I have known the colony between forty and fifty years. At my first remembrance of them they were called the Tinklers (tinkers) of Yetholm, from the males being chiefly then employed in mending pots and other culinary utensils, especially in their peregrinations through the hilly and less populous parts of the country. Sometimes they were called Horners, from their occupation in making and selling horn spoons called cutties. Now their common appellation is that of Muggers, or what pleases them better, Potters. They purchase, at a cheap rate, the cast or faulty articles, at the different manufactories of earthen-ware, which they carry for sale all over the country; consisting of groups of six, ten, and sometimes twelve or fourteen persons, male and female, young and old, provided with a horse and cart to transport the pottery; besides shelties and asses to carry the youngest of the children and such baggage as they find necessary. In the country, they sleep in barns and byres, or other out-houses; and when they cannot find that accommodation, they take the canvass covering from the pottery cart, and squat below it like a covey of partridges in the

snow.

Mr. Smith states that most of the Gypsies resident at Kirk Yetholm have leases of their possessions, granted for a term of nineteen times nineteen years, for payment of a small sum yearly, something of the nature of a quit-rent.'

The Gypsies above mentioned, though they mostly remain at home during the winter, recommence their state of vagrancy with the milder weather of the spring, and do not relinquish their wanderings till the winter forces them to return. When Mr. S. became first acquainted with this settlement of Gypsies at Yetholm, their king or leader was named William Faa, who lived to a great age; and his present descendants are said to take the name of Fall from the Messrs. Fall of Dunbar, whom they boast to be of the same stock. In the reign of Mary Queen of Scots, John Faw, who assumed the title of Lord and Earl of Upper Egypt, came into Scotland with a multitude of followers; some of whose descendants appear to survive in the Tinklers of Kirk Yetholm.

From the answers to some queries which Mr. Hoyland circulated in the different counties of England in 1815, no very distinct or conclusive information was obtained with respect to the numbers, habits, union, or dispersion of the Gypsies.

6

In the county of Herts,' says the author, it is computed there may be sixty families having many children. Whether they are quite so numerous in Buckinghamshire, Bedfordshire, and Northamptonshire, the answers are not sufficiently definite to determine. In Cambridgeshire, Oxfordshire, Warwickshire, Wiltshire, and Dorsetshire, greater numbers are calculated upon. In various counties, the attention has not been competent to procuring data for any estimate of families or individuals.'

All this is too vague and indefinite to form the basis of any practical results. The following are some of the other particulars which Mr. Hoyland obtained :

More than half their number follow no business; others are dealers in horses and asses; furriers, smiths, tinkers, braziers, grinders of cutlery, basket-makers, chair-bottomers, and musicians.' The women mostly carry baskets with trinkets and small wares; and tell fortunes.'. Those who profess any religion represent it to be that of the country in which they reside; but their description of it seldom goes beyond repeating the Lord's Prayer, and only a few of them are capable of that.' They marry for the most part by pledging to each other, without any ceremony.' 'Not one in a thousand can read.'

6

The Empress Maria Theresa was the first European sovereign who made any thing like a systematic attempt to reclaim the Gypsies from their vagrant habits, and to induce them to enter the pale of more civilized life. That attempt was prosecuted in the reign of her son Joseph II., but with the ill success which attended other measures of reform that were projected in his capricious government. Despotism may issue its fiats, but it cannot always ensure the execution of them. Even when its mandates design a public benefit, they are liable to be counteracted by some inveterate habit, or thwarted by some opposing interest; and barriers are often found either in opinion or inclination, which securely defy the most positive ordinances of arbitrary power. In some instances, Joseph II. had the children of the Gypsies, who were of a certain age, violently torn from the arms of their parents, and sent to be educated in a different part of his dominions: but regulations which are at war with the natural sentiments of mankind are not likely to be permanent.

Mr. Hoyland seems to think that the progeny of the Gypsies might, without any considerable inconvenience, be educated at the different charity-schools in this kingdom, from the age of six to fourteen; when the boys might be put out as apprentices, and the girls sent to service. He also suggests that the expence might be defrayed out of the county-rates.Philanthropy is always warm-hearted: but its very warmheartedness is sometimes apt to mislead the judgment, and to divert the mind from those considerations of fitness and expediency, which it is of great moment not to overlook in questions of political economy.

ART.

ART. XIII. Elements of Plane and Spherical Trigonometry, with their Application to Heights and Distances, Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic Operations. By Olinthus Gregory, LL.D. of the Royal Military Academy. 12mo. pp. 244. 5s. Boards. Baldwin and Co.

WE

E have frequently been surprized that, among the numerous introductory works which have of late years issued from the London presses, no reputable Treatise on Trigonometry has made its appearance, calculated to answer all the purposes of a school-book. The necessary conditions of such a publication are that its price shall be moderate, its demonstrations concise, its arrangement natural, and its selection of practical exercises be made with judgment and solved with perspicuity. The treatise of Trigonometry by Mr. Bonnycastle possesses many of these requisites, but it is too large and too expensive to become popular in schools. The same may be said of Keith's Trigonometry; and the treatise by Mr. Woodhouse on this subject is certainly not well adapted to the common purposes of teaching.

The little volume at présent under review, besides fulfilling the requisite conditions as to arrangement and general execution, is offered, considering the closeness of its pages, at a very moderate price; and we have no doubt that it will find its way into most of our principal seminaries and places of public education, at least if one part of its plan, which we consider as among its principal recommendations, should not operate to its disadvantage. We have in several instances had occasion to observe that, in most of our elementary treatises, too much has been sacrificed to simplicity; this object being constantly kept in view, while the mental discipline of the student has been almost entirely overlooked. Hence the solution of problems has been rendered nearly as much of a mechanical operation, or a mere matter of practice, as the firing at a target; and a knowlege of principles in the one case seems as little necessary as that of projectiles in the other. An author who succeeds in this kind of simplification is almost certain of rendering his book popular, because it greatly facilitates the progress of the student, makes him expert in the solution of problems, and does apparent credit to his tutor; and few are able to appreciate the superficial nature of his acquirements. Dr. Gregory has not fallen into this common erfor, but, although simplicity has not been overlooked, the grand object of leading on the student to investigation has above all been kept in view; so that the work assumes more of

the

the analytical form than our elementary treatises usually present.

It is singular, as the author observes, (and we have frequently made the same remark,) that in England, the birthplace of the modern analysis, and where it has received some of its most valuable improvements, a prejudice is cherished against its general introduction, and a decided preference is given to the geometrical and synthetic method. * On this account, Dr. Gregory deems it necessary to state his reasons for appropriating so large a portion of his book to the analytical or algebraical mode of deducing properties and theorems; which statement, as it is difficult to abridge, we shall give in the author's own words:

1. It is more concise, and therefore allows of the introduction of a much greater quantity and variety of matter, in any proposed space, than could possibly be exhibited and demonstrated according to the geometrical method of the antients.

2. This method is more uniform than the other, as well as more general and comprehensive. In the geometrical method as it is usually conducted, however convincing and elegant, the demonstration of one property or theorem may not have the remotest analogy to that which will serve to establish the truth of another. The demonstrations of a series of propositions, such as are obviously connected in the logical arrangement of a treatise, may probably have nothing common in their appearance, except that they are all geometrical; nor shall the manner of demonstrating one proposition suggest necessarily a single hint that may apply to the demonstration of the very next. The separate chains of demonstration of the two propositions may be as distinct (if I may be pardoned so familiar an allusion) as the processes by which a sword and a needle are manufactured. In the one case both are geometrical, in the other both are mechanical; but neither of the two, whether geometrical or mechanical, although beautifully adapted to their purpose, need be at all alike. It is not thus with regard to the analytical method: the processes have all more or less of resemblance, they are all conducted by the same general rules; and they commonly lead to universal results, from which particular corollaries are deducible at pleasure. The analytical method is at the same time much the most comprehensive. There are several

curious and useful theorems to be found in the analytical treatises on trigonometry, which have not yet, to my knowledge, been demonstrated in any other way; and not a few which I am persuaded do not admit of any other kind of proof.

3. This method is also much the easiest. The processes themselves are, in the main, conducted with the greatest possible simplicity; the substitutions and transformations are generally natural, and obvious: in truth, so much so, that a student no sooner at

*See our review of Cresswell's Maxima and Minima, M. R. vol. lxxv. p. 202.

REV. DEC. 1817.

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tains

tains a competent acquaintance with the manner of conducting his investigation, than he will be enabled to develope practical theorems nearly as fast as he can write them down. Nor is the mode of inquiry such as need encumber the memory; the operations being general, the requisite first principles few. This is a great recommendation; because every unnecessary load upon the memory tends more or less to weaken our mental elasticity, and impede the intellectual operations. I am happy to fortify my opinion on this point by an observation of the most profound mathematician and natural philosopher now living, Laplace. "Préférez (says he) dans l'enseignement les méthodes générales, attachez-vous à les présenter de la manière la plus simple, et vous verrez en même tems qu'elles sont presque toujours les plus faciles."

4. The analytical method of establishing the principles, and deducing the formula of trigonometry, has this farther advantage, that it connects it more intimately with the principal topics of mixed mathematics, and causes it to become a portal to the higher mechanics and the celestial physics. Any person who has looked, however cursorily, into the best treatises on statics, dynamics, and physical astronomy, especially those which have been published on the continent, must have observed that they abound with trigonometrical formula. And they who have gone a little below the surface, know that several of the most striking results of physical astronomy turn upon some obvious trigonometrical truth. Thus, to select only one class of instances, our countryman Simpson, in his researches into that part of the celestial physics which relates to the moon, (Miscellaneous Tracts, p. 179.) having shown that no terms enter the equation of the orbit but what are expressible by the cosine of an arc, or the cosines of its multiples, and, therefore, that no terms enter that equation but what by a regular increase and decrease return to their former values; immediately infers that the moon's "mean motion, and the greatest quantities of the several equations, undergo no change from gravity." Frisi advanced still farther in the same line of induction. And farther yet Lagrange and Laplace; who have demonstrated that no term of the form A XT, or A tan nт, or a cosec nTM, or (T denot

A

ing the time) can enter the analytical expression for any of the inequalities of the planetary motions, or those of their satellites: and have thus proved that the system is stable, all its irregularities being confined within certain limits; just as all the modifications in the magnitude and position of the sines and cosines of arcs in the same circle are confined within limits, such as the theory of trigonometry assigns them. This consideration stamps a value upon the researches in this department of science which they would not otherwise possess; and in order that the mathematical student may fully avail himself of it, it is requisite that he understand the analytical method.

Lastly, this method is preferable to the geometrical, because it tends to communicate to the student the habit of investigation, which that does not. It is one thing to be able to demonstrate, or

to