108 M. Maurice's Abstract of Fourier's Demonstration 



4> 7T r 9 . b h. We shall then have, for unity of time, the equation 



4- 7r r 9 . b h = 2 it r- . a h 



'fd<p. cos <p.f(<p) 9 

 or, simplifying, 



But if the intensity of the rays does not vary with their in- 

 clination, we shall have t /(<f>) = 1, and taking the integral be- 

 tween the proper limits, b = ^ a ; so that the central molecule 

 could only acquire a temperature equal to half that of the 

 spherical inclosure ! — a result which is absurd, being con- 

 stantly contradicted by experience. If on the contrary we 

 make f(§) — sin <p, we find rigorously b = a; that is, that 

 the final temperature of the molecule is equal to that of the 

 inclosure, — agreeably to experiment. 



8. It is easy to explain the rather singular result at which 

 we have just arrived; namely, that if the intensity of the rays 

 of heat emitted were independent of the angle of emission, the 

 central molecule would only acquire half the temperature of 

 the inclosure in which it is placed, even after an indefinite 

 time. For whilst the inclosure from its spherical form can 

 only transmit to the central molecule such rays as are normal 

 to its own surface, its calorific energy being thus independent 

 of the angle of emission of the other rays, the molecule itself 

 dissipates heat in all directions, and (according to the hy- 

 pothesis) with equal intensity; it is evident (see art. 5.), from 

 the equation h = g, which is then applicable, that it will lose 

 in unity of time twice the quantity of heat which it receives ; 

 its temperature therefore will only be half that of the inclo- 

 sure*. 



9. We shall next proceed to show the necessity of the ma- 

 thematical law of radiation by proving that its existence is 

 essential, in order to account for the uniformity of tempera- 

 ture pervading a space of which the limits are kept during a 

 sufficient time at a constant temperature, — a fact which experi- 

 ence demonstrates. 



1 0. Let us consider in the interior of the bounding sides 



* These facts tend also to establish the rigorous connexion betweeu 

 the absorptive and emissive powers of bodies for radiant heat. If in the ex- 

 periment above described, the central molecule had one of these properties 

 in the slightest degree in excess over the other, it might acquire an infi- 

 nitely high or an infinitely low temperature. Thus by these elementary 

 views the necessity of these two fundamental laws discovered experimen- 

 tally by Professor Leslie is illustrated. — Tuanslator. 



