138 
SOLUTION OF THE EQUATIONS 
Heat Radiation and Luminosity. 
101. It is now practicable to measure the heat received from a star 
by the use of a radiometer. Considerable sensitiveness in the method has 
been developed*. But the results attained are as yet very limited and in 
general we have to infer the total amount of heat emitted from the light 
emittedf. This involves a knowledge of the luminous efficiency of the 
energy emitted by stars of different types. 
If the star is radiating as a black body of temperature T e we know by 
Planck’s Law the amount of radiation 1' (A, T e ) dX of wave-length A to 
A + dX. Measurements have been made in the laboratory of the quantity 
of energy of different wave-lengths necessary to give the same amount of 
light as judged by eye; hence we know the factor p (A) by which the energy 
must be multiplied in order to give luminous intensity. The average 
factor for the whole radiation is then 
p = \p (A) 1' (A, T e ) dX h- \r (A, T e )dX (10M). 
The maximum of p is found to occur at about T e = 6500° so that stars 
of types F to G have the greatest luminous efficiency. Presumably that 
is because our visual sense has been developed with special reference to 
sunlight. It is convenient to take the maximum as standard, and to define 
the scale of bolometric magnitude so as to agree with visual magnitude 
at this effective temperature. At any other temperature p will be smaller 
and the star will be brighter bolometrically than visually. 
Table 15. 
Reduction of Bolometric to Visual Magnitude. 
T e 
V 
Am (Vis.-Bol.) 
2540 
•092 
m 
+ 2-59 
3000 
•206 
+ 1-71 
3600 
•417 
+ 0-95 
4500 
•723 
+ 0-35 
6000 
1-000 
0-00 
7500 
•985 
+ 0-02 
9000 
•893 
+ 0-12 
10500 
•749 
+ 0-31 
12000 
•616 
+ 0-53 
* It is said that the equipment at Mount Wilson could detect the heat of a 
candle on the banks of the Mississippi. 
f The deduction of bolometric magnitude from heat measurement is not really 
more direct than from light measurement, because large corrections must be applied 
on account of atmospheric absorption in the infra-red, and this involves assuming 
a spectral energy distribution just as the reduction of light measurements does.