In every cultivated language, however, the progress of style is decidedly towards more and more of first-sight intelligibility, iu so far as that depends upon precision of phrase, and the use of words in certain limited meanings. This has been remarkably the history of the English language, at least for the last two hundred and fifty years, during which we have been fixing both our grammatical forms and our rules of eyntax to an extent that would surprise most persons if the evidences of it were stated in detail. Whether all that has been done in this way has really improved the lauguage,—whether it has been thereby rendered more expressive, more flexible, more fitted for the various ends which a language ought to aubserve, may perhaps be questioned. The gain in point of precision may possibly be more than balanced by the lona both in ease and in variety of style.
In another respect, however, English prose eloquence has undergone a change of character in an opposite direction, by the greater infusion which it has received of a colloquial tone and phraseology within the I last century and a half. Till towards the close of the 17th century, the language of books, except in the comic drama and other light coin ' positions of a kindred character, generally preserved a formality of gait and manner which distinguished it nearly as much from living con ' venation as the critics have held that the language of verse should be ; distinguished from that of prose. Among the most eminent of the writers who first broke through this species of restraint were Cowley, i in his Essays; Dryden, in his prefaces and other prose discourses ; Sir William Temple; and the third Earl of Shaftesbury. The example set by them was followed by Swift, Addison, Steele, and their associates and imitators, till, in the earlier part of the last century, the colloquial ease and liveliness, which had thus become fashionable, threatened to ) degenerate into a slovenliness, or shambling fluency, alike without either ) elegance or precision. It must be admitted, that of all the writers of the second quarter of the 18th century, Lord Bolingbroke, whatever ) opinion may be entertained of his depth of thought or weight of matter, wrote the best style, at once the most flexible and idiomatic, f and the purest, most refined, and most musical. But probably the
writer who on the whole did most to restore measure and emphasis to t our prose style was Johnson : his manner has not been much copied in El all its peculiarities or in its entire character, but yet more or less of its There are then one negative root and two positive roots, and there fore four imaginary ones. The reader will easily find that the positive roots lie between 1 and 2, and the negative root between —1 and — 2.
The exhibition of the process, leaving out the actual performance of multiplications, has 400 figures in Mr. Young's work. Fourier has merely written down the derived functions, which is done at sight, and formed the criteria for x= —10, x--se —1, x= —h, x=e 0 , x= + h, x=1, x=10, which may all be done at eight also. From this he finds that there must be one negative root between —1 and —10, that there may be two roots between 0 and 1, and two more between 1 and 10. All this might be done before v, could be found and written down as above. It is to be hoped either that Fourier's theorem will be com pleted by the addition of a teat for imaginary roots, or that Sturm's functions will be exchanged for others of less C)mplicated opera tion. But in the meanwhile it must be remembered that Fourier, Sturm, and Horner have completely changed the aspect of the solution of numerical equations : at the beginning of the period men tioned, it would have been thought too good to expect that any certain method of predicting, or easy one of calculating, the roots of such equations, should be found, after the failure of all analysts from Des cartes and Newton down, to Euler and Lagrange, the best heads of France and England, Germany and Italy. It is a lesson against de spairing of the attainment of any result, however illustrious the investigators who have not aucceeded, and also against imagining that the hints of preceding ages are exhausted. All the contents of the present article arise out of a new mode of looking at the theorem which Descartes gave more than two hundred years ago.