350, Experiments on. Prussic Acids [Mays 
a] a"*-* Ut, &c, and consequently putting for m,p, m; and for. 
Poa | 
a de ab tT an 8s big ee. = 7/1 (0% 4 Ue ot, 
4a"? lt + &e. F 
but by the binomial theorem for entire numbers, the part. on, the. 
left under the radical sign is = (a@,+_ 1)”, and therefore 
a” + a at" L + i enF b?, &e. = WA (a +b)" = 
(a + b)" 
which is the binomial formula for fractional exponents. As 
(ar + Qf ota ght Gf 4 Bota qeti—3 a) (a” + Yr gr-} ri 
+ 2]r qr? 1?) : 
c= (ahtetr + ot att gh tItr—1 | 4 Yoratr ghtg+r=s I, &e; 
we have, puttingp +9 +r=w,andp+q=w—r7, 
atm HN! et Th bib ear amirtc by &e. = 
ge.) I ae PAI a 9a epee, é 
a+ ina —'b 4+ 2a? 6, &e. 
This equation will be true for any value of r and w, and conse- 
quently also for w = 0, by which we have. 
aa es Ea ee, = 
1 1 ‘ 
ee at ae ae Er) gate (a + by (a 7 d) ~ and 
consequently the truth of the theorem is also proved for any nega- 
tive number. I 
Articie IV. 
Eaperiments on Prussic Acid. By M. Gay-Lussae.t 
(Presented to the Institute, Sept, 18, 1815.) , 
Tue experiments which I have the honour to communicate to 
the Class have for their object the nature of prussic acid and its 
combinations. Few bodies have been more. studied,:and yet few 
are less known. After the labours of Macquer, Scheele, and, Ber; 
thollet, which form an epoch in the history of. prussic, acid, many, 
other distinguished chemists made experiments, upon, it. 1 shall not 
however attempt to write a history of these ; but merely notice the. 
end ¢ ta i. 9 ' F t 3 
principal results which they have furnished, in order to point out the 
place from which I started. 
* The ¢ase for a fractional exponent having already been proved, 
+ Translated from the Ann, de Chigi, yol. xcv, p. 136, “My AE 
