1815.] On Flusxions. 42} 
monstrates simply and rapidly where some eminent mathematicians 
demonstrate complexly and tediously. 
As fluxions are a part of the theory of rates, I subjoin an alge- 
braical investigation and demonstration of the fluxional problem. 
Definition. 
Fluxions is a method for finding the rate of change in a quantity 
and its function. 
Problem. 
Yo find the fluxion of x”; » being any positive, integral, number ; 
and # or 1 being assumed, as it may be, for the fluxion of a, while 
x varies uniformly. 
a” may be represented thus, x x x X x X x....with x as often 
employed as there are units in m; and if it is only the first x that 
varies, the fluxion must be 1 2*—'%; but if every x varies in suc 
cession, the fluxion must bez 2*~*2. Q.E. I. and D. 
If = 14#=1 x 1 be represented by a square whose side is = 
4, » a" ~* # may be represented by an oblong with | for one of its 
sides, and 7 «*~* for the other ; consequentiy, 
As the square : the oblong :: 1 #: 7 a" "4a. 
If a learner find any difficulty in conceiving that if # vary uni- 
formly, ¢ or 1 is the fluxion of x, he will easily learn that, in 
comparing the rate of variation or change, in an uniform motion 
of 16, feet in a second, with the law of descent of heavy bodies, 
the rates at the end of each successive second are, as 1: 2, as 1: 4, 
as 1: 6, &c., the space gone over by the uniform motion being 
represented by x. > 
If those ancients, such as Archimedes, who understood varying 
quantities, had subjoined the rate of variation, they would have 
taught us fluxions ; but perhaps they had not a proper notation. 
In your 33d number the reader may insert &c. after great, 
p- 179, 1. 25 reduced for referred, p. 179, 1.33; # bemg = 1, 
p. 180, 1. 30, after coefficients; rigour for vigour, p. 181, 1.45 
letter for latter, p. 182, 1. 7 ; and he may efface the words between 
the first rate and of, p. 182, 1. 41. 
Iam, my dear Sir, yours faithfully 
ALEX. CHRISTISON. 
Articte VIII. 
Letter from Wm. Henry, M.D. F.R.S. correcting some defective 
Statements in different Histories of the Introduction of Bleaching 
by Oxymuriatic Acid. 
(To Dr, Thomson.) 
DEAR SIR, Manchester, Oct, 1815. 
The fourth volume of Mr. Parkes’s useful work, lately pub- 
lished, contains an account of the introduction of the mode of 
