Page:Scientific Memoirs, Vol. 1 (1837).djvu/55

A similar construction will give the curves $a''b''c''d''e''f''g''$, $a'''b'''c'''d'''e'''g'''$, $a^{IV}b^{IV}$, representing the decreasing intensities of the three other radiations.

Let us now suppose the screen cut by any plane ($PP'$) parallel to $ON$; the emergent rays of the detached plate will be determined by the points at which the plane intersects the curves; so that $PP'$, $PP''$, $PP'''$ will represent the quantities of heat that issue from the plate $OP$ when exposed to the first three sources; for the rays of the fourth are completely extinguished at the distance of one millimetre. We now see that the ratios of the distance from those points of intersection to the axis $OM$ decrease in proportion as the thickness of the interposed layer is less. The distances from those points to the axis are pretty nearly equal when the section coincides with the ordinate $aa'$ at which the observations commence; they will become yet more so in the interior of the first layer $Oa$, so that within a limit very close to the surface at which the rays enter the differences will almost vanish^[1].

The first infinitely thin plate will therefore transmit sensibly equal quantities of radiant heat from the four sources. The diminutions however which the rays from each source will suffer in the interior of this elementary plate, though so exceedingly small that they may be disregarded in reference to the quantities transmitted, must nevertheless bear very different ratios to one another; for it is to such diminutions, several times repeated by the action of the successive layers, that we are to attribute the remarkable differences in the quantities of heat transmitted from each source by a screen of a given thickness.

The law of Delaroche did not show whether the variable interception

1.  I have been unable to procure plates of glass thinner than ${\frac {7}{100}}$ of a millimetre. But we shall see presently that all other diaphanous substances, whether natural or artificial, are in their effects more or less analogous to glass. Now there are several crystals which spontaneously separate into plates of great tenuity, and are, consequently, well calculated to show that the ratios of the quantities of heat transmitted by a screen exposed to the radiations of the four sources approximate to equality in proportion as the thickness of the screen is reduced. Thus a plate of sulphate of lime 2^mm·6 in thickness gave for the four transmissions respectively,

   14,5,0,0.

   These transmissions became

   38,18,7,0

   when the thickness was reduced to 0^mm·4; and

   64, 51, 32, 21

   when the thickness was reduced 0^mm·01.

   A plate of mica, 0^mm·02 thick, gave for the four transmissions

   80, 76, 39, 26.

   
   

   An extremely thin flake was taken from this plate (which was however not coloured): the four transmissions through this flake were,

   86, 85, 61, 46.