IRIS

, another name for the Rainbow; which see.

Iris also denotes the striped variegated circle round the pupil of the eye, formed of a duplicature of the uvea.

In different subjects, the Iris is of several very different colours; whence the eye is called grey, or black &c. In its middle is a perforation, through which appears a small black speck, called the sight, pupil, or apple of the eye, round which the Iris forms a ring.

Iris is also applied to those changeable colours, which sometimes appear in the glasses of telescopes, microscopes, &c; so called from their similitude to a rainbow.

The same appellation is also given to that coloured spectrum, which a triangular prismatic glass will project on a wall, when placed at a proper angle in the sunbeams.

Iris Marina, the Sea-Rainbow. This elegant appearance is generally seen after a violent storm, in which the sea water has been in vast emotions. The celestial rainbow however has great advantage over the marine one, in the brightness and variety of the colours, and in their distinctness one from the other; for in the sea-rainbow, there are scarce any other colours than a dusky yellow on the part next the sun, and a pale green on the opposite side. The other colours are not so bright or so distinct as to be well determined; but the sea-rainbows are more frequent and more numerous than the others: it is not uncommon to see 20 or 30 of them at a time at noon-day.

IRRATIONAL Numbers, or Quantities, are the same as surds, or such roots as cannot be accurately extracted, being incommensurable to unity. See Surds.

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 , the root, according to Cardan's rule, will be , which is in the form of an impossible expression, and yet it is equal to the quantity 4: for , and , therefore there sum is x = 4. The other two roots of the equation are also real.

Algebraists, for almost three centuries, have in vain endeavoured to resolve this case, and to bring it under a real form; and the problem is not less celebrated among them, than the squaring of the circle is among geometricians.

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 irrational or surd form; because the root in this case is compounded of two equal surds with contrary signs, which destroy each other; as if , then x = 4. In like manner, in the Irreducible case, where the root is rational, there are two equal imaginary quantities, with contrary signs, joined to real quantities; so that the ima- ginary quantities destroy each other; as in the case above of the root of the equation , which was found to be .

It is remarkable that this case always happens, viz one root, by Cardan's rule, in an impossible form, whenever the equation has three real roots, and no impossible ones, but at no time else.

If we were possessed of a general rule for accurately extracting the cube root of a binomial radical quantity, it is evident we might resolve the Irreducible case generally, which consists of two of such cubic binomial roots. But the labours of the algebraists, from Cardan's down to the present time, have not been able to remove this difficulty. Dr. Wallis thought that he had discovered such a rule; but, like most others, it is merely tentative, and can only succeed in certain particular circumstances.

Mr. Maseres, cursitor baron of the exchequer, has lately deduced, by a long train of algebraical reasoning, from Newton's celebrated binomial theorem, an infinite series, which will resolve this case, without any mention of either impossible or negative quantities. And I have also discovered several other series which will do the same thing, in all cases whatever; both inserted in the Phil. Trans. See Cardan's Algebra; the articles Algebra, Cubic Equations; Wallis's Algebra, chap. 48; De Moivre in the Appendix to Sanderson's Algebra, p. 744; Philos. Trans. vol. 68, part 1, art. 42, and vol. 70, p. 387.