the title of periodical publications. See Encyclopedia. The principal British Journals are: The History of the Works of the Learned, begun at London in 1669; Conspira Temporum, in 1708. About the same time there appeared two new ones; the one under the title of Memoirs of Literature, containing little more than an English translation of some articles in the foreign Journals, by M. de la Roche; the other, a collection of loose tracts, intitled, Bibliotheca Curiosa, or a Miscellany. These, however, with some others, are now no more, but are succeeded by the Annual Register, which began in 1758; the New Annual Register, begun in 1780; the Monthly Review, which began in the year 1749, and gives a character of all English literary publications, with the most considerable of the foreign ones; the Critical Review, which began in 1756, and is nearly on the same plan; as also the London Review, by Dr Kenrick, from 1775 to 1780; Maty's Review, from Feb. 1782 to Aug. 1786; the English Review, begun in Jan. 1783; and the Analytical Review, begun in May 1788, dropt in 1798, and revived in 1799, under the title of the New Analytical Review; but again dropt after two or three months trial; the British Critic, begun in 1792, and still carried on with much spirit and ability; the Anti-Jacobin Review and Magazine, commenced in 1798, for the meritorious purpose of counteracting the pernicious tendency of French principles in politics and religion; the New London Review, January 1799; A Journal of Natural Philosophy, Chemistry, and the Arts, which was begun in 1797 by Mr Nicholson, and has been conducted in such a manner, that it is one of the most valuable works of the kind to be found in any language; the Philosophical Magazine, begun in 1798 by Mr Tillock, and carried on upon much the same plan, and with much the same spirit, as Nicholson's Journal.

Besides these, we have several monthly pamphlets, called Magazines, which, together with a chronological series of occurrences, contain letters from correspondents, communicating extraordinary discoveries in nature and art, with controversial pieces on all subjects. Of these, the principal are those called the Gentleman's Magazine, which began with the year 1731; the London Magazine, which began a few months after, and has lately been discontinued; the Universal Magazine, which is nearly of as old a date; the Scotch Magazine, which began in 1739, and is still continued; the European Magazine; and the Monthly Magazine, a miscellany of much information, but not of good principles.

JOYST or JEVST, the second month of the Bengal year.

IRRATIONAL NUMBERS or Quantities, are the irrational same as surds, for which see Algebra, Encycl.

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.

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 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.