nexion whatever with the separate symbols d, .' In some parts of the work, a letter, P for example, stands for a function of r; in others, the same letter is used simply as a coefficient: We may perhaps be told again, in a note, that P here is merely a coefficient, and different from the P of the preceding chapter;' but when a reader dips into this work for occasional reference, is it to be wished that he should be com pelled to hunt out these notes, before he can tell in what light to contemplate the symbols he meets with? Some of these ambiguities in notation are mere inadvertencies in the author, and might have been avoided with a very little additional care and reflection; but others are inevitable consequences of the foreign notation, and can only be escaped by rejecting that notation altogether. Let us, however, attend to Mr. Woodhouse's reasons for adhering to it.

In a former work, I adopted the foreign notation, and the present occasion furnishes some proof of the propriety of that adoption. In the calculus of variations, it is necessary to have symbols denoting operations, similar to those that take place in the differential calculus: now, d being the symbol for the latter, & is a most convenient one for the former: analogous to a there is no symbol in the English system of notation. If then I had used the fluxionary notation with points or dots, I must have invented symbols corresponding to and the characters formed by means of it. But, the invention of merely new symbols is in itself an evil. M. Lagrange indeed, whose power over symbols is so unbounded that the possession of it seems to have made him capricious, has treated the subject of variations without the foreign notation; this he rejects altogether; and, which is strange, has employed the English notation, but not adopted its signification. Thus, with him, x is not the fluxion, but the variation of x; the fluxions or differentials of quantities are not expressed by him, but solely the fluxionary or differential coefficients; thus, if u be a function

of

x, u'

du dx

or =

) is the differential coefficient. What advan

tages are to arise from these alterations it is not easy to perceive: yet they ought to be great, to balance the plain and palpable evils of a confusion in the signification of symbols, and of the invention of a system of notation to represent what already was represented with sufficient precision. No authority can even sanction so capricious an innovation.' Preface, pp. vi, vii.

Now, besides that there is a very forcible objection which presents itself to the mind of every mathematician when he first thinks or hears of prefixing one algebraical letter to another, the former to denote an operation performed upon the latter which represents a quantity,-there is no advantage that we can perceive in point of either facility or elegance, which

* Principles of Analytical Calculation, 1803.

the foreign possesses over the English notation. We are persuaded, indeed, that no unbiassed person can examine the table of the foreign and the corresponding English notation,' given by Mr. Woodhouse at the end of the preface of the work before us, without deciding in favour of the English method. In various inquiries where the fluxions of a connected series of quantities, a, b, c, d, e, &c. are to be employed, they are denoted with perfect freedom from ambiguity by the English notation; but how are they to be represented by the differen tial notation? Must the series be broken for the purpose of excluding the d? What then becomes of the universality of algebraic representation? And, what if the d should stand for density, or diameter, or distance, or any other subject whose initial is d-must we lose the advantage of employing the initial, because the differential notation has monopolized the use of that letter? But, says Mr. Woodhouse, analogous to d there is no symbol in the English system of notation. If I had used the fluxionary notation with points or dots, I must have invented symbols corresponding to d, and the characters formed by means of it.' Well: and where would have been the difficulty of effecting this? Let the variation be denoted by a dot below the quantity, as the fluxion is uniformly represented by one above it; and, in that case, we fancy both d and ♪ may very safely be dispensed with, as representatives of operations. In that case,

6

and either of them will be equivalent to . We have put down these expressions solely to shew that the thing is not impossible, according to the English notation; and by no means intend to affirm that we have struck out the best method of accomplishing it. As to the conduct of Lagrange, which has called forth Mr. Woodhouse's animadversions, there can be but little doubt that he was forced into it by a conviction of the ambiguities and disadvantages attending the foreign notation; while he employed the dot, by way of experiment, to see whether it was not possible to triumph over the English philosopher, nearly a century after his death, by appropriating his notation to a purpose widely different from its original use, and obtaining currency to the new modification. Such are the arts by which foreigners try to cast the greatest of mathematical inventions into oblivion: First, they give the science a new name; then, they devise a new character to denote the specific operations; then, they hide the invention under the jargon of a new metaphysics; and, finally, they deprive the

English invention of its last distinguishing vestige, its notation, and appropriate it to another use! And yet, there are to be found two or three Englishmen, and five or six Scotchmen, who, notwithstanding all this, extol the liberality, as well as the talents of French mathematicians; and seem as utterly unconscious of the injury attempted to be done to their great countrymen, as are even the illustrious dead, on whose reputation foreigners thus trample, and whose imperishable memory they are thus labouring to extinguish!

Art. III. A View of the Ancient and Present State of the Zetland Is land; including their civil, political, and natural History, Antiquities, and an Account of their Agriculture, Fisheries, Commerce, and the State of Society and Manners. By Arthur Edmonston, M. D. 2 vols. Sro. pp 709. price 183. Ballantyne and Co. Edinburgh. Longman and Co. 1809.

WE have more than once expressed our wish for the appearance of a work, bearing some such attractive title as the one we transcribe; but we cannot profess ourselves much satisfied with the manner in which this task has at length been performed by Dr. Edmonston. His volumes, however, contain a good share of useful information; and we shall, therefore, without farther preliminary censure, proceed to offer a pretty copious analysis of their contents,adhering, for the most part, to the arrangement of discussion which the author has thought proper to adopt.

The Zetland Islands are in number above a hundred, but only thirty-four are inhabited. Their general appearance, though they are adorned by some interesting scenes of wildness and grandeur, is represented as extremely unengaging, -the coasts rocky and unequal,-and the hills, which are numerous, (the highest Rona's,) bleak and mossy. Most of the large islands are intersected by deep winding bays, affording facilities for internal conveyance, and harbours at once safe, sheltered, and capacious. Several lofty headlands project with a grand and imposing aspect into the sea; among which are the noted cliffs of Foula, interestingly situated about 16 miles from Mainland. The currents between the islands are rapid, and in every direction. Except in a few gardens, there are no trees nor shrubs. The cultivated land bears but a small proportion to the extent of the country, and is chiefly on the sea coast and the sides of the various bays.

The climate, though variable and damp, is said not to be unwholesome for the inhabitants. Spring usually commences about April, but there is little warmth till the middle

of June; summer generally ends with August; and winter often begins in the middle of October. Westerly and north-westerly gales of wind blow violently in September, and will often destroy the greater part of the crops in a single night. Snow seldom lies long, nor is the cold ever intense. The medium temperature of winter may be taken at 38, and of summer at 65°. Our author is much displeased with the various writers who have invidiously proclaimed the great want of light in this country during the winter; and triumphantly adduces for their dishonourable refutation the following overwhelming fact-- the sun, on the 22d of December, is five hours and twenty five minutes above the horizon! Here, indeed, the Doctor particularly exerts himself, and is anxious, we perceive, to be allowed to finish the chapter.

But if the winter be dark and gloomy, it (sicut suus est mos!) is amply compensated by the continued light of the summer months. The nights begin to be very short early in May, and from the middle of that month to the end of July, darkness is absolutely unknown. The sun scarcely quits the horizon, and his short absence is supplied by a bright twilight. Nothing can surpass the calm serenity of a fine summer night in the Zetland isles. The atmosphere is clear and unclouded, and 1 the eye has an uncontrolled and extensive range:-the hills and the headlands look then more majestic, and they have a solemnity superadded to their grandeur:-the water in the bays appears dark, and as smooth as glass-no living object interrupts the tranquillity of the scene, but a solitary gull skimming the surface of the sea; and there is nothing to be heard but the distant murmuring of the waves among the rocks.'— Vol. I. p. 12.

The second chapter is on the general history of the islands, -than which we scarcely ever, perhaps, have read any thing more heavy or tasteless; a circumstance to be peculiarly regretted, because, in designs of this nature such a department is so manifestly of prime importance. Having duly brought his testimonies from Pliny and Tacitus to prove Zetland to be the Thule of the Romans, our author proceeds to conjecture, that the earliest inhabitants came from the islands of Orkney, previously populated from the north of Scotland; and these, he thinks, were succeeded by the Peti or Picts, who, three centuries before the Christian æra, issuing from Scandinavia towards Caledonia, left here, he imagines, and at Orkney, a colony on their way. In the year 875, or as Pinkerton, in opposition to Torfæus, argues in 910, Zetland was invaded and subdued by Harold, king of Norway, who bestowed its government, united to that of Orkney, on Ronald earl of Merca; in whose family it remained, passing by marriage in 1330 into a Scottish earldom, till its transference in 1470, under sanction of the

Danish crown, to the sovereignty of Scotland. Leases of it have since been successively obtained by various noblemen; and the grant, coming last from the family of Morton, is now in the possession of Lord Dundas. Christianity was introduced about 985 by the interference of the Norwegian king, Olaus Triguesson :—the singular means used for its introduction and establishment, we have already noticed in our review of Barry's History of the Orkneys. Dr. E. is professedly indebted to Torfæus for his earlier historical information.

He proceeds to consider, but in a very superficial manner, the remains of antiquity, and the language and literature. He makes some remarks on the remains of Pictish and Norwegian architecture; on concentric circles of stones which are now and then met with; on triangular polished stones of green porphyry, called by the people thunderbolts; on flint arrow heads; and on certain vestiges of camps or fortifications, probably introduced by the Picts in imitation of the Ro mans;-subjects which at present, we learn, busily engage the connoisseurs in antiquarianism, but on which there is nothing here worthy of extraction. A few Roman coins, it appears, have been seen; those of Denmark, Holland, and the north of Germany are in free circulation. The ancient language was Scandinavian and Norwegian, but is now a sort of English; the common dialect is a mixture of Norwegian, Dutch, English, and Scotch. There are only two schools at which the elements of Latin are taught. Opulent gentlemen educate their sons at home under private tutors, or entrust them to the tuition of parochial clergy; and after wards send them to the universities of Aberdeen or Edinburgh.

There follows a good chapter on the tenures by which the lands are rented, and the different exigible payments. The enclosed and improved land, inclusive of both arable and meadow, amounts to somewhat less than a twelfth part of the surface of the country. The rents are paid in cash, and fish, butter, oil, &c. besides other exactions, the value of which cannot be strictly ascertained. The tenant's working three days in the year for his landlord, when required, may be mentioned as one. The claims of the donee of the crown rents, the clergyman, and the common taxes of the legislature, must also be regularly answered.

Dr. E. passes on to the agriculture of the islands, which seems never to have been an object of particular attention. The soil is various,' but chiefly 'moss.' The im