82 
MR. T. E. STANTON ON THE PASSAGE OF HEAT BETWEEN 
tlie equation for the passage of heat will be 
or writino- 
o 
„ P--« B'* 
dx (2r)3-" A '' ° 
W = D»'7rr^ 
- 0 
• • • ( 2 ), 
the slope of temperature along the ]3ipe is given by 
dt 
A 
L» 
p2-K 
(2/-) 
3-n 
10 
(To - 0 
(3). 
This is supposing that the conductivity of the water, as compared with the viscosity, 
does not enter; but as it probably does, for ultimately it Is conductivity by which the 
heat passes from the walls of the pipe to the water, there will probably be a coefficient 
f{c/n 
the form of which can be determined by experiment. 
Application of Professor PvEynolds’ Theory to the Experiments. 
Assuming the variation In the value of t to be small, say, not greater than 6° in the 
whole length of the pipe, then, integrating equation (3), 
where 
To ~ b 
To -h 
r/_ 
1) 
p2-« 
IV" ^ 
= initial temperature of the water in the pipe, 
^2 — final ,, ., ,, ,, 
L = length of the pipe, 
p 2 -/i _ value of P~“", for the water In the pipe. 
(T), 
Now, from equation (4) the value of n can be determined by a set of experiments, 
in which 
p2-« 
has the same value in each. 
This was done by plotting the logarithmic homologues of 
log and 10 , 
when it was found that the points plotted all lay approximately on a straight line, 
there being no systematic deviation. 
