its upper half in the flask. The next operation 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. éf (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 centre of the wheel. Fig. 2. is a section of the two flasks when put together; but the core is not put in: ll are the holes for the metal, and g h i k 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 purchase 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 yet is real. Thus in the equation, x3— 90 x ——— 100=0, the root, according to Carden's rule, will be x = 50+ √ 24500 + No50-√ 24500, which is an impossible expression, and yet one root is equal to 10; and the other two roots of the equation are also real. Algebraists, for two centuries, have in vain endeavoured to resolve this case, and bring it under a real form; and the estion is not less famous

C. WHITTINGHAM, Printery

103, Goswell Street.

among them than the squaring of the circle is among geométers. 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 x = :5+ √5+5—√5; then x = 10; in like manner, in the irreducible 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:

50+√ 24500=5+ √ −5; and 5024500—5— ✔✅ —5. But 5+✓−5+5−√ -5=10=r, the root of the proposed equation.

Dr. Wallis seems to have intended to shew, that there is no case of cubic equ tions irreducible, or impracticable, as he calls it, notwithstanding the common opi nion to the contrary.

Thus in the equation r3— 63 r = 162, where the value of the root, according to Cardan's rule, is, r = √/ 81 + ✔ — 270) +81 ✔ - 2700, the doctor says, that the cubic root of 81 + ✔ — 2700, may be extracted by another impossible binomial, viz. by ¦ + 1 ✔ —; and in the same manner, that the cubic root of 81✔ - 2700 may be extracted, and is equal to 2-3; from whence he infers, that +✓ 3 + 2 − } √ −3 = 9, is one of the roots of the equation proposed. And this is true: but those who will consult 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 +✔ - 2700 is of the same degree of difficulty, as the extracting the root of the original equation r3 — 63 r =162; and that both require the tri-section of an angle for a perfect solution.

IRREGULAR, in grammar, such inflections of words as vary from the original rules: thus we say, irregular nouns, irregular verbs, &c.