RADIATION AND ABSORPTION. 87 
face as the centre of a hemisphere whose radius is equal to unity, 
and if we call e the total quantity of heat emitted by this element 
in all directions, the quantity of heat emitted on a single element 
of the hemisphere, which is at an angular distance w from the 
normal, is expressed by ‘ 
— COS w, 
Tw 
and is consequently proportional to the cosinus of the angle of 
emission, this angle being reckoned to begin from the normal. 
It is easy, starting from this value, to re-ascend by integration 
to the primitive expression eé sin? w. 
This demonstration is perhaps more elementary than that 
which has been given by M. Fourier* ; it does not suppose any 
consideration relative to the temperature, and applies conse- 
quently to all temperatures; it is deduced from a single condi- 
tion, which is, that we have 4 = sin? w, and, as the quantity of 
heat which the globe receives from the inclosure is independent 
of the heating or the cooling of the globe itself, we see that it is 
not less strict for the case of heating or cooling than for the case 
of equilibrium. 
Constant of Emission.—After having found the relation 
a, 
ma + constant, 
MM. Dulong and Petit remark (page 74) that it represents the 
total radiation of the inclosure, and that, the origin of the tem- 
peratures being arbitrary, we may assume it so that the constant 
may be null, which would reduce the expression to m a’. 
But there remains some difficulty upon this point; for, in 
choosing the 0 of the thermometric scale so that § may be equal 
to — o, the first term is null, and the constant remains, so that it 
could only disappear by admitting that it must have a negative 
value: moreover, the value of m necessarily changes with the 
origin of the temperatures; it diminishes in proportion as the 
origin descends and as the temperatures are represented by 
greater numbers, and reciprocally; in short, the value of m is 
such, that the total radiation of the inclosure appears expressed. 
rather by a temperature than by a quantity of heat, and never- 
theless it is difficult to conceive how the total radiation of the 
inclosure can be expressed by a temperature or by a number of 
degrees lost or gained. 
On another side, M. Poisson}, on comparing the functions to 
which he has arrived and those of the law of cooling of MM. 
Dulong and Petit, preserves the constants in the first functions, 
and suppresses them in those of the law of cooling, which re- 
* Annales de Chimie et de Physique, tom. iv. p. 135. 
+ Théorie de la Chaleur, p. 42. 
