PROPORTION OF ilGHT AFFORDED BY CANDLES, Q\ 



given the detail of his experiments, but feems in fome mea- 

 fure to have difcovered this refult by argument, from the fup- 

 pofed nature of the fubjed." * 



In the table in my paper above mentioned, the laft column Obfervations of 

 contains the diftances oi' the candles from the wall, when the cfndlesT'and of 

 fliadou's were equal; and the fourth column contains the the weights con- 

 weights of thofe candles confumed in a given time, and thefe "'"^ * 

 are all the data required for making the calculations, to (how 

 whether my dedu6tion is true or falfe. The mode of calcu- 

 lating feemed to me, at the time I wrote that paper, too eafy 

 to need any illuftration, but as I now (land charged by your 

 correfpondent, of having deduced a general law from doubtful 

 principles, a further explanation becomes neceflary. 



To inveftigate rules for this purpofe, I , Let M reprefent the Invefllgation of 

 mould caiidle, a its diflance from the wall, on which the (ha- ^'^^ ^^^^-^^ ^^ 

 dows were compared, x its quantity of matter confumed in a 

 given time, (t) and Q the quantity of light emitted by M in 

 the fame time : 2. Let wj reprefent any other candle, b its dif- 

 tance from the fame wall, and y its quantity of matter con- 

 fumed, in the time t. 



Then as the intenlities of light are direflly as the fquares of 



the diftances of the two candles from the wall, we have, as 



t* X Q 

 o* : Q : : i* : - — ^ — = the quantity of light, emitted by 



m in the time. 



Then let us fuppofe that the quantities of light are direflly 

 as the quantities of matter confumed in the time t, and we 



have. As x : Q : : 3^ : ■: = the quantity of light 



emitted by m In that time, by hypothefis. 



i* X Q Y X O 



Now, when 5— -^ (Theo. 1 .) is = — ~— -i (Theo. 2.) 



the quantities of light of M and vi are direflly as their quan- 

 tities of matter confumed in any given time. 



By thefe rules, the calculations contained In the following 

 table, were made from the experiments mentioned at the be- 

 ginning of this paper. 



* See Philofophlcal Journal, Vol. V. page 219, 



No. 



