1815.] MR. EDITOR, Mr. Taylor on Infinite Series. I AM much obliged to your Corre spondent Philomath for his endeavouring to solve the instances proposed by me in your magazine, of deficiency in the aggregates of infinite series. But though I have no doubt his reply to me is exactly such as would have been made by the greatest of modern mathematicians, it is certainly by no means satisfactory, as I trust the following remarks will abundantly evince. 215 1-1) 1 (=1+1+1+1+1, &c. and, consequently, 1 divided by 1+1+1+1 +1, &c. gives 1—1, relative nothing, or an infinitely small quantity. By no means, therefore, must it be admitted, as Philomath says, “that nothing divided by any number inust give nothing for the quotient;" for this assertion does not apply to relative but to absolute nothing. And 1-1, -1, and other expressions of a similar kind, while they remain in this form, are something belonging to quantity, i. c. are infinitely small quanti ties, as I have largely shewn in my Ele= ments of the True Arithmetic of Infinites. Your correspondent says that "I have combined an imaginary quotient with the true quotient," when I assert that 1-1+1-+-, &c. is the true quo tient of 1 divided by 2+1-1. Now, that this is the true quotient is indisputable, if it be admitted to be universally true, that in all legitimate division the divisor multiplied by the quotient is equal to the dividend; and that this must be admitted I think no mathemati--+, in the above instance, ought, cian will deny. Let this quotient, then, be multiplied by 2+1-1, as follows: And it is evident that the product is 1, the dividend. For I am sure I need not inform Philomath that in the multiplication of an infinite series the product is to be collected in this way; as this is demonstrated by Saunderson, in the first volume of his Algebra. To which may be added, "that if no thing divided by any number must give nothing for the quotient," the remainder, when divided by 2+1-1, to give no thing, on the supposition that 1+1 is absolute nothing. So far, however, is this from being true, that the sum of the terms of the quotient, when continued to infinity, is++, &c. Nor will the sum of the terms, in whatever way they may be collected, be absolute nothing. 1 8-2 In short, Sir, I contend that 4-1+}— -, &c. is as much the true quotient of 1 divided by +1-1, as)—1 2+1; and that the latter is only the true +}¬¿+4—¿, &c. is of 1 divided by quotient, as well as the former, because in either case the quotient multiplied by the divisor is equal to the dividend. Till it can be shewn that this postulate is not universally true, some other method of solving the difficulty than that of" taking the remainder into the account" must be adopted. Besides, Sir,the reasoning of Philomath does not apply in any respect to other instances of a similar nature. Thus, in the following instance, 3+2-1) 1 (−2+3~8; +91-41}, &c. 1+1-4 But to say, Sir, as your correspondent does, that because the remainder in dividing 1 by 2+1-1 is -1+1, and the quotient is, "the sum of all the terms in the quotient, (after 1,) to whatever extent the division may be carried, will be nothing, because nothing divided by any number must give nothing for the quotient," appears to me not a little extraordinary. For Philomath is doubtless well acquainted with the distinction made by Dr. Cheyne, in his Philosophical Principles of Religion, between relative and absolute nothing; that, as the Dr. says, in p. 8, of the second part of the first quotient is 4, and the remainder that work,"relative nothing is an infi- . But is not the true quotient; nitely little quantity;" and "that unity divided by an infinite number of unities makes the quotient relative nothing." That this indeed is most true is at once evident. For it is well known that the and, consequently, the sum of the terms after it is not imaginary, but in conjunction with forms the true quotient. Here, however, when the sum is collected by making an actual subtraction and addi◄ 216 The Philosophy of Nature and the Monthly Review. [April 1, tion of the terins, the quotient will be equal to, instead of 1; and yet while the quotient remains in its present form, and is multiplied by the divisor, it produces the dividend. J I shall only observe farther at present, that the following example incontrovertibly proves the existence and evinces the power of what Dr. Cheyne calls relative nothing. country clergyman may be permitted to give an opinion on a subject of taste, I should at once be bold enough to assert, that an admiration of what God has been pleased to grant us, through the medium of Nature, is not only not a sign of barbarism, but, on the contrary, that it operates as a decided evidence of a rich, elegant, and highly-cultivated mind. The article in which the above pas 2—1)1+1+1+1+1,&c. ad infin.({+}+? sage appears, is a review of the Philo ++, &c. MR. EDITOR, IN the number of the Monthly Review for last December, a passage occurs which is so extraordinary, that I regard it as almost an imperative obligation in its editor to give an explanation; since, in the present state of society, I should suppose it to be called for by the unanimous voice of all his readers: for, as the passage now stands, it is not only a direct affront to all lovers of landscape, but a premeditated insult even to God himself. The passage alluded to is that in which the reviewer says, that "the love of scenery, particularly of the bolder cast, characterizes either a philosopher or a barbarian;" or words to that effect. Surely it would require the subtlety of a Thomas Aquinas to point out even one analogy between a philosopher and a barbarian; and how an ardent admiration of Nature, particularly of her sublimer features, can be said to associate us with barbarians, deranges all my ideas of religious feelings as well as of common sense. One thing I can assure the learned writer in the Monthly Review, from my own experience, and that is, that bar barians have no more taste for landscape thau an elephant, a wasp, a monkey, or a whale; in fact, no more taste for natural beauty than the reviewer himself; and that, I think, is saying a great deal of truth in few words. It a sophy of Nature,-a work which I bave perused more eagerly, and with greater pleasure, than any book within the last four or five years. The review pays the writer of that work some laboured and reluctant compliments; but the whole is written on so unphilosophical a principle, that the praise, so niggardly bestowed, can, I should suppose, give the author no pleasure. For my own part, I will frankly confess, that I was utterly astonished as well as disgusted that the editor should have committed such a learned and beautiful production to the care of such a feeble, ignorant, and tasteless reviewer. I think, too, it was a little impolitic in the editor to admit such a wretched piece of criticism into the society of articles so much better written, since it serves to open the eyes of the public as to the fallibility of reviews in general, when they see how little learning, and how little intellect, is required to form a writer, even in the Monthly Review, which, it must be confessed, is not the worst of the brotherhood. Should the review in question meet the learned writer of the Philosophy of Nature, while sailing down the Rhone, or sauntering on the banks of the Loire, as it is possible it may do, he will naturally call to mind Mr. Locke's Essay on the Gradations of Beings. Ascending from the caterpillar and the beetle, from fishes, birds, and animals, up to man, he will doubtless continue his sublime speculation on the gradation of intellects, till he arrives at that gigantic or der of intellectual beings, at the head of which towers like a pyramid that most dreadful and most wondrous critical Goliath, who wrote the criticism on his most elegant work in the Monthly Review. There, of necessity, he will stop; for "The force of nature can no farther go. -Poor Swift expires a driveller and a show." Will you permit me to sign myself an admirer of such critics as Johnson, Blair, and Beattie; but one whom modern cri MR. EDITOR, 217 tims to superstition, they yielded themselves an easy prey to monsters who plunged them into the deepest misery. Among the more cultivated Romans, too, the idea of the supernatural re-appearance of the dead was very generally received. Thus Virgil relates that Æneas, in his search after Creusa, is addressed by her manes : Quarenti, et tectis urbis sine fine furenti Creüsæ Visa mihi ante oculos, et notâ major imago: Obstupui, steteruntque comæ, et vox faucibus hæsit. En. ii. 771. I HAVE just been reading in your magazine a paper on the melancholy existence of popular superstition in this country. The very general prevalence of such notions is most undoubtedly a fact, and a fact which certainly deserves the most serious attention of all, both as degrading to the national character of man, as well as being the source of Tunc sic affari et curas his demere dictis; the utmost mischief to those whose minds" Quid tantum insano," &c. are weak enough to yield to their influence. That such fancies should take possession of vulgar and illiterate minds is not at all to be wondered at; but that men highly cultivated, whose abilities and attainments are by no means despicable, and even highly esteemed that such men should stoop to so humiliating a degree of credulity-is utterly unaccountable. Yet such there have been. The opinions of Johnson on this subject are well known: "That the dead are seen no more," says Imlac in his Rasselas, "I will not undertake to maintain against the concurrent and unvaried testimony of all ages and nations; there is no people, rude or unlearned, among whom apparitions of the dead are not related and believed." It is, indeed, true that many, in all ages and nations, have yielded to a be lief in the appearance of spectres, and have even endued them with the power of speech. The Peruvians relate, that long before the arrival of Europeans to their coasts, an oracle had predicted to them that a new race of mortals, unlike those they had been accustomed to see, would invade their kingdom, and destroy their religion; that, subsequently to this, Gabuarhaocac, the son of one of their Incas, beheld a spectre with a long beard, and robes flowing down to its feet, and mounted on an extraordinary animal. It informed him that he was the offspring of the sun, and was called Virachoca. Long after this, on the arrival of the Spaniards, they recognized their long beards, full garments, and the unknown animals on which they were mounted; not doubting but that they were all the sons of Virachoca, they considered it impious to resist them, and immediately offered them their homage: thus, vic Vid. Lettere d'una, Peruviana, p. 19, In Homer also is an instance of the Iliad, xxiii. 68. Hence, then, it is evident, that the grounds on which Johnson chiefly rested his belief are undoubtedly true, though the inferences he drew from them were false and ridiculous. If, merely because a notion has been generally received, it should consequently be laid down as correct, what limits can be set to such an argument? We must then inplicitly give credit to the predictions of oracles, for Cicero brings precisely the same argument in favour of that at Delphi. (Vid. De Divin. lib. i.) Innumerable other absurdities might be mentioned, which have ever been sanctioned by the credulous "of all nations and ages." If, indeed, one might judge from appearances, our own countrymen seem, even at this enlightened period, peculiarly to render themselves the dupes of foolish credulity. Instances pass daily before our eyes where an eagerness to snatch at any thing marvellous has led them actually out of their senses. I very much doubt whether the most strenuous exertions of reason will ever be able to overcome the superstition of the present day; and, however foolish it may be, it is too deeply rooted in their imaginations to yield to any arguments which may be used to persuade them to the contrary. Goblin stories will still be told and credited; the witch will still continue her nocturnal rides; the raven will still croak in prophecies; and the 218 Epitaph on an Infant-Sir N. Dance. deatle-watch sound the signal for our grave. "While, well attested, and as well believed, Heard solemn, goes the goblin-story round, Till superstitious horror creeps o'er all. THOMSON. If, then, it is a fact, as I very much fear it is, that our exertions would be unavailing to eradicate entirely superstition from the minds of the present genera tion, it becomes a sacred duty in us to guard well the yet tender minds of children from the intrusion of such mischievous notions. Their understandings are yet unbiassed by prejudice, and stand as yet open to the best as well as the worst impressions, according to the principles that are now inculcated. And what can more effectually conduce to so desirable an end than a more general dissemination of knowledge over the poorer classes of the community? That barbarous state of ignorance which at present pervades the lower order, may justly be considered as one of the great est sources of evil to our country; almost every villanous act which is perpetrated -almost every vice which blackens the page of history of our present times— may be traced to that primary source. Let not the fears of a few cold-blooded politicians tend, even in the slightest degree, to abate that ardour of true patriotism, which has within these few years evinced itself; rather let them incite us to increase our exertions, to dispel that gloomy mist of ignorance which blinds the eyes of so many of our countrymen, and renders vice and poverty, at the present day, too nearly synonimous. MR. EDITOR, SCIO. I HAVE been somewhat surprised in observing, at p. 557 of your number for January, "An Epitaph on an Infant," and the same Latinè redditum. Now this epitaph I had always understood to have been originally composed in Latin, and placed by the late Dr. James in the church at Rugby, over the tomb of a young man who died while under his care. In your pages, however, it appears as if composed for a female. Many years ago I remember to have been much pleased with the lines, and to have attempted a translation, or rather, perhaps, a paraphrase of them. Should you think this attempt worth insertion, it is very much at your service. [April 1, Ever innocent, joyful, and blest, MR. EDITOR, from yourself, and so much information HAVING received so much attention bound to send you the following account from your correspondents, I feel myself of Sir N. Holland, which I have gleaned from various sources, and which I have extracted from my unpublished work of in England. In the hope that this ac Memoirs of Artists who have practised count of the person inquired after will prove satisfactory, I am, March 2. JOHN CHAMBERS. 43, London-street, Fitzroy-square. the name of Holland, was the third son Sir Nathaniel Dance, who assumed of Mr. Dance, the city surveyor, who erected the Mansion-house, and died holds that situation, and to the late 1768, brother to the gentleman who now James Dance, who took the name of Lowe, and performed as a comedian at Drury-lane Theatre. Sir Nathaniel was the pupil of Hayman, and went to Italy. During his stay at Rome he became acquainted whom he roamed over Italy, and for with the late Angelica Kauffman, with whom, it was said, he felt a tender attime on becoming Lady Reynolds, did tachment; which the lady, bent at that his studies at Rome be derived his chief not return with equal warmth. During support by making excursions to the seaand, on his return to this country beports, and drawing fortuitous portraits; came a particular friend of Mr. and Mrs. Garrick, with whom, and the study of Sir Nathaniel was more justly famed for music, he forgot his inexorable fair.his professional talents as a painter, than for the borrowed splendour of the immarriage with the Yorkshire Mrs. Dummense wealth which he obtained by his mer, and the title which it commanded. This accession of fortune he ostentatiously displayed in endeavouring to purchase, in order to burn, all the pictures which he had formerly painted, among which were many of high and deserved. celebrity: this he did at the cost of some thousands, in order to enter the pictorial world again as an amateur, in short of his expectation. The mortifiwhich strange project his success fell cation of not being able to purchase and 1815.] On Chanting Prayers in the Communion Service. destroy his inimitable whole-length of Garrick as Richard III., for which he offered the late Sir Wm. Wynne 1,000 guineas, is said to have deeply affected his mind to the end of his life. He possessed by his union with Mrs. Dummer estates to the amount of 18,000l. per annum; and among these was the aucient and beautiful abbey of Netley, on the Southampton river, which it seems derived nothing from Sir Nathaniel's taste on the score of preservation. He represented the borough of East Grinstead many years in Parliament; and is supposed to have amassed nearly 200,000l., most of which he bequeathed to his relatives, the Duminer estate being strictly entailed on that family. Sir Nathaniel was a royal academician; was created a baronet in 1800; and died at Winchester, at the age of 82, (but in what year I have yet to learn.) While on a visit to that city, he was viewing the monument of the late Dr. Littlehales, accompanied by Mr. Sturges, one of the clerks, and complained that he was very cold; on leav ing the cathedral he went to Mr. Hume's, in King-street, still complaining he was very cold, and sitting on the sofa, reclined his head on Lady Holland, and almost instantly expired.-Sir N. painted the picture of Tinion of Athens, which now decorates the Queen's Palace. MR. EDITOR, IN page 6 of your last magazine, your correspondent HOMO SUM," objects to the practice of singing the response," Lord have mercy upon us, and incline our hearts to keep this law," in the Communion service, as" relaxing, in his opinion, that serious tone of mind which a person praying and petitioning for grace ought to possess." As the letter in question is not only well written, but I am sure well meant, I know "Homo sum" will excuse me if, in the language of Terence, to which his signature leads me, "humani nihil a me alienum puto." I have however other motives of a nature not quite so general, that prompt me to answer him: first, my love of music, and a consequent jealousy of its honour; and, secondly, my fondness for what is called church music, including in that term, all the features of choir or cathedral service. But to the point.→ Your correspondent seems to me to disparage the expressive powers of music, when he limits its use to praise and 219 thanksgiving. It is very true, St. James has said, "Is any afflicted? let him pray; is any merry? let him sing psalms." But he is not in that chapter giving directions for public worship, or, indeed, rules for worship at all: in the verses immediately preceding he is exhorting Christians to patience under trials, and to the use of the simple affirmative and negative terms yea and nay," in preference to swearing by heaven or by earth. Then follows the question, "Is any afflicted?" &c. evidently implying, that under the pressure of adversity they could find no better resource than prayer, as in the hour of prosperity and mirth the heart will with more safety and improvement vent its feelings in songs of praise than in any other channel. It is not then quite fair. for Homo, applying the above, as he expressly does, to the "service of the church," to draw as an inference from such premises, that "therefore singing is applicable to praise, but not to prayer." If any such inference might be drawn from St. James, even for the proper manner of conveying private devotions, it would at the most be only of the indirect sort. But, as it is plain, public worship, or the manner of conveying and expres¬ sing the united devotion of a congrega tion, never entered into the mind of the apostle, we must not be led by the mere expression," sing psalms," to put a veto with apostolic authority on our cathedral manner of singing the response in question. As to Dr. Roberts's opinion "that it is not proper or usual to call a prayer a hymn," though he may be very right in thinking, that the hymn sung by our Lord and bis disciples after the last supper, was not the Lord's Prayer, it does not follow, that because a prayer is not properly called a hymn, a hymn or psalm may not be called (and with propriety too) a prayer. For what is at least one third of the Book of Psalms but prayers? Even in the other psalms, whether thanksgiving, prophetic, historical, or didactic, how many pious strains of prayer occasionally break forth! and will either Dr. Roberts or "Homo" deny, that those prayers were all of them originally sung to musical accompaniment by their inspired writer, and many of them adopted and sung in public worship in the Jewish temple? If then we have such high authority as that of the inspired and royal psalmist for making musical sounds the auxiliary vehicle of our prayers as well as praises, we need not be surprised that the reformers of our church, though |