Netivork of 

 Conductors. By Andrew Gray, M.A., F.R.S.E., Pro- 

 fessor of Physics in the University College of North Wales*. 



THE following elementary proof of the principal theorems 

 of a network of conductors may be of interest. It will 

 be necessary to consider first the well known and, for our 

 purpose, typical case of a network of five conductors, shown 

 in the figure. We assume the so-called laws of KirchhofT, 

 namely the principle of continuity applied to the steady flow 

 of electricity in a linear system ; 

 and the theorem (at once deducible 

 from Ohm's law) that in any closed 

 circuit of conductors forming part 

 of a linear system, the sum of the 

 products obtained by multiplying 

 the current in each part taken in 

 order round the circuit by its resist- 

 ance, is equal to the sum of the 

 electromotive forces in the circuit. 

 Let the wire joining A B contain 



Remark thatthis astonishingly great force of a quarter of a pound 

 x lare foot (! !) is the resistance due to uniform laminar flow of water 

 between two parallel planes ^ - of a centimetre (-A^ of a foot!) asunder 



foot, 

 per squar 



two parallel planes ^ of a centimetre ( T6 

 when one of the planes is moving relatively to the other at K)' feet (300 

 centimetres^ per second, if the water be at the temperature 0° Cent., for 

 which the viscosity, calculated from Poiseuille's observations on the flow 

 of water in capillary tubes, is 134x 10~ 5 

 centimetre. 



* Communicated by the Author. 



of a gramme weight per square 



