the mean temperature of the entire volume of the gas passing such a
section in any given time. Since the velocity of flow will of a
certainty vary across the section, this second mean temperature, which
is one tacitly assumed in most instances, may vary materially from the
first. The two mean temperatures are only approximately equal when the
actual temperature measured across the section is very nearly a
constant. In what follows it will be assumed that the mean temperature
measured in the second way is referred to. In English units the
temperature difference is expressed in Fahrenheit degrees and the
transfer rate in B. t. u.'s per hour per square foot of surface. Pecla,
who seems to have been one of the first to consider this subject
analytically, assumed that the transfer rate was constant and
independent both of the temperature differences and the velocity of the
gas over the surface. Rankine, on the other hand, assumed that the
transfer rate, while independent of the velocity of the gas, was
proportional to the temperature difference, and expressed the total
amount of heat absorbed as proportional to the square of the difference
in temperature. Neither of these assumptions has any warrant in either
theory or experiment and they are only valuable in so far as their use
determine formulae that fit experimental results. Of the two, Rankine's
assumption seems to lead to formulae that more nearly represent actual
conditions. It has been quite fully developed by William Kent in his
"Steam Boiler Economy". Professor Osborne Reynolds, in a short paper
reprinted in Volume I of his "Scientific Papers", suggests that the
transfer rate is proportional to the product of the density and velocity
of the gas and it is to be assumed that he had in mind the mean
velocity, density and temperature over the section of the channel
through which the gas was assumed to flow. Contrary to prevalent
opinion, Professor Reynolds gave neither a valid experimental nor a
theoretical explanation of his formula and the attempts that have been
made since its first publication to establish it on any theoretical
basis can hardly be considered of scientific value. Nevertheless,
Reynolds' suggestion was really the starting point of the scientific
investigation of this subject and while his formula cannot in any sense
be held as completely expressing the facts, it is undoubtedly correct to
a first approximation for small temperature differences if the ad