IRR 
it* upper half in the flask. The next ope- 
ration is lifting the pattern out of the lower 
flask, before which the workman wets the 
sand around the pattern, that it may adhere 
together, and not be broken by lifting the 
pattern. The two pins projecting from the 
wheel where the hole is to be, leave their 
impressions in the sand, forming two holes. 
e f (fig. 2) one in each flask. These holes 
receive the ends of a core, which is exactly 
the shape and size of the hole required in 
the wheel : the core is formed of a mixture 
of plaster of Paris and brick-dust, and is 
made just the length and size of the pins in 
the pattern, that it may be truly in the cen- 
tre of the wheel. Fig. 2. is a section of the 
two flasks when put together ; but the core 
is not put in: 1 1 are the holes for the metal, 
and g h ik the hollow cavity to receive it. 
The iron is melted in a furnace, and 
brought from it in a ladle (fig. 11) which 
has three handles, and is carried by two 
men, the forked handle, M, giving a pur- 
chase to the man holding it, to turn over 
the ladle to deliver its contents. If the 
work is very small, the metal is conveyed 
to the flasks in common ladles. 
The more intricate cases of iron-foundry, 
as the casting of cylinders for steam engines, 
crooked pipes with various passages, &c. 
are cast in moulds formed of loam or clay, 
and are done nearly in the same manner as 
the moulding of plaster cast from busts, &c. 
but our limits will not allow us to describe 
these curious branches of the founder’s art. 
IRONY, in rhetoric, is when a person 
speaks contrary to his thoughts, in order to 
add force to his discourse. 
IRRATIONAL, an appellation given to 
surd numbers and quantities. See Surd. 
IRREDUCIBLE case, in algebra, is used 
for that case of cubic equations where the 
root, according to Cardan’s rule, appears 
under an impossible or imaginary form, and 
yetis real. Thus in the equation, x 3 — 90 x — 
100 =0, the root, according to Carden’s rule, 
wi ll be x = */ g0 _]_ ^ _ 24500 _j_ 
y' bO y/ — 24500, which is an impos- 
sible expression, and yet one root is equal 
to 10 ; and the other two roots of the equa- 
tion are also real. Algebraists, for two 
centuries, have in vain endeavoured to re- 
solve this case, and bring it under a real 
form ; and the question is not less famous 
IRR 
among them than the squaring of the circle 
is among geometers. See Equation. 
It is to be observed, that as in some other 
cases of cubic equations, the value of the 
root, though rational, is found under an ir- 
rational or surd-form ; because the root in 
this case is compounded of two equal surds 
with contrary signs, which destroy each 
other; as if * — 5-j- ^5 + 5 — ^ 5; 
then x = 10 ; in like manner, in the irredu- 
cible case, when the root is rational, there 
are two equal imaginary quantities, with 
contrary signs, joined to real quantities; so 
that the imaginary quantities destroy each 
other. Thus the expression : 
— 24500 = 5 -j- ^ — 5 ; and 
~ \/ — 24500 = 5 — */ — 5. But 
t>-\- V — 5 + 5 — y' — 5 = 10 = x, the 
root of the proposed equation. 
Dr. Wallis seems to have intended to 
shew, that there is no case of cubic equa- 
tions irreducible, or impracticable, as he 
calls it, notwithstanding the common opi- 
nion to the contrary. 
Thus In the equation r 3 — 63 r ~ 162, 
where the value of the root, according to 
Cardan’s rule, is, r = y 81 _j_ ^TZT^oo 
+ $/ 81 — v — 2700, the doctor says, 
that the cubic root of 81 -(- ^ — 2700, 
may be extracted by another impossible 
binomial, viz. by | -(- i ^ - and in the 
same manner, that the cubic root of 81 
■/ — 2700 may be extracted, and is equal 
to | — i </ — 3 ; from whence he infers, 
that f + j c/ — 3+| — — 3 = 9, is 
one of the roots of the equation proposed. 
And this is true : but those who will con- 
sult his algebra, p. 190, 191, will find that 
the rule he gives is nothing but a trial, both 
in determining that part of the root which 
is without a radical sign, and that part 
which is within : and if the original equa- 
tion had been such as to have its roots irra- 
tional, his trial would never have succeeded. 
Besides, it is certain, that the extracting 
the cube root of 81 + y' — 2700 is of the 
same degree of difficulty, as the extracting 
the root of the original equation r 3 — 63 r 
= 162 ; and that both require the tri-section 
of an angle for a perfect solution. 
IRREGULAR, in grammar, such inflec- 
tions of words as vary from the original 
rules : thus we say, irregular nouns, irregu- 
. lar verbs, &c. 
END OF VOL. III. 
C. WHITTINGHAM, Printer, 
103, Goswell Street. 
