METAL SURFACES AND LIQUIDS IN CONTACT WITH THEM. 
81 
water, without reference to the theory, and which expression lias been shown to be 
of the form given in equation (1). 
The Author is indebted to Professor Osborne Eeynolds, who kindly offered to look 
through the paper before joublication, for the following theory of the subject. 
The outline of this theory, as has been previously stated, was published in 1874.* 
The discovery of the law of resistance in parallel channels, made b}^ Professor 
Eeynolds, in 1883,t enables this theory to be definitel}" stated. 
According to this theory, the motion of heat from the surface of the pipe follows 
the same laws as the motion of momentum to the surface, whether by conduction or 
convection (though not by radiation and absorption, through the material, which 
unquestionably plays an important part in the so-called conduction of water). 
Taking x as the direction of motion. 
r = radius of pipe, 
t = temperature of the water, 
Tq = temperature of surface of pipe, 
D = weight of unit volume of water, 
j) — pressure of water per unit area, 
W = weight of water discharged per second, 
?(; = velocity of the water flowing through the pipe, 
P = (1 -f -0336^ -f -000221^)-^ 
A, B, and n constants depending on the nature of the surface. 
Then, above the critical velocity, the loss of pressure is given by the equation 
Writing this in the form 
dp r,» 
dx • A ■ + 
,3 JL 
w’‘ ^ 
IP 
A ■ 
(1), 
then, in (1), Trr'^idpldx) is the loss of momentum due to diffusion and convection, so 
that, according to the above theory, substituting 
and 
for TTl 
0 dp 
► iV 
dx ’ 
W (Tq — t) for — IV , 
* ‘ Proc. Mancliester Lit. aud Phil. Society,’ 1874, p. 8. 
t ‘Phil. Trans.,’ 1883, p. 976. 
: ‘ Phil. Trans.,’ 1883, p. 976. 
VOL. CXC.-A. 
M 
