37 
40-43] Effective Temperature 
from the star be 1/m times that received from the sun. Then each square 
centimetre of the star’s surface must emit H 2 /ra times as much radiation as a 
square centimetre of the sun’s surface, and hence 
effective temperature of star = n^m - ^ x 5750 degrees abs. 
Of recent years the angular diameters of a number of stars have been 
measured by means of an interferometer attached to the 100-inch telescope 
at Mount Wilson, and the measurements so obtained have made it possible to 
calculate directly the effective temperatures of the stars in question (cf. §§ 54 
and 55 below). 
The Pressure of Radiation. 
42 . Maxwell shewed on theoretical grounds that radiation must carry 
momentum as well as energy with it, and it will subsequently be found (see 
Chap, x) that this transport of momentum by radiation plays a fundamental 
part in the dynamics of stellar structures. As a consequence of its carrying 
momentum, radiation must exert a pressure on any material surface it en 
counters. Maxwell proved that a beam of radiation, all travelling in the same 
direction, would exert a pressure in the direction of its motion equal to its 
energy per unit volume*. For radiation in thermodynamical equilibrium with 
matter at temperature T this is equal to aT 4 . The existence of this pressure 
was confirmed experimentally by Lebedewf and by Nichols and HullJ. 
In the interior of a body which is at a uniform temperature T, radiation in 
thermodynamical equilibrium with the matter travels equally in all directions. 
After allowing for the different directions of travel, the pressure of radiation 
in any direction whatever is found to be p R given by 
P»-\*T* (421). 
Great caution is necessary in applying this formula to astronomical 
problems, since the interiors of astronomical bodies are not at uniform 
temperatures, with the result that stellar radiation is not generally in perfect 
thermodynamical equilibrium with matter (cf. § 73 below). 
The Partition of Radiant Energy. 
43 . The partition of energy by wave-length which is expressed by formula 
(40-3) is exhibited graphically in fig. 3, in which X is taken as abscissa and 
E K as ordinate. It might at first be thought that there would be a whole 
series of different curves corresponding to different values of the temperature 
T. But on drawing the curves it is found that differences of temperature are 
represented merely by differences in the horizontal and vertical scales on 
which the curve is drawn; this property follows from the circumstance that 
the law of partition of energy is of the general type given by formula (40 2). 
* Treatise on Electricity and Magnetism (1873), § 792. 
t Annalen der Physik, vi. (1901), p. 433. 
X Physical Review, xm. (1901), p. 307.