TO CALCULATE THE LOSSES.

The requisite data are furnished by the experiments conducted some years
since by President D.M. Greene, of Troy College, for the Bureau of Steam
Engineering, U.S. Navy.

According to these experiments, the heat which is lost per hour by
radiation through a metallic plate of ordinary thickness, exposed to dry
air upon one side and to the source of heat upon the other, for one
degree difference in temperature, is as follows:

Condition. Heat units.

Naked...................................... 2.9330672
Covered with hair felt, 0.25 inch thick.... 1.0540710
" " 0.50 " .... 0.5728647
" " 0.75 " .... 0.4124625
" " 1.00 " .... 0.3070554
" " 1.25 " .... 0.2746387
" " 1.50 " .... 0.2507097

If now t' = temperature of steam at the ordinate,
t = temperature of the surrounding atmosphere,
dS = surface of the cylinder included between each ordinate,
k = that figure from the table satisfying the conditions,
then the power loss (dR) per minute will be:

k (t'-t)dS
dR = ( -- ) ----------. (2)
60 33,000

To the same scale as the power gains, upon each ordinate, set off the
appropriate power loss, as calculated by this equation (2).

There will result the curve r, r, r, which determines the power which at
any point in the diagram is to be regarded as a loss, to be carried to
the debit side of the account. This curve of losses intersects the curve
of gains at a point (it is evident) where each equals the other.

Therefore this is the point at which expansion should cease, and this
absolute pressure is the economic terminal pressure, which determines the
number of expansions profitable under the given conditions.

In the foregoing example are taken k = 0.3070554, t' = 331.169, t = 60,
while the back pressure was taken at 7 pounds.

By way of further illustration, first let the back pressure be changed
from 7 to 5.

By equation 1 there will result a new curve of gains, W, W, W, a portion
only being plotted.

Second, let t' = 331.169 as before.
t = 150 instead of 60.
k = 0.2507097 instead of 0.3070554.

There will result the second curve of losses, R, R, R, intersecting the
second curve of gains at the point F, the new economic point for our new
co