100 Prof. Draper on the Productio7i of Light 



seeking the development, to take the more general form a"'^'', 

 log {x + h), &c., and to proceed as above, afterwards making 

 A = 0; for we shall thus always be Jed to true developments, 

 and thence to the cases in which the sought developments are 

 impossible, these being indicated by the hypothesis of // = 

 causing the coefficients to become infinite. And it is obvious, 

 from the method above described, that the coefficients of the 

 development of ¥{x-\-h) are just as readily obtained as those 

 derived from F(,r) in the usual way. 



In thus recommending that x be replaced by x-\-h, when 

 the development of F(t) is required in powers oi x, it will be 

 observed, from what is said above, that it is merely proposed 

 to deduce D,,, Dj, D,,, &c. from F [h). If these are infinite 

 when h=.0, the inference will be, that, isoithjimte coefficients^ 

 the development is impossible. Butif we leave h undetermined, 

 and put, in the series, x — h for x, we shall then get the deve- 

 lopment of F(.x-), with finite coefficients, in powers of x — h; 

 and as h is arbitrary, we may thus approach as near to the 

 proposed development as we please. And although for the 

 purposes of actual numerical computation, the coefficients 

 would become more and more unmanageable, from their in- 

 creasing magnitude, as h approaches to zero, yet even in this 

 extreme case — in which the coefficients actually become infi- 

 nite — the development, regarded as the last of the series of 

 developments here spoken of, will still be analytically true. 



Belfast, Jan. 5, 1848. 



XVI. On the Production of Light hij Chemical Action. By 

 John Willi.\m Draper, M.Z),, Professor of Chemistry in 



the University of New Yor-Jc"^. 



'X'HE production of light and heat by the combustion of 

 ■*- various bodies is, of all chemical processes, that which 

 ministers most to the comfort and well-being of man. By it 

 the rigour of winter is moderated, and night made almost as 

 available for our purposes as the day. 



One would suppose that, of a phasnomenon on which so 

 much of our personal and social happiness depends, and whicii 

 must have been daily witnessed by every man that has ever 

 lived, all the particulars ought to have been long ago known. 

 Among scientific men its importance has been universally re- 

 cognized. The early theories of chemistry, such as those of 

 Stahl and Lavoisier, are essentially theories of combustion. 



It is nevertheless remarkable how little positive knowledge 

 we still possess on tliis subject. Some chemists believe that 

 • Communicated by the Author. 



