48 
I’P.OfESSOR E. G. COKER AND MR. S. B. CLEMENT ON THE VARIATION 
relation of slope to velocity is a perfectly definite one at a definite temperature for 
the flux, lieing expressed by the equation 
2 = 
If we write v = and -- , - ~ = i, we obtain = — i, and tliis relation between 
Try'- I o/j. 
V and i, plotted logarithmically, is, at a definite tem])erature, a line inclined at 45° to 
the axes. 
Slightly al) 0 ^■e critical velocity, it can be shown experimentally that no definite 
relation exists, bid well above this point, where the motion is perfectly eddying, it 
can be shown experimentally that the relation between v and i is a perfectly definite 
one at a definite temperature, and is exjiressed by some straight line inclined at an 
angle tan“^ n, where n is a constant for any particular pipe. 
It tlierefore appears that the minimum critical velocity is the intersection of the 
t wo branches of the logarithmic honiologue; and throughout this paper this point has 
lieen taken as the critical velocity for the temperature considered. 
As the ex})eriments below the critical velocity require apjiaratus for measuring 
pressures of extreme accuracy and limited range, while above the critical velocity the 
limit of accuracy is relatively less important and the range is large, it simplifies 
matters to take a series of runs at diflerent tenqjeratures below the critical velocity 
without any cliange, and afterwards to take runs above the critical velocity. AVith 
this method tlie variation of temj^eratiire during a single series is small, and the 
correction to a standard temperature is generally negligible. 
Ai^parafus used in the Exp)eriments. 
The experimental tank A, fig. 1, is of cast-iron, 5 feet square in section and about 
30 feet in height, its base resting upon the earth, so that the water in it is not easily 
distur])ed by external causes. It is provided with a steam heater for the inflowing 
* Lamb’s ‘ Ilydrocfynamics,’ p. 5:!]. 
