SECT. II.] GENERAL NOTIONS. 35 



an oblique direction, and the most oblique rays are wholly inter 

 cepted. 



The same consequences apply to all the points which are near 

 enough to the surface to take part in the emission of heat, from 

 which it necessarily follows that the whole quantity of heat which 

 escapes from the surface in the normal direction is very much 

 greater than that whose direction is oblique. We have submitted 

 this question to calculation, and our analysis proves that the in 

 tensity of the ray is proportional to the sine of the angle which 

 the ray makes with the element of surface. Experiments had 

 already indicated a similar result. 



47. This theorem expresses a general law which has a neces 

 sary connection with the equilibrium and mode of action of heat. 

 If the rays which escape from a heated surface had the same in 

 tensity in all directions, a thermometer placed at one of the points 

 of a space bounded on all sides by an enclosure maintained at a 

 constant temperature would indicate a temperature incomparably 

 greater than -that of the enclosure 1 . Bodies placed within this 

 enclosure would not take a common temperature, as is always 

 noticed; the temperature acquired by them would depend on the 

 place which they occupied, or on their form, or on the forms of 

 neighbouring bodies. 



The same results would be observed, or other effects equally 

 opposed to common experience, if between the rays which escape 

 from the same point any other relations were admitted different 

 from those which we have enunciated. We have recognised this 

 law as the only one compatible with the general fact of the equi 

 librium of radiant heat. 



48. If a space free from air is bounded on all sides by a solid 

 enclosure whose parts are maintained at a common and constant 

 temperature a, and if a thermometer, having the actual tempera 

 ture a, is placed at any point whatever of the space, its temperature 

 will continue without any change. It will receive therefore at 

 each instant from the inner surface of the enclosure as much heat 

 as it gives out to it. This effect of the rays of heat in a given 

 space is, properly speaking, the measure of the temperature : but 



1 See proof by M. Fourier, Ann. d. Cli. et Ph. Ser. 2, iv. p. 128. [A. F.] 



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