f a pyrometer placed in a
furnace are hard to interpret and such temperature measurements can be
of little value. If the furnace gases absorb the radiations from the
fire and from the brickwork of the side walls and in their turn radiate
heat to the boiler surface, it is scientifically correct to assume that
the actual or sensible temperature of the gas would be measured by a
pyrometer and the amount of radiation could be calculated from this
temperature by Stefan's law, which is to the effect that the rate of
radiation is proportional to the fourth power of the absolute
temperature, using the constant with the resulting formula that has been
determined from direct experiment and other phenomena. With this
understanding of the matter, the radiations absorbed by a boiler can be
taken as equal to that absorbed by a flat surface, covering the portion
of the boiler tubes exposed to the furnace and at the temperature of the
tube surface, when completely exposed on one side to the radiations from
an atmosphere at the temperature in the furnace. With this assumption,
if S^{1} is the area of the surface, T the absolute temperature of the
furnace gases, t the absolute temperature of the tube surface of the
boiler, the heat absorbed per hour measured in B. t. u.'s is equal to

_ _
| / T \ / t \ |
1600 | |----|^{4} - |----|^{4}| S^{1}
|_\1000/ \1000/ _|

In using this formula, or in any work connected with heat transfer, the
external temperature of the boiler heating surface can be taken as that
of saturated steam at the pressure under which the boiler is working,
with an almost negligible error, since experiments have shown that with
a surface clean internally, the external surface is only a few degrees
hotter than the water in contact with the inner surface, even at the
highest rates of evaporation. Further than this, it is not conceivable
that in a modern boiler there can be much difference in the temperature
of the boiler in the different parts, or much difference between the
temperature of the water and the temperature of the steam in the drums
which is in contact with it.

If the total evaporation of a boiler measured in B. t. u.'s per hour is
represented by E, the furnace temperature by T_{1}, the temperature of
the gas leaving the boiler by T_{2}, the weight of gas leaving the
furnace and passing through the setting per hour by W, the specific heat
of the gas by C