ditive
constant, which in his paper he assumed as negligible, is given a
value.[83]

Experimental determinations have been made during the last few years of
the heat transfer rate in cylindrical tubes at comparatively low
temperatures and small temperature differences. The results at different
velocities have been plotted and an empirical formula determined
expressing the transfer rate with the velocity as a factor. The exponent
of the power of the velocity appearing in the formula, according to
Reynolds, would be unity. The most probable value, however, deduced from
most of the experiments makes it less than unity. After considering
experiments of his own, as well as experiments of others, Dr. Wilhelm
Nusselt[84] concludes that the evidence supports the following formulae:

_ _
[lambda]_{w} | w c_{p} [delta] |
a = b ------------ | --------------- |^{u}
d^{1-u} |_ [lambda] _|

Where a is the transfer rate in calories per hour per square meter
of surface per degree centigrade difference in temperature,
u is a physical constant equal to .786 from Dr. Nusselt's
experiments,
b is a constant which, for the units given below, is 15.90,
w is the mean velocity of the gas in meters per second,
c_{p} is the specific heat of the gas at its mean temperature
and pressure in calories per kilogram,
[delta] is the density in kilograms per cubic meter,
[lambda] is the conductivity at the mean temperature and pressure in
calories per hour per square meter per degree centigrade
temperature drop per meter,
[lambda]_{w} is the conductivity of the steam at the temperature of the
tube wall,
d is the diameter of the tube in meters.

If the unit of time for the velocity is made the hour, and in the place
of the product of the velocity and density is written its equivalent,
the weight of gas flowing per hour divided by the area of the tube, this
equation becomes:

_ _
[lambda]_{w} | Wc_{p} |
a = .0255 ------------ | --------- |^{.786}
d^{.214} |_ A[lambda] _|

where the quantities are in the units mentioned, or, since the constants
are absolute constants, in English units,

a is the transfer rate in B. t. u. per hour per square foot