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' Hifiory of the Poor. · Where there are seminaries instituted for educating children in habits of industry, the poor should be compeiled to send their children to them in those parishes where they reside; the migrated families, by the alternative of the attendance of their children at the school of industry, or an order of removal of themselves to their place of settlement.

• These terms being complied with; the poor might, without fear of their becomirg vagrants, or negleét of industrious habits in the rising generation, be permitted to seek their bread, by means of labour and industry, wherever good wages 13 nable them best to find it ; and a foundation of a iund would be laid for their maintenance when in distress, which would be productive in proportion as the number of the migrants increased, or in other words, as the total fum earned by the industry of the nation increased.'

Our author observes, that there seems uniformly one false prineiple, inconsistent with freedom, constantly pervading the laws respecting the poor, exclusive of the restraint which the law of certificates occasions. The principle alluded to, is the right claimed by the officers of a parish to remove those whom they may deem likely to become chargeable; a degree of powa er which, Mr. Ruggles thinks, may be perverted to the purposes of caprice, interest, or private reteniment; and therefore ought not to be entrusted to the officers of a parish. .

This author joins entirely in opinion with Mr. Locke, that the most effectual means of preventing the public inconveniencies arising from the increase of the poor, is that of establishing schools of industry for the children of labouring people. This salutary expedient has been adopted in different parts of the country, in some with more, and in others with less obvious advantage; but under due regulations, suited to the local circumstances of the different districts, it might doubtless be rendered of extraordinary benefit to the interests of the public.

The observations in the present volume, relating almost entirely to remarks or proposals suggested by preceding writers, admit not of being exhibited to our readers in detail, without repeating what has formerly been noticed in various parts of our Review. Those therefore who wish for more particular information, we must necessarily refer to the work; where they will be satisfied with the diligent researches, the just remarks, and the judicious reflections of the author, whose sentiments on this important subject are worthy the attention of the public.

Table

41. 4s. Sberler, Author'every second of emotior,vod, aint THE labours of w" ingrave. Detagefimal xadranı, 6

Table of Logarithms of all Numbers from One to 101,00d, airi

of the Sines of Tangents to every Second of the Quadrant, by Michael Taylor, Author of the Sexagesimal Table. 416 41. 45. Shects. Wingrave. THE labours of Napier, Briggs, Vlacq, and Gardiner, arder I well known to every person engaged in mathematical pursuits, and the invention of logarithms, though they were brought nearly to perfection in the author's lifetime, has given rise to the successful exertions of others in the same career. By their labours we had tables for sines and tangents to every ten seconds of the quadrant, and we seemed to stand in need only of a further improvenient for every second of the quadrant, to make them answer all the purposes for which they could be introduced into astronomy. This work was undertaken by Taylor, who was interrupted by death in the progress of it, and the five last pages of logarithmick fines ef tangents, which alone remained unfinished at the press, were printed off under the inspection of the present astronomer royal.

The two first chiliades of numbers occupy two pages. The other numbers, from 1000 to 101,000, are with their lo garithms, differences of proportional parts distributed, so as to make two tables in every page. In the same manner for the fines, cosines, tangents, and cotangents, there are two tables in each page : the one page being dedicated to the fines and cosines, the opposite to the tangents and cotangents. The degrees are marked at the top and bottom of the page : each table is divided into thirteen columns; in the first are the sea conds from 0 to 60; at the top of each of the other columns are the minutes, under which are the indexes of the logarithms, and under them. the two firit decimal places for each minute : the other five places are found opposite to each second ; at the bottom of the table are the minutes corresponding to the des grees at the bottom of the page. By this arrangement the logarithm of any fine is found with great facility, and the tabies are more compact. For the accuracy of them we may, rely on the great care and industry of the compiler, and the character of the editor.

Prefixed to the tables is an explanation of them by the edi. tor, who has also added examples of great use and importance to the astronomer and the navigator. His mode of finding the true distance of the star from the moon's centre, is particularly neat, and may, by the ease with which it is performed, bring the nautical almanack into more general use among faile ors than it has hitherto obtained. Every case of plane and spherical triangles is folred, so that the practical altronomer C. R. N. AK. (11.) axday, 17946

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does not require the ashitance of any other book of trigonometry. Instances are given also from various branches of arithmetic, and the rule of proportion adopted, as it is not generaliy knowi), may be useful to many of our readers. .

It is cuitomary to lay down two rưles for proportion in books; this is general and will satisfy all cases. Among the cerims of the question, that, which is of the same kind with the unknown term, is called the homologous term, the others are called correlatives, cither of the unknown or of the ho. mologous term. "The dividend will be compofed of those correlatives of the unknown term, which have a direct ratio to it, that is, which make the unknown term incréase or decrease as they increase or decrease themselves ; of the homologous term, aiid of those correlatives of the homologous term, which bear an inverse ratio to the fame, that is, which make the homologous term decrease or increase, as they themfelves increase or decrease. And the divisor will be composed of those correlatives of the unknown term, which bear an inverse ratio to it, and of those correlatives of the homologous: term which bear a direct ratio to it.'

"Example. If 2801. serve 120 men for 32 wecks, how much will serve 360 men for 48 weeks ? Answer, 12601.

· The unknown term is a sum of money, therefore 2801. is the homologous term, whose correlatives are 120 men and 32 weeks, the correlatives of the unktown term are 360 men and 48 weeks.. Now the correlatives of the unknown term bave both a direct ratio :o it, therefore 360, 43, and 280, will be the factors of the dividend. Also the correlatives of the homologous term have both a direct ratio to it, therefore 120 and 32 will be the factors of the divisor, and the lum= 360 x 48 x 280

126cl.' The reafon of the rule is seen at 120 x 32 once, by analysing the ratios, of which the whole is compounded.

The nature and properties of logarithms are explained, by conceiving a geometrical proportion, 1:140:1te:ī+23, &c. in which e is fuppofid indefinitely fmall, so that the ratio of 1:1*e approaches nearer to equality than by any given distance. In this series, fome terms will evidlcitly coincide with others in the arithmetical progreilion, 1, 2, 3, 4, S. &c. and with the intermediate terms. Then e multiplied into the index of the term in the geometrical, is the logarithm of the number to which the term is equal in the arithmetical progretlion. Thus etiae is the logarithm of 1+2, 2c is the logarithm of it, and ne the logarithm of item. from this principle, all the rules in the use of logarithms

may

may indeed be derived ; but as the scientific editor has condes scended to introduce his readers to an acquaintance with this branch of knowledge, it is to be wished, for the sake of learners, that he had made the treatise complete, by shewing the relation which logarithms bear to the hyperbola, and the theories laid down on this subject by other authors. Perhaps howa ever he concluded, that no one would purchase fo large a work, who had not been previously instructed in the nature of its contents : and it is not necessary for us to say, that no astronomer will think his library complete, unless he has these tables of logarithms in his poilellion.

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A Sketch of a Plan to exterminate the casual Small-pox from

Great Britain; and 19 introduce general Inoculation : to which . is added, a Correspondence on the Nature of Variolous Contaa gion, with Mr. Dawson, Dr. Aikin, Profeffor Irvine, Dr. Percival, Profeffor Wall, Profeffor Waterhouse, Mr. Henry, Dr. Clark, Dio Odier, Dr. James Currie : and on the best llians of preventing the Small-pex, and promoting Inoculacion, al Geneva s with the Magifirates of the Republic. By John Huygarth, M. B. 2 Vols. 8v6. 8s. Boards. Johnson. 1993. As we are precluded, by the author's request, from any per

sonal observations, we can only remark, that the delign is à molt benevolent one; the views of the author judicious, and the general plan highly faluiary. That it is practicable; that, in a free country, the restraints will be patiently born; or that the general principles are always well established, may admit of some doubt. The former part must be ascertaincd by experience; but we shall follow Dr. Haygarth in the latter, with fome care, as, on these, the future operations will principally depend.

Dr. Haygarth's 'Inquiry how to prevent the small pox,' we noticed, with respect, in our LXth volume, p. 215. But we there stated a view of the question, which we must not now overlook.--As the small pox are, at times only, epidemic, as infection is, at other times, received with difiiculty, and the disease is communicated only in a few instances, there must be some circumstances in the state of the air and the constitus rion, which impede its communication or reception. This opinion we shall adhere to, and with more confidence, as the whole tenor of our author's, and his correspondents obferva. tions, support it. What this principle may be, we know not; but, if we establith its existence by facts, we need not be anxious to explain it. We know, to use a familiar illustration of

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Dr.

Dr. Franklin, that our china, if unsupported, will fall to the ground; and, though we do not know the cause of gravity, we can preserve our china without such inquiries.—But this question, with some other remarks on the nature of the variolous matter, will cccur in order.

A judicious Introduction, on the importance of these inquiries, first engages our attention; and Dr. Haygarth is fully of opinion, that the deaths from small pox are greater since the practice of inoculation has been common, than before. This is true from fact, and from theory, for the small pox was once the dreaded enemy, and avoided with care : it is now a familiar danger, and disregarded. In general, from an average of the numbers of deaths in France, Sweden, and four principal towns in England, about one in 7 dies of the small-pox; but probably before inoculation was practised, 60 in 100 escaped the disease, while not more than 5 in 100 now escape it, and four of these may not be susceptible of the infection., That many lives might be saved by a little care in guarding against the disease, is sufficiently obvious from numerous facts, mentioned in this part of the work.

One great principle, which seemed to be established in the inquiry, was the limited sphere of the infection from the variolus virus. This seems to be more fully established from the following facts, mentioned in the French translation of Dr. Haygartlı’s works. The experiments were tried by Dre O'Ryan.

I have established a house in the neighbourhood of this city (Lyons) for the reception of inoculated patients. Many people false. ly perfuaded that, a person infected by a good kind of small-pox, would have the distemper in the like favourable manner, brought their children to visit my patients with an intention that they should be infected by conmmunication with those who were inoculated.

i jster many unsuccessful attempts to convince these people of their error, feeiny that they rejected my offers to inoculate these children, and not doubting in spite of my arguments and expresa prohibition, that fooner or later they would seize another and perhaps a less favourablc opportunity, I exposed them to the following experiments, after they had undergone a due course of preparation,

"I placed a large dofiil of cotton, soaked in variolous matter, on the middle of an oval table whose least diameter was three feet: I fested fix children around it, three on each side of the table, in such a manner, that all were situated within half a yard of the insectious cotton. This experiment was sometinies made in the open air, fome: times in the house; I took care to renew, every second day, both the variolous matter, and the substance which contained it: I alternately used the poiton taken from the inoculated and from the

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