fortuitous charity, forbad these peti- To the Editor of the Monthly Magazine. tioners to ask an alms. Among this latter number, however, was a negro, whose figure seemed to speak the numiliating truth that he car ried his whole possessions on his person, and was equally an object of relief as the former characters. SIB. has laid before your readers two OUR correspondent, W. Singleton, instances of inaccuracy which occur ia Murray's Grammar, and submits an amendment worded by himself; the sentence alluded to, with the different inodes of reading are as follow: "He was more beloved, but not so much aduired as Cinthio.” The garb of poverty was the only attire that decked his sombre complexion; while his countenance pourtrayed the symptoms of a weak and afflicted body." He was more beloved than Cinthio, Distress, indeed, appeared to be the but not so much admired.” only inheritance of this son of Ham; yet the event fully manifested, that even in the breast of sable humanity dwelt those virtues which adorn the European and the Christian. Passing onward a few paces, still gazing attentively upon the sailors, he made a sudden pause, and, as if actuated by an impulse of more than common feeling, drew forth his mite and put into the hand of one of the beggars, accompanied by a look which beamed benevolence and pity; and, having tendered this gift at the shrine of charity, he walked away. "He was more beloved than Cinthio, but not so much admired as he.” The two former quotations are evi. dently ungrammatical, but the anendment, by Mr. Singleton, wants that conciseness of style which it was too evidently the intention of the author to adopt. Will you, therefore, allow me, without intending the least disparagement to your ingenious correspondent, to offer a fourth manner of reading the passage, by which the meaning is fully expressed, with more brevity than in either of the foregoing examples. "He was more beloved, but less admired than Cinthio. Woburn. E. T. PILGRIM. A SIR, My eve followed him as he departed, and I could not restrain the wish, that the bessing of Him that maketh rich might descend on this individual, who, from a fellow-feeling of poverty, could To the Editor of the Monthly Magazine. thus unasked divide his scanty pittance on a needy stranger, and whose conduct may well raise a blush in thousands, on whom Providence has bestowed competence or wealth. For surely, though I, if this poor man has a heart to give of his little store, himself a child of woe, how much more should those who abound in the means of alleviating wretchedness, administer to the wants-of the necessitous! If this untutored African, probably ignorant of pure and undefiled religion, can act a part so worthy the man, how ought those on whom christianity has shed its genial influence, to exhibit the philanthropy it inculcates. From this instance of real goodness therefore, may the stoical learn to cultivate kindness; the penurious character a spirit of liberality and, while it invites to a motive for promoting civilization, let not Britons longer withhold from Africa's race that mental culture which wil raise them, not in the scale of nature, for they are our equals in blood, but in the improvement of their moral character, and open to the savage a bright day of intellectual light. Evesham. JOHN MANN, DEEP consideration of Mr. Farey's incoherent letter on tuning piano-fortes, (v. xxxii. 424,) has not enabled me to discover in it any distinct meaning, nor praise-worthy intention. Let me inquire, what is the use of continually thrumming upon the quantity of alteration necessary in flattening the fifths, to produce the equal temperament, making a parade of what is so much known, and so easy to acquire? In tire practice of tuning, is the difficulty. A man, knowing by heart the whole of Mo zart's Violinschule, may, nevertheless, be a very inefficient performer on the violin. Let ́our “most able theorists" employ the tuning hammer themselves, and then teach us, if they can, a practical method of tuning a fifth with that nicety for which they contend. Let them do something more than speculate. The only better method of proceeding than Mr. Broadwood's, as far as we know, is tuning by a table of beats; but we have experienced, that the sounds of piano-fortes are of too short duration to admit of our counting the beats made in a given time. And an insuperable objection to the general practice of this method, (supposing it possible, possible'), would be, the necessity of having an assistant with a pendulum. As Mr. B.'s temperament is, acoiding to Mr. F.'s state neat, "one-fortieth of an undefined semitone," how can his “must able calculator" presume to tell as the number of beats of the fifths in that system? Further, the fifths which Mr. Ė. has gi beted with the assistance of two notes of ad niration, are just to the taste of the said theorist; for in a published letter of bis, which I have read, he has expressed his preference of fiths, whose beats are too rapid to be counted, to other fifths beating at a slower rate. With respect to any one system being, on the whole, better than another, these arithmetical gentlemen have never advanced any thing but their opinions: do not, therefore, let us dream that they are arguments. We have heard "the coarse and imperfect harmony" of the "isotonic" scale, and have thought it not intolerable; nay, we have felt it extremely pleasing. We have heard, and been highly gratified by Mr. Liston's perfect organ: the concords were exceedingly fine, as were also the "direct" discords; but the "inversions" of the latter, were detestable. It is hoped that Mr. Farey is in error, in believing Mr. Broadwood would impose on the world” willingly, or could, in this case, ignorantly. Without doubt, he knows what should be done in practice, and how far it can be done. In theory, our coachwheels are perfect circles; but in prac tice there are less or greater deviations, depending on the degree of mechanical skill of the workman. And it cannot be shown, that the wheelwright's labour would be much improved by a complete knowledge of the mathematical proper. ties of the circle. After all, I may have mistaken Mr. Farey's views. Such a mistake would be very excuseable, his mode of expression having obliged me to conjecture his meaning. If there be any meaning in the following sentence, it will be right that Mr. Farey should explain it,-"But where have they done so, or this system of Mr. B. ever before been heard of?" This sentence is a fair sample of his composition, and by no means selected as the worst I could find. December, 1811. A. BODORGAU. To the Editor of the Monthly Magazine.、 at that part of their extensive costliness which grows out of the imperfection of our roads and wheels, we shall be induced to respect the legislative endeavours that are making to remedy these imperfections; and each to lend what helping hand no may, in the same pursuit. Observation, theory, and experi ment, have been commendably resorted to; and these seem to lead, with strong conviction, to the establishment of the following points: First. That narrow wheels, in winter, cut our roads into ruts, or macerate them into s'ub. Secondly. That rounding our roads affords hardly any preventive against these mischievous effects; and that, therefore, the danger which they occasion, to stage coaches in particular, is incurred, without a requisite good effect in compensation for such danger. In very violent rains, such as hardly occur twice in a year, if the moment of the phenomenon is luckily caught, some rua of water down the sides of such rounded roads may be discerned, but never else; so that we endure a serious evil through 199 days, for the sake of a very trivial benefit from it on the 200th. A very experienced carrier, Mr. Deacon, has observed, that "the more roads are rounded, the more difficult it is for horses to travel; and the more likely they are to be sprained in the fetlock joint.” Thirdly, That, on hard roads, broad wheels, which would effectually prevent both ruts and slub, run equally well as the narrow wheels which occasion them; and, on soft roads, considerably better. But, in order to establish the full preference due to the broad wheel over the narrow, we are to look beyond the immediate comparison of the movements of the two: we are to go on and see how much better roads we shall have; and, consequently, how much better draught, at, perhaps, one quarter part of the present turnpike tolls. A few days in the year, from the peculiar state of the air and road, broad wheels clog: that is, they gather up the slub which, but for the narrow wheels, would hardly exist. The dust of summer would also be less. So that, by double consequence, road materials, which every year grow more and more distant, would be greatly increased in their duration. A wheel three yards in circumference has been made, with half that circumference narrow, and half broad: the wheel has been loaded, and its effect tried on a 1 gravel gravel walk, previously dug and rolled. The narrow half cut the walk to pieces presently the broad half made better what was good. Then, lifting the wheel, and giving it an exact half turn, and going over the same ground, the bad was soon made better by the broad half, and the good cut to pieces by the narrow half.-This wheel is in the Repository of the Agricultural Society. Fourthly, That the rounded road, ineffectual as it is to its purpose, is the grand argument urged against the adop tion of cylindric broad wheels with all their saving properties: but it may be truly observed, that cylindric broad wheels will find infinitely less inconvenience on rounded roads, if rounded roads must be persisted in, than the topheavy stage coaches do, which must take down their horses from their proper speed, as often, and often it is, that they have occasion to cross them. Fifthly, Another circumstance in wheels has been brought into comparison; namely, dished wheels, and wheels undished or vertical. In this comparison, it has been decisively found, that the horizontal axle arm forces on the vertical wheel, with considerably more ease to the drawing power, and in a more natural and undistorted movement, than the bent axle arm does the dished wheel; the load and height being the same in each. The dished wheel, to be sure, affords greater width to the waggon-bed, than the vertical one; but this additional stowage room is purchased at such a waste of costly power, as waggoners are not aware of. The use of the dished wheel in heavy waggons is general; and therefore, say they, dished wheels must be best, beyond all necessity of comparison by experiment. While these points have been in discussion, a sixth circumstance has been brought into view; namely, whether, or not, a carriage-wheel acts with any lever advantage as to its roling advance? It has been asserted by one gentleman, and denied by another. As I view the subject, I think the error of the no-lever opinion must be instantly seen, if we divide the progress work of the road, as the circumstances of the road actually divide it, into its natural parts and différences, hill-work, obstacle-work, and no work at all. On an horizontal smooth impalpable road such as a railway, there is (putting the friction of the axle quite out of view) hardly any thing to be done; neither hill-work, nor obstacle-work. The axlearm forces the wheel, by its prise on the ground to roll forward; by which operation a new supporting line, or prop, is, from instant to instant, brought under the load; this on a smooth impalpable road, is all that is done. Whereas, where we have obstacle-work to do, the axle-arm still forces the wheel to roll forward; and now we have in the wheel, in one moment, a mere supporting line, as before, and in the next, this line be comes both prop and lever; and this, exactly as the road changes, from smooth and impalpable, to obstacle-work. On a smooth impalpable ascent also, there is nothing but hill-work, answerable to the angle of the hill, to be done; no obstacle work whatever. Hill-work, most indubitably, can get no assistance from the lever of the wheel; non tuli auxilio Res eget: the pulling power inust suffice to all the exigency, by direct and sheer pulling. In obstacle-work, whether ou a level or on an inclined plane, it is exactly otherwise: the pulling power (mixed of the horses and of the Vis Inertia of the carriage and its load) being addressed to the axis of the wheel, the further this axis is from the encountered edge of the obstacle, the fulcrum in the case, (that is, the higher the wheels be,) the less power will suffice to transfer the load, residing as it does in the floor of the wheel, from the ground below up to the top of the obstacle: and the doing this, is what the obstacle exacts shall be done; and it is done, as to facility or difficulty, in exact lever ratio; the powerend of the lever, the center of the wheel, describing in air the usual power-end curve. Where, then, as on a rail-way, there is no obstacle-work, it is not true that there is no lever; but only that there is no lever-work: produce the obstacle, and the lever is instantly ready with its lever power to surmount it. The lion paces the woods with all his muscles relaxed: let occasion for their prowess spring up, and in the instant they are braced into requisite action. Tum demum movet Arma Leo. The occasion over, they are down again. I consider this question of the lever as by no means an idle one in the subject; for I have little doubt but it was the persuasion, that there was no lever as to the rolling advance of the wheel in any road, which led one of these gentlemen to give the weight of his opinion to the doctrine, that wheels from two to four feet diameter, would be best for practice. practice. Were this doctrine of low wheels generally acted upon, the error (as I hold it to be) would stand the kingdom in a very costly waste of horsepower. But, to return to the more immediate subject of this paper-The conclusion seems pretty strong, that the adoption of broad cylindric vertical wheels, running upon horizontal axle arms, on roads not rounded, would be of immense benefit to the carriers and commerce of the kingdom. But, notwithstanding these probabilities, there has appeared an hesitation to go into an Act of Parliament, that shall oblige the whole kingdom, bon grè mal grè, to take to these wheels. This hesitation must be praised; for it has its rise in the kindest intentions to wards the public, the object of the benefit. In this state of suspense, but with as full conviction of the advantages of the cylindric broad wheel plan, as experiment can give me, I wish to throw it down for consideration, whether some subordinate and partial measure may not, for a time, and for fuller trial, be gone into, as thus: Let it be enacted, that the county of Kent be taken for the scene of full experiment in the case. It is a terminating County, with no thoroughfare but through itself. Let, then, all the provisions of the broad-wheel and road bill pass into an Act, and forthwith take place in the county of Kent. The kingdom, it may be granted, might dislike the measure, were this Act to take place on them; and the most immediate reason is, that it would put them to a heavy expence to change, thus, the system of their carts and waggons, without being quite certain of the beneficial effects so confidently promised. The very same objection may be expected from the county of Kent; and I propose to meet it, and produce good will, by the following terins. Let a statement be authentically made, by each individual in the county, of the expence he incurs, by the change he is called on, for the sake of the king dom, to make; and, on the other side, let the residue of the kingdom, and with the exception of the county of Kent, be thrown under soine small tax (a small one, and for a very short time, would suffice) to make good this expence to the men of Kent. As for the roads of Kent, I should be inclined in the outset to do nothing with them, except noticing how rapidly they grew better, merely by the change of wheels thus purchased by the whole MONTHLY MAG. No, 228. kingdom, and submitted to, for a time, by one busy patriotic corner of it; a corner, by the way, well situated for the observing eye of the metropolis. There is little doubt, any where, but the roads of Kent would become and keep better than they have ever been known; and that the labour of draught would be found considerably less than before. And if two or three years shall prove it, there can be little doubt but the kingdom would ask, and almost ciamour, for a like revolution in wheels to be made over the whole of it. De re probabili fiat experimentum. WILLIAM MILTON. Heckfield, Hartfordbridge, To the Editor of the Monthly Magazine. A SIR, CCORDING to the view of the zodiac, published in your Magazine for March last, the beautiful figures on the Portland Vase, now in the British kind from the second division of the Museum, represent the passage of manzodiac, or the Saturnian age, to the third compartment, or the brazen age.* the Celestial Venus, seated under a The central figure is Venus Urania, or grape-vine, and resigning her last breath amidst the ruins which surround her. A male figure, representing mankind, is abbefore him. The celestial Venus casts sorbed in contemplation of the scene her dying eyes on Minerva, who, according to the following lines, is destined to be her champion: ης πελεκυς, θηριων ταμνων προθελυμνα καρηνα πανδερκούς εκάτης, † πάθεων ηνυσε γενέθλην "Whose axe, cutting off radically the heads of the beasts of all-seeing Hecate, has put an end to the origin of our sufferings." On the other side of this celebrated urn, Venus Thalassia, or the Terrestrial Venus, occupies the centre. She reclines under a pomegranate tree, while Cupid, with his bow and flaming torch, hovers over her. The goddess directs her blan * Cœlus reigns in the first compartment, beginning with the sign Taurus; Saturn reigns in the second compartment; Jupiter in the third, and Apollo in the last. + Orphic Hymn to Minerva, in the manuscripts at the British Museum, vol. 1752, page 13. that no law in nature, no principle of reason, nor even the profoundest veneration for the "ever-to-be-revered names" of the authors of a doctrine leading to such a conclusion, can possibly justify; and, to attempt to reconcile the idea of such a value to the mathematical mind, it should be admitted that one of the an nuitants can never die, but must live for ever and a day, and continue alive for ever and ever after that, which is preposterous. Will Philo-Mathematicus now aver, "that I have not demonstrated, that the eminent authors whom I have named, have pursued a wrong principle?" Let us now examine that gentleman's own principles, agreeably to the following declaration: "Mr. Hawes has forgotten, that, by attempting to overturn the present mode of estimating the probabilities of life, he tries to overturn the way by which his own numerators are calculated, which are nothing more than the sums of the fractions expressing the chances of living one, two, three, &c. years, to the end of the term named." I mentioned that I found the probability of a person aged fifteen years, continuing 9.5837 in being ten years, to be 10.0000 years, according to the observations of M. De Parcieux. The sum of the probabilities, 842 835 by the present mode, being + 848 848 comes 1 x2 The fluent of this -9 2n is the sum itself for the time r; and this, when x=n, bean, and gives the expectation of the assigned life, or the sum of all the probabilities just mentioned, for its whole possible duration." Thus taking up with a principle upon trust, without proof and without examination, and which is inadequate to produce the end proposed. I wonder Dr. Price should assume a mode so extremely circuitous, to attain an object which it can never reach; and the more especially when the direct path leading to such an object is as plainly to be seen as the sun at noonday. It may be proper to remark, that the adherers to the generally-received doctrine, do make their probabilities of the duration of life to consist of persons without time, and those persons converted into fractions denoting chances; whereas my probabilities of the duration of life do consist of persons and time, and that time converted into fractions denoting periods. Here then are two opinions on the fundamental principles of the science, which should be thoroughly investigated to enable us to come What could be thought of the conduct to a right knowledge of the subject. of that court of aldermen, who, after inbring the prices only into the account, specting the meal-weighers' returns, should and leave the quantities wholly out of the reckoning, and then proceed to settle the assize of bread by the tossing-up of a half-penny, or the casting-forth of a die? Would not "the future provision of thousands, and the valuation of very extensive property," he materially affected thereby? To ascertain the probability of the duration of a life, and to find the average price of a peck of meal, are similar questions, and the answers to them should be respectively adjusted after the same manner; for to proceed otherwise |