68 
MR. T. E. STAXTON ON THE PASSAGE OE HEAT BETWEEN 
formation of a film, the rapidity of the agitation of the water by the stirrer had a 
maiked effect on the amount of heat transmitted. This fact has been often observed 
in experiments on steam boilers, in which the rate of evaporation has been shown 
to depend upon the rapidity of the convection of the water in the boiler. 
Hence, in order to determine the rate of transmission for the case of the ordinary 
heating surfaces of boilers, it would be necessary to first determine the rate of convec¬ 
tion of the water to and from the surface. The difficulty of measuring the convection 
in sucli a case is very great, and seemed an effectual bar to all experiment. 
A means, however, of measuring the rate of convection appeared in the case of 
water flowing through metal pipes, at fairly high velocities, which could be 
determined, and it is to this case that the experiments described are confined. 
Ihe theory of the transfer of heat under these conditions has been stated by 
Professor Osborne Eeynolds.=^ According to this theory, the heat carried off by 
any fluid from a surface is proportional to the internal diffusion of the fluid at or 
neai the surface, that is, for a given difference of temperature between the fluid and 
the surface. 
Piofessor Ixeynolds further points out that the rate of this diffusion will depend on— 
(1.) The natural internal diffusion of the fluid when at rest. 
(-2.) The eddies caused by visible motion which mix the fluid up and continually 
biing flesh particles into contact with the surface, and that the combined effect of 
these two causes may be expressed as follows :— 
fl — A.t -p iipvt .(l)) 
where t is the difference of temperature between the surface and the fluid, p is the 
density of the fluid, v its velocity, and A and B constants depending on the nature 
of the fluid ; If being the heat transmitted per unit of surface in unit time. In the 
same paper experiments were described giving evidence in favour of the truth of the 
above theory. 
Ihe chief difficulty in any experimental determination of the rate of transmission 
in metal pipes, lies in the fact that the tenijierature of the surface of the pipe varies 
from point to point along the pipe, and again tends to adjust itself by lateral con¬ 
duction along the pipe. Hence, in order that any definite results may be obtained, it 
IS necessary that the temperature of the pipe shall be constant throughout its length. 
It occiiiied to the author that this result might be obtained in the following way :_ 
In fig. 1, AB represents a tube placed vertically, and surrounded by a second 
tube CD, the annular space between them being used as a water-jacket. Now, if hot 
water at a temperature Tj initially, flow down the water-jacket, and cold water, at 
a temperature p flow down the pipe, then heat will be transmitted through the 
* ‘ Proceedings, Manchester Lit. and Phil. Soe.,’ 1874, p. D. 
