METAL SURFACES AND LIQUIDS IN CONTACT WITH THEM. 83 
For the three pipes used in the experiments the slopes of the logarithmic horno- 
logues were found to be :— 
For pipe No. 1, 1'39 centim. diameter; slope = — 0'14, or n = 1'86. 
No. 2, 1-07 „ „ „ = - 0-175, or = 1-825. 
„ No. 3, -736 „ „ „ =—0-170, or 71 = 1-83. 
In pipe No. 1, the velocities of the water had values between 28 7 and 123*2 
centims. per second. 
In pipe No. 3, the velocities of the water had values between 60 and 393-7 centims. 
per second. 
It will be seen that the values of n given above correspond with the values we 
should expect to find for smooth copper pipes from the law of the resistances, the 
value for glass being about 1*73, and for smooth metal rather higher, rising to a 
value of 2 for rough metal surfaces. 
Effect of Viscosity and Conductivity. 
If the conductivity of the water at the bounding surface be neglected, then for 
experiments at constant v^elocity equation (4) gives the value of 
l02 
I’ — /■ 
'■0 ‘'I 
o T — f 
Xa (/a 
p3-re 
constant for different values of t. 
Preferring to the results given in the tables, it is seen that the value of this 
expression rises with the value of the mean temperature (4;) of the water, which 
seems to show that the conductivity of the water at the boundary has an effect. 
It was also seen, in the experiments quoted above, p. 79, that the heat transmitted 
depended on the values of Tq and t, and that this effect would be represented by 
coefficients of the form 
(1 + aTo) and (1 + (3t). 
From experiments at constant values of n> and t„i, the value of a is found to be 
a = -004, 
and that of y8 is 
/3 -01. 
The slope of temperature of the water in the pipe is then given by 
£=rD^»"“^(T„-0(l + »T„)(l + /30 . 
M 2 
(5). 
