times, would assuredly produce an infinity of time. It is here that "Homo's" friend outruns his data, as the following considerations will shew. First, the finite distance between the two hands, being equal to the sum of all its parts, necessarily comprehends the whole of those diminutory portions by which it is successively reduced, or, in other words, the whole of its subdivisions, which become infinite in number only by decreasing ad infinitum, or becoming infinitesimally small. Secondly, this finite distance and its subdivisions, being measures of the times in which they are respectively performed, occupy proportionally decreasing periods of time for their completion; from which it follows, that these periods, though infinite in number, like the spaces by which they are measured, are merely corresponding subdivisions of a finite period of time. Homo" will thus perceive, that although it takes 5 minutes to diminish the original distance of 5 minute spaces to it does not require another 5 minutes to diminish this to, and another to reduce it again to, &c. It is in the neglect of this simple fact that the fallacy consists. The supposition of uniform, or, at least, non-decreasing times for these successive dimunitions, is precisely the data which is wanting in this redoubtable argument, and which is necessary to render its conclusion "logically true." At the same time it is evident that such data, if granted, would at once render the conclusion" practically" true-that is, true in point of fact; and hence, in either case, the hypothesis of its being "practically false" while "logically true," must fall to the ground. of successive journeys requires an infinite number of successive portions of time. Minor.-The minute hand in endeavouring to overtake the hour hand, has to perform an infinite number of successive journeys. Conclusion.-Therefore the minute hand in endeavouring, &c., requires an infinite number of successive portions of time. Taking this conclusion as the minor premise of another syllogism, we have Major.-An infinite number of successive portions of time (supposing them non-decreasing, but not otherwise) constitute a period of time which can never end. Minor. The minute hand in endeavouring to overtake the hour hand requires an infinite number of successive portions of time. Conclusion.-Therefore the minute hand in endeavouring, &c., requires a period of time which can never end. The falsity of the conclusion is here again shown to be owing to the false predicate of the major premise. With regard to the fact of the conjunction of the hands, as a subject of itself, I have here, of course, nothing to say; but it might be interesting to show, that the various arithmetical aspects under which it may be viewed, are strictly consistent with the preceding explanation.-ANTIZENO.-The discussion of this subject must now be brought to a close.-EDS. 142. How to obtain Ease and Power in Debate. "Tante-ne animis cœlestibus iræ "?-or, has "Rolla" (like honest Dogberry) mistaken the "excommunication" of my person for the "examination" of my remarks? I may be allowed to add, as some of your correspondents appear to think the point must be decided by formal logic, that I cannot agree with those who represent the argument as illogical "I am Sir Oracle, merely on the ground of its being irreducible to And when I ope my lips, let no dog bark," syllogistic form. On the contrary, this spurious seems to be the style in which Rolla views himargument may be reduced to syllogism, and in self, as compared with those who may dispute his this form its fallacy may be shown to consist in infallibility. This character is by no means suited the false assumption above explained. The argu- to my own taste. I shall, therefore, neither brand ment taken continuously forms a sorites: thus- his sentiments as being " commou as street balA is B.-The minute hand in endeavouring to lads among a despicable class," nor accuse him overtake the other, has to perform an infinite of" literary pride." I leave "Timon" and those number of successive journeys; viz., 5, &c. interested in the present topic to estimate the B is C.-The performance of an infinite number controversial value of the oft-repeated phrases, of successive journeys requires an infinite"height of dogmatism,"" greatest assurance," &c., number of successive portions of time. and to compare them with my own simple declaration that Rolla had fallen into "a grave error." C is D.-An infinite number of successive portions of time (supposing them non-decreasing, but not otherwise) constitute a period of In return, however, for" Rolla's" milder banter time which can never end. on my supposition that the compositor had posA is D.-Therefore the minute hand in endea-sibly wronged him, I will ask who is answerable vouring to overtake the other requires a period of time which can never end. From this we see, that while the conclusion is strictly legitimate as an inference, its truth fails by reason of the unsound predicate of the third proposition, which rests on suppositional data not granted in the question. Hence the conclusion is not "logically true;" for although logic insures syllogistic accuracy of inference, it nowhere declares that a conclusion thus obtained is true of itself, unless drawn from certain premises. It only remains to obviate objection, by expanding the preceding sorites into two distinct syllogisms of the first figure: thus Major. The performance of an infinite number for the extraordinary apposition of "synthetic ་་ "Rolla s" remarks are so discursive that I think it necessary to state the origin and subject of the present discussion. If I mistake not, the practical answers to "Timon's" question are to be found, in the remarks of "Etna," and in the last para. graph of my own reply. "Timon" complained of an inability to reply to the arguments and objections brought forward in a debating society, in the specified time required." But "Rolla," passing by these points, read "Timon" a harsh lecture on his assumed “lack of logical continuity." In the first paragraph of my own remarks, I expressly left this delicate point to "Timon's" conscience, endorsing the truth of "Rolla's" practical advice in case the defect existed; and I then proceeded to oppose "Rolla's" theory, on the grounds that it was erroneous in itself, and at variance with his ultimate advice. The question, then, between "Rolla" and myself, was the relative value of analysis and synthesis. "Sir J. Mackintosh on his legs in the House of Commons was out of his proper element," "his speaking was a constant effort, a tug up bill." It would be easy to multiply instances. Secondly, I did not remark on “ Rolla s" observations as to fiction, as I conceived that their one-sided character was sufficient to condemn them. The sweeping censure he has passed on fiction does him but little honour. Whatever be the precise value of particular works, fiction has its value. The exquisite and touching parables of the New Testament, and the almost divine productions of poetry, are not less fictional than the threevolumed works which encumber the shelves of our circulating libraries. The novel bears much the same relation to our own day that the drams did to the days of Elizabeth. Shakspeare and Scott belong to the same brotherhood, and their points of resemblance are neither few nor small There are fictions which will as assuredly go "Rolla" declares that I have not attempted down to posterity as those reviews which engross "to explode" his principles. Let the reader judge the whole of "Rolla's" sympathies. "Rolla" between us. I represent synthesis as "the high-scorns the idea of Bacon being a novelist; does est power of the intellect;" while he terms ana- he know that Bacon embodied his gorgeous lysis" the nobler" faculty. I trace the origin of visions of his own philosophy and its results, in analysis to the "feebleness" of man; while he the shape of a fiction, in his "New Atlantis? declares synthesis to be" natural, easy, and plea. Rolla attributes the composition of novels to " the sing to the mind." He claims the great reviews workings of the synthetical faculty;" but if I as analytical criticism: I claim them as synthe- mistake not, this idea is based only on the confu tical disquisitions."* It surely requires no sion of the literal with the philosophical meaning Solon to perceive that the two lines of argument of the term. Analysis gives the novelist a comcannot co-exist; that if one be true the other is mand over the "raw materials" of his art-the false. "Rolla's remarks rest on " Rolla's" simple emotions and passions of man: the moment be assertions, while my view of the relative value of commences his work he enters on a new sphere, analysis and synthesis is supported by a quota- and the words analysis and synthesis can so tation from Whateley, and my observations on more be applied to the composition of a novel reviews are supported by examples; and yet than to the painting of a portrait; both may by a "Rolla" represents my article as "point blank quibble) be termed synthetical, since they are, contradiction." and as "baseless as the fabric of a respectively, a putting together of sentences and vision!" "Rolla asserts hat I "accidentally of paint. A novel is an analytical tabiran of the admit the premises of our (Rolla's) theory," and human passions and emotions, artistically ar then strings together a series of contradictions as ranged. The synthetical faculty is required by "the drift of my "advice to Timon." This the novelist only in that test of his powers,-the "accidental admission I can nowhere discover construction of a good plot. in my remarks, and it certainly never existed in my thoughts. I appeal to any reader to say whe ther I ever allowed that " fiction, idealism, poetic flights, unconnected sentences, &c." were the results of he synthetic iaculty; whether I ever represented synthesis as synonymous with mere " compiling and producing, There were two points in "Rolla's" original remarks which I did not controvert in express words; but as he complains that I did not sufficiently explode his premises, I will now attempt to do so. First then, I assert that" lack of ease and power in oral debate (the only species to which "Timon" refers) does not necessarily arise from "detective mental tu tion." In proof of this point. I will take two of those reviewers whom "Rolla has chosen as representatives, par emi nence, of the cultivated intellect of the present century :--John Foster, who could never succeed in the simplest departments of oral debate, and Sir J Mackin oh, of whom Macaulay says, that Ra, instead of answering my remarks on reviews, has abused them. He will find an exact transcript of my sentiments in the first sixteen lines of age so of this magazine. Why, then, does he con descend to write in pages which give utterance to views" common as street ballads ?" Rolla triumphantly inquires on what grounds I declare Euclid's reasoning to be purely synthe tical. I do so, because it exactly accords with the definition of synthesis, i. e., it "pursues a series of relations, commencing with what is given, and ending with what is sought." I adust that he who truly understands a given prop tion in Euclid, and can see "through it from the beginning to the end," will also be able to see through it back again from the end to the bestning. It is for this reason I say to" Timon "Learn to synthetize-you may then analyt with safety." The reverse of this is not true; he who understands the analytical proof of an er absurdo demonstration is not thereby nalled to demonstrate the same proposition syntacticaly "Rolla" has only illustrated the point for whic I contend-the superior value of synthesis. It is true that "Algebra and the Different al Ca culus" are chiefly analytical; and who does not know that algebra could never explain the mys tery of imaginary quantities (e. g. √-1) until geometry came to its aid? Rolla" will, perhaps, bow to the opinions of Newton. "Newton used to speak with regret of his mistake, at the beginning of his mathematical studies, in having applied himself to the works of Des Cartes and other algebraical writers, before he had consi dered the elements of Euclid with the attention they deserve."(Pemberton's "View of Sir I. Newton's Discoveries.") Need I mention the inscription which Plato placed over the door of his house-"Whoso knows not geometry, let him not enter here," or quote the opinions of Whewell, Sedgwick, Mill, Stewart, &c.? "Rolla" asserts, in contradiction to my remarks, that "the omniscience of Deity is as purely analytic as synthetic, urging as a reason the undoubted truth that" perfection is the leading characteristic of all the attributes of Deity." How far the premises warrant the conclusion may be seen by the declaration, that "Analysis has its origin in the mere imperfection of our senses, and is truly the art of the blind."-(Brown's "Philosophy of the Human Mind.") What can be thought of a philosophical critic who tells us that Bacon "exploded the Cartesian system of philosophy?" Surely the veriest tyro in philosophy knows that Des Cartes (the author of Cartesian philosophy) flourished 40 years later than Bacon; that when Bacon died, Des Cartes was a young man," unknown as yet to Fame!" Space bids me conclude. I have nothing to retract— nothing to admit--nothing to quality-or I would frankly and gladly do so. It is for the reader to say whose theory stands "intact beneath the broad ægis of truth" Had "Rolla" substituted authority for assertion, and attempted to answer the plain and decisive remarks on analysis and synthesis quoted by me from Archbishop Whately, instead of abusing and carping at my humbler attempt to illustrate the same point, he would at least have shown better faith. Had he passed by my own remarks on Euclid and on Divine Omuiscience, and overthrown the doctrine of the great logician, I should have begun to doubt my views. As it is, I have to thank him for causing me to think more closely on the subject; to earch for and to find the supporting testimony of Newton on one point, and of Dr. Brown on another. I now retire from the controversy, and leave the opposing theories to the critical judgment of the readers of this magazine, only regretting that the defence of that which I believe to be truth has not fallen into better hands.-B. S. 158. Solution of a Geographical Problem.— The mistake made by the travellers to our antipodes, in calling the same day by different names, arises from their having persisted, during their journey in calling different things by the same name. Suppose yourself situated at Greenwich Observatory on Tuesday at noon. Then Tuesday means the space of 24 hours, 12 of which have just passed, and 12 are just commencing. The sun is on your meridian. In precisely 24 hours the sun will be again on your meridian; and in 3 minutes afterwards the sun will be on the meridian of the place at which the traveller will have arrived who star ed westward from Greenwich at noon on Tuesday. He will call the time he arrives there the noon of Wednesday, the sun being then on his meridian. But he is wrong (for the noon of Wednesday has passed 33 minutes), unless Wednesday is to mean a different portion of time from what you at Greenwich call by that name. The next time the sun is on his meridian he will be further advanced in his journey, and For convenience I suppose each of the tra will mean, by the noon of Thursday, an instant 74 minutes after the noon of Thursday at Greenwich.-And so on. The eastward traveller will make similar mistakes; but will be too fast with his noons. When the two meet, their mistakes will have each amounted to 12 hours; one in defect, the other in excess. K. G. asks what the inhabitants of the place will call the day on which they meet? To this I can only answer, that I do not know; and that if I did, it would probably be impossible for me to pronounce or write the answer. K. G. must mean, what is the right name of the day? The answer is,-noon on a Saturday, for the travellers are supposed to be exactly 200 days in the journey, and they started on a Tuesday; but it would there be mid night. It would clearly be inconvenient to make Greenwich time universal, for reasons which I need not enumerate. Therefore I propose to answer the question.-How shall days be named at different places, so that the sun may be at the highest at the middle of the day, and so that neighbours may understand each other? Let the instant, between 12 p.m. Tuesday and 12 p.m. Wednesday at Greenwich, when the sun is on the meridian of any place, be called the noon of Wednesday at that place; and to distinguish the Wednesdays of different places the longitudes of the places should be affixed: thus the Calcutta Tuesday must be called Tuesday (90 E). The following table will illustrate iny meaning Greenwich....noon, Tuesday..9 p.m. Thursday Calcutta......6 p.m. Tu. (90 E.)3 a.m. Fr.(90 E.) New York ....7 a.m. Tu.(75 W.)4 p.m. Th. (75W.) Hobart Town. .9 p.m. Tu (135E.)6 a m. Fr.(135E.) Sandwich Isles 3 am Tu.(135 W.)noon,Th (135 W.) The second and third columus show what noon of Tuesday, and 9 pm. Thursday, will be called at the places in the first column. This plan would make it easy to determine the day and the hour at any place, when its longitude is known; for we need only add to or subtract from our own time an hour for every degree of east or west longitude respectively. In longitude 180 deg. (but nowhere else), there would be two names for the same day; thus 2 p.m. Wednesday at Greenwich would be 2 a.m. Wednesday (180 W.), or 2 a.m. Thursday (180 E.), according to the rule. Fortunately for my plan, nobody lives on the line of this difficulty, nor does it lie between any neighbours. Of course it follows from this, that in crossing the meridian of longitude 180 deg. from West to East we must add a day, or the traveller must change the name of the day of his arrival from Wednesday (180 W.) to Thursday (180 E.), and vice versa.-J. B. 165. The Nature of the Sun's Body.-If the sun were a body of fire, R S. will perceive that the nearer we advanced to it the warmer we should become, and the further we went from it the colder we should get. Take, for instance, an ordinary fire, and sit down directly in front of it, and as close to it as you possibly can, and you feel the heat from it; but gradually move your position back, and you gradually feel less and less of the influence of the fire. Now R S. will please to vellers to pass through the same longitude each day; this will make the number of miles travelled over in different days somewhat unequal. transport this idea into "space," and imagine the sun to be a body of fire, and then answer the question, "Which part of our earth ought to be the warmest, the tops of the mountains or the plains beneath?" Why, according to this theory, it ought to be the mountain-tops; but so far from this being the case, very many of them are covered with a "winding-sheet" of "eternal snow." The plains are the warmest; they receive the most of the germinating influences of the sun; consequently, the sun cannot be a "body of fire" What, then, is the proper theory of heat? and to this question R. S. has himself furnished an answer; the sensation of heat which is felt is produced by the action of the above atmosphere (sun's) upon the latent caloric of the bodies of animals.' We think, also, that our atmosphere has something to do with the production of heat. The atmosphere, R. S. no doubt knows, decreases in density according to its distance from the earth; the highest part being the most rare, the lowest part, or the part next the earth, the most dense. On this ground then, we think, that the action of the sun's luminous atmosphere on the atmosphere of the earth increases or decreases, according to the density or rarity of the earth's atmosphere, because we find that where the atmosphere is rare, the heat is at its minimum; but where it is dense, the heat is at its maximum. This hypothesis (which was first introduced to the science of astronomy by the great Herschell, and was afterwards reduced to system by the equally great French astronomer, La Place) holds that all matter (that is, the sun, with all his pla nets and satellites, and all the stars that "inhabit our milky way," and all other parts of the uni verses, scattered through the "vast immensity of space") originally existed as a species of luminous nebulæ, this nebula had a motion similar to that which the earth has now, and the effect of that motion was to inake the matter condense into its centre, but as the process of condensation was going on, luminous rings were occasionally detached from the rest, these luminous rings also maintaining the motion which the parent mass had, gradually condensed also; these luminous rings in course of time became planets, and the great central mass became a sun, thus forming a planetary system; and an immense number of these systems form the universe. R. S. will perceive by this theory what the nature of the sun is; he will perceive that it was not created pos terior to the earth, nor yet anterior to it, but they were created simultaneously. For a fuller explanation of this theory, I would refer R. S. to "Mitchell's Planetary and Stellar Universe;" Collins' edition, price 2s. He will find "Hitchcock's Religion of Geology," also price 2s., to be an excellent expositor of the nature of the earth. Again, most of the astronomers of the present day hold the theory of the "Nebular hypothesis."-WALTER, The Young Student and Writer's Assistant. LOGIC CLASS. Junior.-Vide "Art of Reasoning," No. VII., Vol. I.-What is it necessary that man should learn? By what has man purchased his superiority in physical science? Why do the laws and principles of the human mind exist? What is intuition? What is truth? What truths does intuition reveal? How does sensation operate? On what do we rely for the accuracy of sensederived information? How do you prove that "the evidence of the senses" is worthy of dependence? How may the theory of "Necessary Truths" be made compatible with the senseorigin of knowledge? What is memory? How does it operate? What is analogy? Of what use is it in science? Define testimony, and mention in what it is useful. What are the principles on which we confide in testimony? What laws ought to regulate our belief in testimony? What CLASS I. In which Present, Past," and Perfect Participle are alike. is probability, and by what law is reasoning from probability governed? Provectior.-Exercise No. VII., Vol. II. Senior.-Imagination: its Nature and Office; its Dependence on Memory and Consciousness (see Rhetoric," Imaginative Faculty," &c.; Akenside's "Pleasures of Imagination;" Addison's "Essays," Spectator, Nos. 411-21; Brown; Stewart; Payne; Reid, Essay IV., &c.). GRAMMAR CLASS. Exercises in Grammar. No. XVI. Junior Division. Perform Exercise No. VII., Vol. III. p. 316. Senior Division. Prepare a form like the one given, and arrange the irregular verbs in Exercise XIV., p. 198, and their inflexions under their proper heads. 2. Gender is the distinction of nouns answering to sex in persons or animals. 20 200 4000 -1820-19 =4000 feet. Question 34. 2·25 × 5236 = 5·96413125 feet= the solidity of the globe, and 852 .. 5.96413125 × -317-5899890628 lbs.-Ans. SPES. 3. There are three methods adopted for the distiuction of gender. 1. Different words; as, boy, girl; horse, mare. 2. Different prefixes; as, man Question 35. The number of lbs. in one imservant, maid servant; he goat, she goat. 3. Difperial gallon being 10, nearly, the number of galferent terminations; as, count, countess; mayor, F. T. lons in 317-5899890625 lbs. will .. =3175899890625, nearly.-Ans. Question 36. Diameter of shot 5 feet; content =53×·5236=065-15 feet. Now, according to the law of floating bodies, if a heavy body be weighed in water, the weight lost will be equal to the weight of water having the same bulk as the Question 29. Interest of £500,000, at 4 per body; hence, on the weight of a cubic foot of the cent, for 1 year,, 500000 × 4 =£22,500 100 Question 31. Let M=the amount of £1 at the end of 1,000 years. Then, according to the usual formulæ, M=P R” = P (1 + ?)". Here P. 1:r=·05; n=1000. .. M (1·05)1000. .. the compound interest-M-1=(105) 1000-1. J. B. M'C. Question 32. Suppose S=the sum. Then S++17+, &c. (1), Multiply each side of the equation by 12, and we have 128=1+++++, &c. (2) Subtract equation (1) from equation (2), and 11 S=1; wherefore, S. SPES. |