206 Remarks on the Game Laws. every head of game for their own amusement, and that the farmer's crop is devoured, and he is compelled to warn off even his own friends." It seems but common sense, that if the proprietors of lands preserve the game, they should be most entitled to it; neither can the farmer or tenant complain of the hardship of their being requested (it is ridiculous to say compelled) to warn off persons, even their own friends, because the tenant promises and agrees to warn off all persons on his taking the farm; and it is only performing this promise when called upon, which is very seldom required, when the tenant, and particularly his friend, are accustomed to sport in a proper manner. As to the devouring his crop, it generally forms a consideration with the tenant on taking the farm. But I particularly beg to observe that it is not the GAME LAWS on these points that are to be complained of as a bardship, it is the law of the tenant's own signing with his landlord. The next assertion is," that no person can be followed by a dog without being insulted by gamekeepers." Here PUBLICOLA again proves himself totally unacquainted with the game laws to suppose gamekeepers are vested with any such authority by them; and if he will trouble himself to look into those statutes, he will find that this vexatious and troublesome man, the gamekeeper, is very little spoken of throughout the whole, except in the authority to be granted to him to kill game for his Jord, &c. I think it quite unnecessary to reply very particularly to the frivolous hardship mentioned by PUBLICOLA of respectable females being debarred from amusing themselves in gathering wild flowers, for I cannot possibly suppose any respectable females would be found wandering out of the regular footpaths in secluded coppices or plantations where game is usually preserved: and as to cottagers' children not being allowed to gather a handful of berries for a pudding, it is a complaint too frivolous to reply to. All these overstrained cases of pretended hardships brought forward by PUBLICOLA, as well as his presumption that the game lazos render landed proprietors OMNIPOTENT, are so vaguely set forth, and so weakly supported, that they do not require this paper to refute them. But it is so obvious that the present laws (from the numerous offenders lately detected) are NOT SUFFICI• · [April 1, ENTLY SEVERE to deter the poacher, who nightly steals the game wholesale, either from the lord of the manor, whose lands and plantations protect it, or from the farmer, whose corn feeds and supports the game when young; or perhaps we had better say from the fair sportsman, who pays an annual tax to government for the privilege of killing game: and these poachers afterwards rob their em plovers (if they have any work the next day) by pretending to do a day's labour after their nightly toils. Then, sir, to conclude, I beg you will allow me to mention (for the consideration of landed proprietors) two kinds of punishment that (if enacted by law), would, in my opinion, much better stop this growing evil; for since daily labour has become scarce, the idle poacher finds himself thrown out of work, and thence the evil has greatly increased.The one is, that any persons found wandering out of the footpaths in plantations or lands where game is preserved after daylight until daylight again (and especially if detected poaching), should be taken before two magistrates to account for their being so found; and if they do not give a satisfactory account, the magistrates to be empowered to order such persons to be publicly whipped the next market day in the nearest market town; and on the second offence, to commit the offender to Bridewell, to be tried at the quarter-sessions, and if guilty, transported for seven years. 2dly. That no person shall buy as well as sell any game under the penalty of 10. at least for each offence, and that the buyer or seller informing may be good evidence to convict, and thereby exempted from penalty, and have a moiety of the same on conviction. VERITAS. Feb. 5, 1816. MR. EDITOR, AS you were kind enough to insert in your number for January some thoughts of mine on the subject of promoting, even in an imperfect degree, the comforts of the poor, I take the liberty of troubling you with a few more observations on the same subject. It would be highly desirable to know some way of securing to the poor the fruits of their industrious savings during a period of many years. A conscientious individual would be scrupulous of receiv. ing the money, lest he should at any future time be unable to repay it; or lest unjust insinuations might be thrown out as to his motive for setting on foot a 1816.] On ameliorating the Condition of the Poor-Major André. 207 charitable institution of this description. The frequent failures of country banks render it hazardous to put the money of the poor in them, there remain therefore only the public funds; and if some mode could be devised for facilitating the purchases to be made in them, for converting the interest into principal, &c., it would be of great advantage. Some of your readers perhaps can state the method pursued in those Saving Banks that have been already established; any one who does so, may be sure he is perforining an important service; as the difficulty of securing what the poor lay up has alone prevented the institution of a Saving Bank in one particular district. Connected with the scheme of securing to the poor their hard-earned gains as a provision for declining life, is that of providing for them an increase of cheap and nourishing food. It is a melancholy fact, that a great proportion of the lahouring poor are without that solid nutriment which can qualify them for exertion as labourers. If not dieted by their employer, their food is bread and cheese, without any beer. Whether this be food of a proper description for a hard-work jag inau, I leave to be answered by those who, without undergoing any extreme bodily or mental labour, are yet in the habit of faring sumptuously every day, and expending upon their appetites sums, a small proportion of which would go far towards the comfortable maintenance of the industrious cottager and his family. A benevolent society has been lately established in London for the supply of fish in greater abundance, not only in the metropolis, but throughout the kingdom. Could their benevolent intentions be carried into full effect, I conceive that the welfare of the nation would be augmented in a degree neither smali nor unimportant; the fisheries, those nurseries of British seamen, would be encouraged, and an employment opened for multitudes of disbanded sailors, who must otherwise have recourse to dishonest practices, or be induced to enter into the service of nations who may at no remote period become our foes; a cheap and nutritious article of food would be provided for the lower orders, who are at present almost precluded from purchasing it. In touching on this subject I may be excused for stating, that while mackarel is procured in such quantity at particular maritime stations as to be had for nothing, it is at no great distance from the coast, that is to say, 30 or 40 * miles island, sold at a price that renders it impossible for the cottager to obtain it. In the year 1812, the distress of the manufacturers in Spitalfields was considerably alleviated by a seasonable supply of mackare!, chiefly through the exertions of this society. This fish was retailed at 1d. a-piece, and such was the good effect of the measure, that butcher's meat, if I am not misinformed, fell 2d. in the pound in this part of London alone. Nor will the benevolent mind rest satisfied with attending to the bodily wants of the necessitous; its attention will be directed to the moral and religious concerns of the poor. It will cherish the parish schools as an useful, nay, most necessary appendage to the parish church; it will labour to diffuse principles of order, loyalty, sobriety, and religion among the rising generation; and in such occupation, it will seek its peculiar and most appropriate gratification. I have only to add, that a person who sets out with a desire to do good, must count the cost before he begins-must not be surprised if he meet with no co-operation from many to whom he imparts his schemes must even reckon on encountering the sneers and taunts of those who are resolved to do nothing-who are ever ready to start difficulties and objections who anticipate nothing but failurein short, who are the stedfast foes to exertion, because it is a tacit reproach on their own selfishness and supineness.--I am, &c. CLERICUS. * Feb. 14, 1816. MR. EDITOR, In the account of Major John André among the collections of your amateur correspondent, that gallant and unfortunate officer is said "to have been hung as a spy by the command of General Arnold." How such a gros- blunder could have dropped from the pen of any person at all acquainted with the English history I cannot conceive; and permit me to say, that the insertion of it in your respectable miscellany, betrays a casual want of care and observation, which it will be well in future to guard against. Major André was sacrificed inhumanly by the American commander in chief, the celebrated Washington, when engaged on a mission to General Arnold, who had a secret intention of passing over to the British lines. Arnold escaped, and poor André perished; but the former was despised through life, while the memory of the sufferer has bocu embalmed by the pity ant tears of 208 Mr. Taylor on the Philosophy of Plato. all who have read his tragical history, MR. EDITOR, AS the doctrine of the periodical mutation of things in the sublunary region forms one of the most interesting dogmas of the philosophy of Plato, I send you for insertion in your valuable Magazine the following elucidation of it. which I trust will be acceptable to all your mathematical and philosophical readers. The passage in which this doctrine is contained is in the Republic, and is as follows: "It is indeed difficult for a city thus constituted to be changed; but as every thing which is generated is obnoxious to corruption, neither will such a constitution as this remain for ever, but be dissolved And its dissolution is this: not only with respect to terrestrial plants, but likewise in terrestrial animals, a fertility and sterility of soul as well as of body takes place when the revolutions of the heavenly bodies complete the periphery of their respective orbits, which are shorter to the shorter-lived, and contrarywise to such as are the contrary: and with reference to the fertility and sterility of our race, although those are wise that you have educated to be governors of cities, yet will they never, by reason in conjunction with sense, observe the proper seasons, but overlook them, and sometimes generate children when they ought not. But the period to that which is divinely generated is that which the perfect number comprehends; and to that which is generated by man, that period in which the augmentations surpassing and surpassed, when they shall have received three restitutions and four boundaries of things assimilating and dissimilating, increasing and decreasing, shall render all things correspondent and effable; of which the sesquitertian progeny, when conjoined with the pentad, and thrice increased, affords two harmonies. One of these, the equally equal, a hundred times a hundred; but the other, of equal length indeed, but more oblong, is of a hundred numbers from effable diameters of pentads, each being deficient by unity, and from two numbers that are ineffable, and from a hundred cubes of the triad. But the whole geometric number of this kind is the author of better and worse generations; of which when our governors being ignorant, join our couples together unseason [April 1, ably, the children shall neither be of a good genius nor fortunate." My comment on this passage is as follows:-All the parts of the universe are unable to participate of the providence of divinity in a similar manner, but some of its parts enjoy this eternally, and others temporally; some in a primary, and others in a secondary degree: for the universe being a perfect whole, must have a first, a middle, and a last part. But its first parts, as having the most excellent subsistence, must always exist according to nature; and its last parts must sometimes subsist according to, and sometimes contrary to nature: hence the celestial bodies, which are the first parts of the universe, perpetually sub-ist according to nature, both the whole spheres and the multitude co ordinate to these wholes; and the only alteration which they experience is a mutation of figure, and variation of light at different periods;-but in the sublunary region, while the spheres of the elements remain, on account of their subsistence as wholes, always according to nature, the parts of these wholes have sometimes à natural, and sometimes an unnatural subsistence; for thus alone can the circle of generation unfold all the variety which it contains. The different periods in which these mutations happen are called by Plato, with great propriety, periods of fertility and sterility; for in these periods a fertility or sterility of men, animals, and plants, takes place; so that in fertile periods mankind will be both more numerous, and, upon the whole, superior in mental and bodily endowments to the men of a barren period: and a similar reasoning must be extended to animals and plants. The so much celebrated heroic age was the result of one of these fertile periods, in which men transcending the herd of mankind both in practical and intellectual virtue abounded on the earth. With respect to the epithet divinely generated, it is well observed by the Greek scholiast, "that Plato does not mean by this either the whole world, though the epithet is primarily applica ble to it, nor the celestial regions only, nor the sublunary world, but every thing which is perpetually and circularly moved, whether in the heavens or under the moon; so far as it is corporeal calling it generated, (for no body is selfsubsistent,) but so far as it is perpetually moved, divine, for it imitates the most divine of things, which possess an ever 1816.] Mr. Taylor on the Philosophy of Plato. vigilant life. But with respect to the perfect number mentioned here by Plato, we must not only direct our attention to a perfect number in vulgar arithmetic, for this is rather numbered than number, tends to perfection, and is never perfect, as being always in generation,--but we must survey the cause of this number, which is indeed intellectual, but comprehends the definite boundary of every period of the world." With respect to the numbers in this extract from the Republic, the obscurity of them is so great as to have become proverbial among the ancients, and they are not elucidated in any of those invaluable remains of Grecian philosophy which have survived to the present time. What follows is an attempt to remove the veil under which they have been so long concealed. In the first place, then, let us consider what Plato means by augmentations surpassing and surpassed; things assimilating and dissimilating, increasing and decreasing, correspondent and effable. Augmentations surpassing, are ratios of greater inequality, viz. when the greater is compared to the lesser, and are multiples, superparticulars, superpartients, multiple-superparticulars, and multiple-superpartients. But multiplex ratio is when a greater quantity contains a less many times; superparticular ratio is when the greater contains the less quantity once, and some part of it besides; and superpartient ratio is when the greater contains the less quantity once, and certain parts of it likewise. Again, multiple-superparticular ratio is when the greater contains the less many times, and some part of it besides; and multiple-superpartient ratio is when the greater contains the less many times, and also some of its parts. But augmentations surpassed are ratios of less inequality, viz. when the less is compared with the greater quantity; as for instance, submultiples, subsuperparticulars, subsuperpartients, and those which are composed from these three. Those numbers are called by Plato assimilating and dissimilating which are denominated by arithmeticians similar and dissimilar; and similar numbers are those whose sides are proportional, but dissimilar numbers those whose sides are not proportional. But he calls those numbers increasing and decreasing which they denominate abounding and dimi As perfect numbers are those which are equal to their parts collected into one, such as 6 and 28, (for the parts of the former NEW MONTHLY MAG.-No. 27. 209 nished, or more than perfect and imperfect. Things correspondent and effable, are boundaries which correspond in ratio with each other, and can be expressed in numbers either integral or fractional, -such as these four terms or boundaries, 27, 18, 12, 8, which are in sesquialter and subsesquialter ratios; since these mutually correspond in ratio, and are effable: for effable quantities are those which can be expressed in whole numbers or fractions; and in like manner ineffable quantities are such as cannot be expressed in either of these, and are called by modern mathematicians surds. But it In the next place, let us consider what we are to understand by the sesquitertian progeny when conjoined with the pentad, and thrice increased, affording two harmonies. By the sesquitertian progeny, then, Plato means the number 95: for this number is composed from the addition of the squares of the numbers 4 and 3, which form the first sesquitertian ratio, (viz. 25,) and the number 70, which is composed from 40 and 30, and therefore consists of two numbers in a sesquitertian ratio :-hence, as 95 is composed from 25 and 70, it may with great propriety be called a sesquitertian progeny. This number conjoined with 5, and thrice increased, produces ten thousand and a million; for 100 × 100—10,000, and 10,000 × 100—1,000,000. must here be observed, that these two numbers, as will shortly be seen, appear to be considered by Plato as analogous to two parallelopipedons, the former, viz. ten thousand, being formed from 10 x 10 x 100, and the latter from 1,000 x 10 x100. These two numbers are called by Plato two harmonies, for. the following reason:-Simplicius, in his commentary on Aristotle's book, De Calo, informs us that a cube was denominated by the Pythagoreans harmony, because it consists of 12 bounding lines, 8 angles, and 6 sides; and 12, 8, and 6, are in harmonic proportion; for the difference between 12 and 8 is to the difference between 8 and 6 (i. e. 4 is to 2) as the first term to the third, viz. as 12 to 6, which, as is well known, is the law of are 1, 2, 3, which are equal to 6, and the parts of the latter are 14, 7, 4, 2, 1, the aggregate of which is 28,) so a diminished number is that which is less than the sum of its parts, as s whose parts are 4, 2, 1, the aggregate of which is 7; and an abounding number is that which is exceeded by the sum of its parts, as 12, whose parts are 6, 4, 3, 2, 1, the sum of which is 16. VOL. V. 2 E 210 Mr. Taylor on the Philosophy of Plato. harmonic proportion. As a parallelo- Again, when he says, "that the number 1,000,000 consists of a hundred numbers from effable diameters of pentads, each being deficient by unity, and from two that are ineffable, and from a hundred cubes of the triad," his meaning is as follows. The number 1,000,000 consists of a hundred numbers, (i. e. of a hundred such numbers as 10,000,) each of which is composed from effable diameters of pentads, &c. But in order to understand the truth of this assertion, it is necessary to observe, that there are certain numbers which are called by arithmeticians cffable diameters. These also are twofold: for some are the diameters of even squares, and others of odd squares; and the diameters of effable even squares, when multiplied into themselves, produce square numbers double of the squares of which they are the diameters, with an excess of unity. Thus, for instance, the number 3 multiplied into itself produces 9, which is double of the square number 4, with an excess of unity; and therefore 3 will be the diameter of the even square 4. But the diameters of effable odd square numhers are in power double of the squares of which they are the diameters, by a deficiency of unity; thus the number 7, multiplied into itself, produces 49, which is double of the odd square number 25 by a deficiency of unity. This being premised, it follows that the number 10,000 will consist of a certain number of heptads; for 7 is the effable diameter of the square number 25: and from what follows it will be found that this number is 1986. But the number 10,000 not only consists of 1386 heptads, but Plato also adds," from two numbers that are in effable," viz. from two numbers the roots of which cannot be exactly obtained nor expressed, either in whole numbers or fractions, such as the roots of the numbers 2 and 3. The numbers 15 and 13 [April 1, are also of this kind; and as we shall see, appear to be the numbers signified by Plato. In the last place, he adds, "and from a hundred cubes of the triad," viz. from the number 270; for this is equal to a hundred times 27, the cube of 3. The numbers, therefore, that form 10,000 are as below: 1386 7 9702 15 13 270 10,000 viz. 1386 heptads, two ineffable numbers, (15 and 13,) and a bundred times the cube of 3, i, e. 270: and the whole geometric number is a million. One Massey, who published a Greek and Latin edition of The Republic, at Cambridge, in the year 1713, observes respecting this most obscure passage, "that what Plato distinctly means by it he neither knows nor cares; since it ap pears to him that what affords so much difficulty has but little weight."-" Quid in hoc loco distinctè velit Plato profecto nescio, nec curo. Quod enim tantum difficultatis præbet minimum ponderis habere suspicor." This is in the true spirit of a mere verbal critic, viz. of a man of no intellect, and of great impa dence. The reason also which he assigns for this carelessness is admirable; since on the same account the higher parts of the mathematics ought to be rejected. What Achilles, however, says of those in Hades, may be aptly applied to such men as these: Ω πόποι, η ρα τις εστι και ειν Αίδαο δόμοισι Iliad, lib. xxiii, v, 123. Such is the critic in the Monthly Review, who takes occasion, (I am told) in reviewing the translation of the Paraphrase of an Anonymous Greek writer on the Nicomachean Ethics of Aristotle, by Mr. Bridgman, to defame me,-because Mr. B., in the preface, had, from motives of gratitude, acknowfrom me in the translation of that work; for ledged that he derived considerable assistance this reviewer begins with saying, "We boded no good of the present performance, when we saw the name of Mr. Thomas Taylor in the writer's preface."-See the malevolence, ignorance, and pride, of these Monthly Reviewers fully exposed at the end of my translation of Proclus on Euclid. |