6 M. MELLONI ON THE FREE TRANSMISSION 
If between the flame of a candle and the eye we interpose a plate of 
glass or any other substance more or less transparent, we find the di- 
minution of the intensity of the light always the same, however the di- 
stance between the plate and the candle may vary. The effect produced 
by distance on the freely transmitted caloric is exactly similar; and if 
at a certain distance from the active source there be a thermoscopic 
apparatus sensible to this portion of heat, the apparatus will always give 
the same indication, whether the screen be laid close to the source or 
to the thermoscope. 
But it is clear that it must happen quite otherwise to the conductible 
caloric ; for this portion of the heat, when it has reached the further sur- 
face of the screen, leaves it in the form of diverging rays which become 
weaker in proportion to the distance. In other words, the further sur- 
face of the screen being heated becomes a new calorific source whose 
intensity of radiation must decrease as the distance increases. 
We possess, therefore, a very simple contrivance for destroying the 
influence of conduction, if we keep the action of the free radiation in- 
tact. This contrivance consists in removing the screen so far from the 
thermoscope that the radiation of its own heat may, on account of its 
extreme feebleness, be totally disregarded. 
There are, however, some precautions to be taken; for in proportion 
as the distance between the screen and the thermoscope is increased, 
the distance between the source and the screen is diminished. The 
latter is therefore more heated, and radiates with greater force upon 
the instrument. It is easy to show by calculation that we always gain; 
that is, that we always weaken the conductible caloric more and more 
by removing the screen from the thermoscope, until we have placed it 
midway between the thermoscope and the source*. Let us, therefore, 
put the screen in this position (which is the most favourable of all), and 
we shall see that its heat has then no appretiable influence on the re- 
* Let a be the distance from the source to the thermoscope, x the distance 
from the thermoscope to the screen, 7 the calorific intensity of the source, we 
shall have G@=ay38 the expression for the radiation which strikes the anterior 
ci 
surface of the screen. This quantity will become (aa) at the further sur- 
face, c being a constant quantity depending on the conducting power of the 
matter of the screen. In fine, the radiation of the further surface on the ther- 
moscope will be expressed by Fae its minimum (y) is to be determined. 
: ine . dy __ 2ci(2x—a : es 
Now, by differentiating we obtain <2 = yh ; the equation which gives 
. . 1 a 
the quantity will then be 22—a=o0, whence a= g. 
