FLU 
FLU 
sulphur may be dissipated by roasting, yet 
that which remains will form a sulphuret 
with the alkali, which is a very powerful 
solvent of metallic bodies. The advantage 
of M. Morveau’s reducing flux seems to 
depend on its containing no uncombined 
alkali. It is made of eight parts of pulve- 
rized glass, one of calcined borax, and half 
a part of powder of charcoal. Care must 
be taken to use a glass which contains no 
lead. The white glasses contain in gene- 
ral a large proportion, and the green bot- 
tle glasses are not perhaps entirely free 
from it. 
Flux, in medicine, an extraordinary 
issue, or evacuation of some humours of 
the body. See Medicine. 
FLUXION, in mathematics, denotes 
the velocity by which the fluents or flowing 
quantities increase or decrease; and may 
be considered as positive or negative, ac- 
cording as it relates to an increment or 
decrement. 
The doctrine of fluxions, first invented 
by Sir Isaac Newton, is of great use in the 
investigation of curves, and in the discovery 
of the quadratures of curvilinear spaces, 
and their rectifications. In this method, 
magnitudes are conceived to be generated 
by motion, and the velocity of the generat- 
ing motion is the fluxion of the magnitude. 
Thus, the velocity of the point that de- 
scribes a line, is its fluxion, and measures 
its increase or decrease. When the mo- 
tion of this point is uniform, its fluxion or 
velocity is constant, and may be measured 
by the space described in a given time, but 
when the motion varies the fluxion of ve- 
locity at any given point is measured by the 
space that would be described in a given 
time, if the motion was to be continued 
uniformly from that term. 
Thus, let the point m be conceived to 
A m m r 
1 1 
R 
move from A, and generate the variable 
right line Am, by a motion any how re- 
gulated; and let its velocity, when it ar- 
rives at any proposed position or point R, 
be. such as would, was it to continue uni- 
form from that point, be sufficient to 
describe the line Rr, in the given time 
allotted for the fluxion, then will Rrbe the 
fluxion of the variable line A m, in the term 
or point R. 
The fluxion of a plain surface is con- 
ceived in like manner, by supposing a 
given right line m n (Plate V. Miscel. fig. 8) 
to move parallel to itself, in the plane of 
the parallel and moveable lines AF and 
BG: for if, as above, Rr be taken to ex- 
press the fluxion of the line A m, and the 
rectangle R r s S be completed ; then that 
rectangle, being the space which would be 
uniformly described by the generating line 
m n, in the time that A m would be uni- 
formly increased by mr, is therefore the 
fluxion of the generated rectangle B m, in 
that position. 
If the length of the generating line m n 
continually varies,, the fluxion of the area 
will still be expounded by a rectangle un- 
der that line, and the fluxion of the ab- 
sciss or base : for let the curvilinear space 
Anm (fig. 9), be generated by the con- 
tinual and parallel motion of the variable 
line m n ; and let R r be the fluxion of the 
"base or absciss A rn, as before, then the 
rectangle Rrs S, will be the fluxion of the 
generated space A m n. Because, if the 
length and velocity of the generating line 
m n were to continue invariable from the 
position R S, the rectangle R r s S would 
then be uniformly generated with the very 
velocity wherewith it begins to be generat- 
ed, or with which the space Am n is, in- 
creased in that position. 
Fluxions, notation of, of invariable quan- 
tities, or those which neither increase nor 
decrease, are represented by the first 
letters of the alphabet, as a, b, c, d, Sec. 
and the variable or flowing quantities by 
the last letters, as, v, w, x, y, 3 .• thus, the 
diameter of a given circle may be denoted 
by a ; and the sine of any arch thereof, 
considered as variable, by x. The fluxion 
of a quantity represented by a single letter, 
is expressed by the same letter with a dot 
or full point over it : thus, the fluxion of 
x is represented by x, and that of y by y. 
And, because these fluxions are themselves 
often variable quantities, the velocities with 
which they either increase or decrease, are 
the fluxions of the former fluxions, which may 
be called second fluxions, and are denoted 
by the same letters with two dots over 
them, and so on to the third, fourth, &c. 
fluxions. The whole doctrine of fluxions 
consist in solving the two following pro- 
blems, viz. From the fluent, or variable 
flowing quantity given, to find the fluxion ; 
which constitutes what is called the direct 
method of fluxions. 2. From the fluxion 
given, to find the fluent, or flowing quan- 
tity; which makes the inverse method of 
fluxions. 
Fluxions, direct method of, the doctrine 
