582 PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



points, denoted by n. If the copiousness of the emission of light from every phy- 

 sical point of the luminous surface were equal, it might in general be denoted by c; 

 but, as that is most probably never the case, I make c stand for the mean copious- 

 ness of light thrown out from all the physical points of a luminous object. This 

 may be found in the following manner. Let c express the copiousness of emitting 

 light, of any number of physical points that agree in this respect; and let the 

 number of these points be n. Let the copiousness of emission of another number 

 of points be c, and their number n'. And if, in the same manner, other degrees 

 of copiousness be called c 1 , c 3 , &c. and their numbers be denoted by n 2 , n 3 , &c. 

 then will the sum of every set of points, multiplied by their respective copious- 

 ness of emitting light, give us the quantity of light thrown out by the whole 

 luminous body. That is, l = cn -f- cV + cV, &c; and the mean copiousness 

 of emitting light, of each physical point, will be expressed by cn + cn + c n > &c » 



= c. It is evident that the mean power, or copiousness of throwing out light, of 

 every physical point in the luminous surface, multiplied by the number of points, 

 must give us the whole power of throwing out light, of the luminous body. That 



is CN = L. 



I ought now to answer an objection that may be made to this theory. Light, as 

 has been stated, is transparent ; and, since the light of a point behind the surface 

 of a flame will pass through the surface, ought we not to take in its depth, as well 

 as its superficial dimensions? In answer to this, I recur to what has been said with 

 regard to the different powers of throwing out light, of the points of a luminous 

 surface. For, as light must be finally emitted through the surface, it is but re- 

 ferring all light arising from the emission of points behind the surface, to the 

 surface itself, and the account of emitted light will be equally true. And this will 

 also explain why it has been stated as probable, that different parts of the same 

 luminous surface may throw out different quantities of light. Since therefore the 

 quantity of light thrown out by any luminous body is truly represented by cn, and 

 that an object is bright in consequence of light thrown out, we may say that bright- 

 ness is truly defined by cn. If however there should at any time be occasion for 

 distinction, the brightness arising from the great value of c, may be called the in- 

 trinsic brightness; and that arising from the great value of n, the aggregate bright- 

 ness; but the absolute brightness, in all cases, will still be defined by cn. 



Hitherto we have only considered luminous objects, and their condition with 

 regard to throwing out light. We proceed now to find an expression for their ap- 

 pearance at any assigned distance; and here it will be proper to leave out of the 

 account, every part of cn which is not applied for the purpose of vision, l re- 

 presenting the whole quantity of light thrown out by cn, we shall denote that part 

 of it which is used in vision, either by the eye or by the telescope, by /. This will 

 render the conclusions that may be drawn hereafter more unexceptionable; for, the 

 quantity of light / being scattered over a small space in proportion to l, it may 

 reasonably be considered as more uniform in its texture; and no scruples about its 



