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Where there are feminaries inftituted for educating children in habits of industry, the poor fhould be compelled to fend their children to them in thofe parishes where they refide; 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 fettlement.

• These terms being complied with; the poor might, without fear of their becoming vagrants, or neglect of induftrious habits in the rifing generation, be permitted to feek their bread, by means of labour and industry, wherever good wages venable them best to find it; and a foundation of a ¡und would be laid for their maintenance when in diftrefs, which would be productive in proportion as the number of the migrants increafed, or in other words, as the total fum earned by the industry of the nation increased.'

Our author obferves, that there feems uniformly one false prineiple, inconfiftent with freedom, conflantly pervading the laws refpecting the poor, exclufive of the restraint which the law of certificates occafions. The principle alluded to, is the right claimed by the officers of a parifh to remove those whom they may deem likely to become chargeable; a degree of power which, Mr. Ruggles thinks, may be perverted to the purpofes of caprice, intereft, or private refentment; 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 increafe of the poor, is that of eftablishing schools of induftry for the children of labouring people. This falutary expedient has been adopted in different parts of the country, in fome with more, and in others with lefs obvious advantage; but under due regulations, fuited to the local circumftances of the different diftricts, it might doubtlefs be rendered of extraordinary benefit to the interefts of the public.

The obfervations in the prefent volume, relating almost entirely to remarks or propofals fuggefted 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. Thofe therefore who wifh for more particular information, we muft neceffarily refer to the work; where they will be fatisfied with the diligent refearches, the just remarks, and the judicious reflections of the author, whofe fentiments on this important fubject are worthy the attention of the public.

Table

Table of Logarithms of all Numbers from One to 101,000, aml of the Sines of Tangents to every Second of the Quadrant, by Michael Taylor, Author of the Sexagefimal Table. 41. 45. Sheets. Wingrave.

4to.

THE labours of Napier, Briggs, Vlacq, and Gardiner, are well known to every perfon engaged in mathematical pursuits, and the invention of logarithms, though they were brought nearly to perfection in the author's lifetime, has given rife to the fuccefsful exertions of others in the fame ca reer. By their labours we had tables for fines and tangents to every ten feconds of the quadrant, and we feemed to stand in need only of a further improvement for every second of the quadrant, to make them anfwer all the purposes for which they could be introduced into aftronomy. This work was undertaken by Taylor, who was interrupted by death in the progress of it, and the five laft pages of logarithmick fines of tangents, which alone remained unfinished at the prefs, were printed off under the inspection of the present astronomer royal.

The two firft chiliades of numbers occupy two pages. The other numbers, from 1000 to 101,000, are with their lo garithms, differences of proportional parts diftributed, fo as to make two tables in every page. In the fame manner for the fines, cofines, tangents, and cotangents, there are two tables in each page: the one page being dedicated to the fines and cofines, the oppofite 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 fe 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 first decimal places for each minute the other five places are found oppofite to each fecond; at the bottom of the table are the minutes correfponding to the degrees 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 induftry of the compiler, and the character of the editor.

Prefixed to the tables is an explanation of them by the editor, who has alfo added examples of great ufe and importance to the aftronomer and the navigator. His mode of finding the true distance of the ftar from the moon's centre, is particularly neat, and may, by the eafe with which it is performed, bring the nautical almanack into more general ufe among failors than it has hitherto obtained. Every cafe of plane and fpherical triangles is folved, fo that the practical aftronomer C. R. N. AR. (XI.) May, 1794

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does not require the affitance of any other book of trigonometry. Inftances are given alfo from various branches of arithmetic, and the rule of proportion adopted, as it is not generally known, may be ufeful to many of our readers.

It is cuftomary to lay down two rules for proportion in books; this is general and will fatisfy all cafes. Among the terms of the queftion, that, which is of the fame kind with the unknown term, is called the homologous term, the others are called correlatives, either of the unknown or of the homologous 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 increase or decreafe as they increase or decrease themselves; of the homologous term, and of thofe correlatives of the homologous term, which bear an inverfe ratio to the fame, that is, which make the homologous term decreafe or increafe, as they themfelves increase or decrcafe. And the divifor will be compofed of thofe correlatives of the unknown term, which bear an inverfe ratio to it, and of thofe correlatives of the homologous term which bear a direct ratio to it.

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Example. If 280!. ferve 120 men for 32 weeks, how much will ferve 360 men for 48 weeks? Anfwer, 12601.

'The unknown term is a fum of money, therefore 280l. is the homologous term, whofe correlatives are 120 men and 32 weeks; the correlatives of the unknown term are 360 men and 48 weeks. Now the correlatives of the unknown term have both a direct ratio to it, therefore 360, 48, and 280, will be the factors of the dividend. Alfo the correlatives of the homologous term have both a direct ratio to it, therefore 120 and 32 will be the factors of the divifor, and the fum 360 × 48 × 280

120 X 32

126cl.' The reafon of the rule is feen at once, by analyfing the ratios, of which the whole is compounded.

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The nature and properties of logarithms are explained, by conceiving a geometrical proportion, 1:1+e:1+ e2: 1 + &c. in which is fuppofed indefinitely fmall, fo that the ratio of 1:1+e approaches nearer to equality than by any given diftance. In this feries, fome terms will evidently coincide with others in the arithmetical progreffion, 1, 2, 3, 4, 5, &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 progreffion. Thus e+1e is the logarithm of 1+e, 2e is the logarithm of 1+e, and ne the logarithm of 1+e".

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From this principle, all the rules in the ufe of logarithms

may

may indeed be derived; but as the scientific editor has conde fcended to introduce his readers to an acquaintance with this branch of knowledge, it is to be wifhed, for the fake of learners, that he had made the treatife complete, by fhewing the relation which logarithms bear to the hyperbola, and the theories laid down on this fubject by other authors. Perhaps how 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 neceffary for us to fay, that no aftronomer will think his library complete, unless he has thefe tables of logarithms in his poffeffion.

A Sketch of a Plan to exterminate the cafual Small-pox from Great Britain; and to introduce general Inoculation: to which is added, a Correfpondence on the Nature of Variolous Contagion, with Mr. Dawfon, Dr. Aikin, Profeffor Irvine, Dr. Percival, Profeffor Wall, Profeffor Waterboufe, Mr. Henry, Dr. Clark, Dr. Odier, Dr. James Currie: and on the best Means of preventing the Small-pox, and promoting Inoculation, at Geneva with the Magifirates of the Republic. By John Haygarth, M. B. 2 Vols. 8vo. 8s. Boards. Johnfon. 1793.

AS

S we are precluded, by the author's request, from any perfonal obfervations, we can only remark, that the defign is a moft benevolent one; the views of the author judicious, and the general plan highly falutary. 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 fome doubt. The former part must be afcertained by experience; but we fhall 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 fmall pox,' we noticed, with refpect, in our LXth volume, p. 215. But we there ftated a view of the queftion, which we must not now overlook. As the fmall pox are, at times only, epidemic, as infection is, at other times, received with difficulty, and the difcafe is communicated only in a few inftances, there muft be fome circumstances in the state of the air and the conftitution, 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 correfpondents obfervations, fupport it. What this principle may be, we know not; but, if we establish 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 unfupported, will fall to the ground; and, though we do not know the caufe of gravity, we can preferve our china without fuch inquiries.-But this queflion, with fome other remarks on the nature of the variolous matter, will occur in order.

A judicious Introduction, on the importance of these inquiries, firft engages our attention; and Dr. Haygarth is fully of opinion, that the deaths from fmall pox are greater fince 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 difregarded. 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 fmall-poxi but probably before inoculation was practifed, 60 in 100 efcaped the difeafe, while not more than 5 in 100 now escape it, and four of these may not be fufceptible of the infection.. That many lives might be faved by a little care in guarding against the difeafe, is fufficiently obvious from numerous facts, mentioned in this part of the work.

One great principle, which feemed to be established in the inquiry, was the limited fphere of the infection from the variolus virus. This feems to be more fully established from the following facts, mentioned in the French tranflation of Dr. Haygarth's works. The experiments were tried by Dr. O'Ryan.

I have eftablished a houfe in the neighbourhood of this city (Lyons) for the reception of inoculated patients. Many people falfely perfuaded that, a perfon infected by a good kind of fmall-pox, would have the diftemper in the like favourable manner, brought their children to vifit my patients with an intention that they should be infected by communication with those who were inoculated.

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After many unfuccefsful attempts to convince thefe people of their error, feeing that they rejected my offers to inoculate these children, and not doubting in spite of my arguments and exprefs prohibition, that fooner or later they would feize another and perhaps a lefs favourable opportunity, I expofed them to the following experiments, after they had undergone a due courfe of preparation.

I placed a large doffil of cotton, foaked in variolous matter, on the middle of an oval table whofe leaft diameter was three feet: I feated fix children around it, three on each fide of the table, in fuch a manner, that all were fituated within half a yard of the infectious cotton. This experiment was fometimes made in the open air, fome. times in the houfe; I took care to renew, every fecond day, both the variolous matter, and the fubftance which contained it: I alternately ufed the poifon taken from the inoculated and from the

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