TRANSACTIONS OF SECTION A. 44.3 
It is well known that the determination of the exact position of the maximum 
ordinate of a curve is very difficult in practice. It is obvious that the error in 
the dominant wave-length, resulting from a very small error in estimating the 
amount of energy, would be extremely large, owing to the flatness of the top of 
the curve, and the error in the temperature would be correspondingly great. 
II. Law of Monochromatic Radiation. 
Although still almost empirical, exponential laws of the form 
Fy = Ce f, 
which give the value of the intensity of radiation for a given wave-length as a 
function of the absolute temperature T, agree very well with experimental results. 
They are very suitable as a basis for the construction of pyrometers on the 
principle of monochromatic photometry or spectrophotometry, which are well 
known, and of which the optical pyrometer of Chatélier and Wanner and the 
absorption pyrometer of Féry and those of Holborn and Kurlbaum are examples. 
In such apparatus it would appear advisable to obtain photometric balance by 
diminishing the brilliancy of the body under test rather than by increasing the 
brilliancy of the comparison lamp, which may detract from its electrical efficiency 
and subject it to unduly severe treatment. This diminution may be effected by 
a diaphragm (le Chatélier), by absorption (Féry), or by polarisation (Wanner). 
On the other hand the regulation of the brightness of the comparison lamp 
(Holborn-Kurlbaum or Morse) has the advantage of great simplicity of con- 
struction and regulation. We are restricted, however, under these circumstances 
to the measurement of temperatures below 1300° or 1400°, the maximum 
allowable temperature of the lamp filament, 
Iti, A law which is much more rigorously established from the theoretical 
standpoint is that of Stefan-Boltzmann, or the law of the fourth power. It is 
too well known for there to be any necessity to insist either upon its theoretical 
basis or upon its numerous experimental verifications. — 
There are, however, a few considerations which may advantageously be kept 
in view in applying this law to pyrometric measurements. Some concentrating 
device, either lens or mirror, is generally necessary, and I have frequently insisted 
upon the difficulty of finding a transparent substance having no selective absorp- 
tion, %.c., an impartial absorption of radiations of all wave-lengths. Such a 
substance would enable an instrument to be constructed which could be calibrated 
by a single experimental check. 
The same difficulties present themselves when employing a metal reflector to 
concentrate the heat upon a thermo-pile. 
A similar remark must be made concerning the absorbing power of the black 
substance (lamp-black or platinum-black) with which the heated junction is 
covered. It would be an advantage to make this junction concave in order 
more perfectly to realise the theoretical conditions. 
Lastly, if we consider a little more in detail the mode of operation of a thermo- 
junction heated by radiation, we see that temperature equilibrium results when 
the gain of heat by absorption is exactly compensated by the loss (a) by con- 
duction through the wires of the thermo-element, (4) by convection, and (¢) by 
the radiation from the heated junction. 
If we may assume that the loss of heat due to the first two causes is pro- 
portional to the excess of the temperature of the junction over that of its 
enclosure, this is not the case with that due to the third cause, which is pro- 
portional to the difference of the fourth powers of the temperatures in accoidance 
with the law of radiation. 
It therefore results that, if we could obtain in practice a thermometric body 
suspended in an evhausted enclosure by a perfectly heat-insulating thread, the 
rise of temperature would follow a more complex law than that of Stefan as a 
function of the temperature of the radiating source. 
