TRANSACTIONS OF SECTION 4. 441 
which the radiation escapes through a small opening. For this radiation, which 
may be called ‘ black-body radiation,’ the following laws hold good :— 
(1) Je E,d\=aT* (Stefan-Boltzmann) 
0 
5H) a peer dig “ ott (From Wien’s displacement law) 
max. a 2 
(3) Fj-C S—— (Planck) 
a 
Here, T denotes the absolute temperature, E, the energy radiated between the 
wave-lengths \ and A + dd, and a, ©,, C,, C and ¢ are constants. 
On all these equations measurements of temperature can be based, The most 
important from this point of view is the third law (which gives the increase of 
each portion of the radiation with the temperature), especially in the simplified 
form 
(3a) E,=Od-5e = (Wien) 
which is valid for small wave-lengths in the visible region. In this case the eye 
can be employed instead of a bolometer, so that the measurement of temperature 
can be carried out by means of a photometer. If the luminosities E, and E, 
correspond to the radiation E, at the absolute temperatures T, ard T,, we have— 
log E,_¢ a 
E, xT T, 
If the constant c is known one must select an initial temperature, and can 
then determine all other temperatures by a comparison of luminosities with that 
at this standard temperature. For ) one chooses for this purpose a narrow region 
in the red, in order to have sufficient brightness even at low temperatures. 
The accuracy of the constant ¢ depends upon data obtained with the gas 
thermometer at temperatures corresponding to the visible region. The most 
recent measurements which are based on the nitrogen thermometer between 
800° and 1600° C, give for ¢ the value 14,200, which in the visible region is 
independent of the wave-length. 
The accuracy of ¢ may amount to about 1 per cent., so that the temperature 
measurement, if the melting-point of gold (1064°) is taken as the starting-point, 
is accurate to 6° at 1500°, to 16° at 2000°, and to 48° at 3000° C. Every 
spectrophotometer can therefore be employed as a pyrometer. The comparison of 
the radiation to be measured with a constant source of light is effected in a 
known way by the reduction of intensity by means of a polariser or a rotating 
sector. For pyrometric purposes attempts have been made to simplify the 
spectrophotometer. We shall give the following examples. 
The instrument of Wanner is a photometer with polariser which permits obser- 
vations to be made in the spectral region of the red hydrogen line. The comparison 
source of light is a small glow-lamp the brightness of which can be controlied 
from time to time by comparison with an amyl-acetate lamp. The angles which 
are read on the divided circle of the polariser after adjustment has been made 
of the two halves of the field of view to equality of brightness are translated 
into temperatures with the help of a table. 
The pyrometer of Holborn and Kurlbaum employs a variable comparison 
source of light, and this also is a small glow-lamp the brightness of which can 
be adjusted by means of an alteration of current-strength, so that the middle of 
the carbon filament becomes invisible when in front of the glowing surface whose 
light is being determined, The indication of temperature is furnished, therefore, 
by the strength of current through the lamp, which before use is standardised by 
reference to a black body of measurable temperature, 
