294 Prof. Daniell 07i the Constant Voltaic Battery. 



10. With respect to the calculation of Q^, Q, , &c. as func- 

 tions of j'j, it may be noted, in conclusion, that, by (15.) and 

 (62.), Q^ is the term independent of 6 in the development of 



2-/1- (« + e^A/^)* (1-/8 e-0A/^)*; {G5.) 



thus Qo = 1, "^ 



Qi = 2-(«-y3), I 



Q2 = 2-2(a2_4«^ + ^2)^ j. . . . (66.) 



Q3=2-3(a3-9«2^ + 9ay82_^), I 

 &c. J 



in which the law of formation is evident. It remains to sub- 

 stitute for a, ^, their values (16.) as functions of 5, and then 

 to eliminate s- by (17); and thus we find, for example, 



Q2=MP-I)(3i^-1); I ,_, 



Q3=l(;^-i)M5p+i); f ^^^'^ 



Q4 = i [p-lf {^5p^~iOp-\Q). J 

 This, then, is at least one way, though perhaps not the 

 easiest, of computing the initial values of the successive dif- 

 ferences of the function P„, that is, the quantities 

 Qo=AoPo=Po, -] 



Q, = A'Po=P,-P„ I . 



Q2= AM^o=P2-2P, + Po, f ^ ^^ 



&c. J 



And we see that it is permitted to express generally those 

 differences, as follows : 



A^Po = / \.-,l{-iy {W [0]--)2 (l+s)'(l-s)*-'-; (69.) 



in which *" = l(l~P) (70.) 



Observatory of Trinity College, Dublin, 

 "Feb. 12, 1842. 



XLIV. On the Constant Voltaic Battery. By J. F. Daniell, 

 For. Sec. R.S., Prof. Chem. in King's College, London ; in a 

 Letter addressed to R. Phillips, Esq., F.R.S., Sfc. 



My dear Sir, 



N the Annates de Chimie et de Physique for December 1841, 

 there is a paper by M. Edmond Becquerel entitled " Sur 

 les piles a Courant Constant," upon which I beg your per- 

 mission to make a iew observations in the Philosophical Maga- 

 zine. The object of the author is thus stated : — 



" A I'epoque actuelle, ou I'on cherche de toutes partes a 

 appliquer les sciences physiques et chimiques, et par conse- 

 quent Taction des forces electriques, aux arts industriels, je 



1 



