1883.] 



On the Motion of Water, 



99 



the units being metres and degrees Centigrade. It will be observed 

 that this value is much less than the critical velocity at which steady 

 motion broke down. 



17. General Law of Resistance. — The log homologues all consist of 

 two straight branches, the lower branch inclined at 45°, and the upper 

 one at n horizontal to 1 vertical, except for the small distance beyond 

 the critical velocity these branches constitute the curves. These two 

 branches meet in a point o on the curve at a definite distance below 

 the critical pressure, so that, ignoring the small portion of the curve 

 above the point before it again coincides with the upper branch, the 

 logarithmic homologues give for the law of resistance for all pipes and 

 all velocities — 



P 2 V P / ' 



where n has the value unity as long as either member is below unity, 

 and then takes the value of the slope n to 1 for the particular surface 

 of the pipe. 



If the units are metres and degrees Centigrade — 

 A=67,700,000, 

 B=398, 



P=l + 0-0336 T + 0-000221 T 2 . 



This equation then, excluding the region immediately about the 



critical velocity, gives the law of resistance in Poiseuille's tubes, those 



-of the present investigation, and Darcy's, the range of diameters 

 being 



from 0-000013 (Poiseuille, 1843), 



to 0-5 (Darcy, 1857) ; 



and the range of velocities — 



from 0-0026 

 to 7 



This algebraical formula shows that the experiments entirely accord 

 with the theoretical conclusions. The empirical constants are A, B, P, 

 and n; the first three relate solely to the dimensional properties of the 

 fluid which enter into the viscosity, and it seems probable that the last 

 relates to the properties of the surface of the pipe. 



Much of the success of the experiments is due to the care and skill 

 of Mr. Foster of Owens College, who has constructed the apparatus 

 and assisted me in making the experiments. 



The Society then adjourned o^er the Easter Recess to Thursday, 

 April 5 th. 



h 2 



| metres per sec, 1883. 



