OF RADIANT HKAT THROUGH DIFFERENT BODIES. 43 



A similar construction will give the curves a''b"c" d" e"f" g", a"'b"' 

 c"'(l"'e"'/"'g"', a^^ 6'^, 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,'" >vill re- 

 present 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 ex- 

 tinguished at the distance of one millimetre. We now see that the ra- 

 tios of the distance from those points of intersection to the axis O M 

 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 a a' at which the observations 

 commence ; they will become yet more so in the interior of the first layer 

 O a, so that within a limit very close to the surface at which the rays 

 enter the differences will almost vanish*. 



The first infinitely thin plate will tlierefore transmit sensibly equal 

 quantities of radiant heat from the four sources. The diminutions how- 

 ever which the rays from each source will suffer in the interior of this 

 elementary plate, though so exceedingly small that they may be disre- 

 garded 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 



* I have been unable to procure plates of glass thinner than -rfri) of a milli- 

 metre. But we shall see presently that all other diaphanous substances, whether 

 natural or artificial, are in tlieir effects more or less analogous to glass. Now 

 there are several crystals which spontaneously sepai-ate into plates of great te- 

 nuity, and are, consequently, well calculated to show that the ratios of the quan- 

 tities 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™™-6 in thickness gave for the four transmis- 

 sions respectively, 



H, 5, 0, 0. 

 These transmissions became 



38, 18, 7, 

 when the thickness was reduced to 0'"'"*4 ; and 



64, 51, 32, 21 

 when the thickness was reduced 0"""-0I. 



A plate of mica, 0"""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. 



