THE ART OF THINKING. FROM THE FRENCH OF DEGERANDO. "Yea, at that very moment, conceptions of the intellect. Such indeed is the imposing authority with which the Author of all things has invested the law of duty, that the conception of it has an effect upon the heart more certain and more absolute, according as it is presented to the mind, under a form simTo envelop and contain celestial spirits." ple and free from all that is foreign to its Shakspere. nature. It is, however, in vain that we MEDITATION, that great and universal seek for the prototype of this conception instructor of the human race, which pre- out of ourselves; externally we are presides over all the creations of genius-the sented with a reflection or image only; it parent of philosophy-the sure guide of the is to be found only within, in the inmost arts in all their applications, because it sanctuary of consciousness. But it is not enlightens them with general principles- sufficient that the conception should merely plays a still more important, and more ex- be presented to the mind; pains must be tensive part in the great process of moral taken to search for it, and to keep it steadily development. It is here that its value is before us; ignorance and inattention cover most conspicuous, for it puts man in pos- it as with a veil. It does not generally session of all his powers, and elevates happen that the law of duty is violated with him to the real dignity of his nature. deliberate intention, but rather by neglectIn science, and in art, thinking elaborates ing to study it; and so far from evil ever the elementary facts furnished by observa- being committed for its own sake, it would tion and experiment; in the work of moral be next to impossible to resist the attraction development, its object is, to explore the which surrounds the good, if we really knew inmost recesses of the mind, to collect to- how to consider it in all its beauty. gether those elementary phenomena which not sufficient simply to glance at our duties, reveal to us the great law of duty, and to they should be deliberately reflected upon; familiarize us with a knowledge of ourselves. their influence should gradually extend In science, and in art, thinking operates through the whole of our mortal nature; only on ideas furnished by the senses and should ramify through, and penetrate its the intellect; in the work of moral educa- inmost folds; should, indeed, take entire tion, it also excites those emotions or feel-possession of us. Such is the end proposed ings which are associated with, or which by the art of thinking, the first and the naturally flow out of our conceptions of most powerful of all arts, since it alone good, and which constitute the immediate enables man to enjoy the exercise of those springs of action. Thinking, indeed, may high faculties which his Creator has endowed be said to be the living principle of wisdom; him with, and invests the mind with true and, if the practice of it be so difficult in causative power. the ordinary course of study, and familiar only to a small number of minds, it becomes still more so, and is consequently less practised, in reference to moral objects. In the acquirement of scientific truth, thought is often aided by images of sense, by descriptions and definitions. In moral speculations, these exterior aids do not exist; the mind is thrown upon its own resources, is fed only by its own aliment, and maintains itself by its own native strength. There is, in reference to morals, not only an intellectual conception, but an emotion or feeling; the one informing the intellect, the other influencing the will, the emotion or feeling flowing naturally from clear It is Struck with the importance and preg nant character of this great art, the ascetic writers and philosophers of antiquity have, with praiseworthy industry, endeavoured to develop its laws, and we are indebted to them for a great number of useful precepts, on a subject on which precepts are indeed essential. The art of thinking has, however, experienced the fate of other arts that have become loaded with didactic rules. It has become embarrassed by rules, useless both to such as are capable of acting of themselves, and to those that are not so; for the first act naturally without their aid, and the others are not in a state to profit by them at all. (To be continued) And 1/1309 .. 24/1309 the length required. = = Remark-Many would solve a Problem like the present, by finding out Algebraical expressions for the various sums disbursed, adding these together, and then forming their equation by the consideration that the sum so formed, together with the money left, must equal the sum with which the person started. This would, of course, give a correct result; but the above is the more direct method. 4. Lay down on paper, by means of a protractor, angles equal to the observed angles. Then join BA and BC, and on these lines describe segments of circles containing angles equal to those laid down. (Euclid, B. iii. Prob. 33.) One point of intersection of the circles will, of course, be B, and the other point of intersection de 2. Since by reinvesting his money, he increased his half-yearly receipt by 6 per cent.-therefore, for every pound of his former dividend he now receives 106 of a pound, and consequently, as his £92 produced before £1 half-yearly, it now produces £1108 We may now apply the common rule of Proportion to deter-termines D. mine what sum produces £1 half-yearly. £1×08 : 1 :: 92 required price. Hence, we find the price of the stock to be 371 = 92 × 1 × × 106 7 4 100 100 5 X 50 5. The figure represents a section of the sphere and horizontal plane, taken through the centre of the sphere and the point of light. ing on friends. remainder after call- SR. Then, by similar triangles PT SR = PL LR Now, as SP is 6 inches PL is 16 inches, Therefore by question, we get the equation, and LR, which is described upon AB and AC, so as to conain equal angles. Take AB, AC for axes f co-ordinates, and call their angle of inlination A. Then the equation of the segents will be of the form x2+y2+2xy cos. A= ax + Py x2+y2+2xy cos. A = Qx + by et y=mx be tangent at A to first circle, hen x my must be tangent at A to econd circle. The conditions that these lines may be ngents, are a+mP 0 mQ + b = 0 nd therefore the equations to the seg ents are x2 + 2xy cos. A + y2 : =a x2 + 2xy cos. A + y2 = b ( y etween which m must be eliminated. sult is evidently m (bx-ay) (x2 + y2+ 2xy cos. 4) =ab (x2-y2) 7. It will not, I think, be necessary to xplain how the boat might be carried to e middle of the stream. In the annexed diagram, let C represent he head of the boat, and BC the direction f its keel. The arrows indicate the direcion of the current, and PA is the rope, astened at A to the mooring. The presure of the water will, (if we neglect the iction and resistance against the side of le boat) tend to produce motion in the diection PM. The tension of the rope, which cts in the direction PA, may be resolved ato two forces:-one in the direction PN, B M motion in the direction of the boat's length. The length of the rope must be such as to allow of the angle between its direction, and that of the boat's keel, to be acute in all parts of the passage. QUESTIONS FOR SOLUTION. 16. If a cubic inch of gaseous ammonia be exposed with proper means to heat, it will be decomposed into its constituent gases, hydrogen and nitrogen. The mixture would, at the original temperature and pressure, occupy two cubic inches, and the evolved volume of the former gas (at a given temperature and pressure) would be three times that of the latter. The specific gravities of hydrogen and nitrogen being '0694 and 971 respectively-find the specific gravity of ammonia. 17. A market-woman bought a quantity of apples, which she sold at 5 a penny, and thus cleared 6 per cent. on her outlay. Had she sold them so as to gain 5 per cent. her receipts would have been three shillings and three half-pence.-What number of apples were purchased? 18. AB, CD are any two chords of a circle, passing through a fixed point O, and EF any chord parallel to AB. Join CE, DF, meeting AB in the points G and H, and DE, CF meeting AB in the points K and L. Show that the rectangle OC, OH, OR, OL. (From Cambridge Problems, 1848.) 3 ELOCUTIONARY EXERCISES. II. NAY, dearest, nay, if thou would'st have me paint A palace lifting to eternal summer Its marble walls, from out a glossy bower To excel them all in love; we'd read no books We'd guess what star should be our home when love III. Pauline, by pride Angels have fallen ere their time: by pride- And a revengeful heart, had power upon thee. Levels all ranks, and lays the shepherd's crook And Passion taught me poesy-of thee, Thou art free, And art thou tired of being? Has the grave From "Ion," a Tragedy. 2-Quotation French. T. W. F.-"Il y a anguille sous e." This is a very ancient French proverb, which be literally translated-"There is an eel under the ," meaning that there is a mystery in the affair. 3-Shadow of the Earth. E. S.-The distance from centre of the earth to the apex of the shadow is about of the earth's diameters. In round numbers, 175,000 s may be given as the length of the shadow. 1-Franking Letters. J. F.-The privilege enjoyed embers of both Houses of Parliament, certain govern: officers and public functionaries, of sending and reng a certain number of letters free, was abolished 10th, 1840. 5-Shakspere's Wife. A. W.-Shakspere was marto Anne Hathaway, before the close of the year 1582, ras then only eighteen years of age; his wife was conably older than himself. She died on the 6th day of 1st, 1623, aged sixty-seven years. 5-Pyrites. B. J.-The round lumps found in the -pits in Berkshire, which look like rusted iron balls riorly, and present a very beautiful metallic appearance crystaline lustre when broken-are masses of the huret of iron. They are composed of twenty-eight s of iron, and thirty-two of sulphur. It is a very mon mineral; it has been used for the production of n vitriol or sulphate of iron, but attention has been ntly turned to it as a source of sulphur. 7-Timocracy. A. K.-In the Quarterly Review, xiv.) will be found an article upon this form of conition. The term is used by Aristotle and other Greek ers, but there are two different senses in which it is 1; in the one sense it represents a state in which the ification for office is a certain amount of property, in other it indicates a government, constituted of the and noblest citizens struggling for the honour of eminence. B-Botanical. A. Y. S.-The term Cruciferoe, the e of a large natural order of plants, is derived from two a words, signifying cross-bearing, from the circumce that the petals of the flowers are in the form of a tese cross. They possess universally anti-scorbutic stimulant properties, combined with an acrid flavour; their seeds uniformly abound in a fixed oil-the proies of which, cress, mustard. and rape-seeds may be n as representatives. To this order of plants belong e of our most common esculents and garden flowers. -Epacts. W. T. M.-Epacts in chronology are the exes of the solar month above the lunar synodical month, of the solar year above the lunar year of synodical ths. The epacts are either annual or menstrual. pose the new moon to be on the 1st of January; since lunar month is 29 days, 12 hours,44 minutes, 3 seconds, the month of January contains 31 days-the menstrual et is 1 day, 11 hours, 15 minutes, and 57 seconds. The ual epact is nearly 11 days: the Julian solar year ag 365 days, 6 hours; and the Julian lunar year 354 s, 8 hours, 48 minutes, 38 seconds. 0-The Zodiac. S. B.-The Zodiac is that belt or e of the heavenly sphere, within which the apparent ions of the sun, moon, and larger planets are confined. en it is said that the Zodiac is about 16 degrees in dth, it is meant, that if you draw a circle through the re of the earth and the poles of the ecliptic, and le that circle into 360 equal parts, the breadth of the lac wonld measure 16 of those parts. When a planet id to have a diameter of 30 seconds, it is meant, that line were drawn through the centre of the apparent of the planet, and terminated by its edge, the angle ided between two lines drawn from the centre of the of the observer to the ends of that line, would be 30 nds. 1-Insects. F. L.-The Eumenidæ are a family of ienopterous insects of predacious habits. Speaking le Odynerus, a species of this family, Mr. Westwood :-"This insect, during the early months of summer, is a burrow in the sand to the depth of several inches, hich it constructs its cell; besides which, it builds with grains of sand brought up in burrrowing, a tubular ance to its habitation, often more than an inch long, more or less curved, the grains of sand which line passage being agglutinated together; each female is several of these burrows, and deposits an egg in cell, together with a number of green caterpillars, ch she arranges together in a spiral direction, to serve ood for the larvae when hatched. When the store of is secured, the insect closes the mouth of the burrow, loying the grains of sand of which the funnel is comd for the purpose. 2-Cycles. S. C. C.-The metonic cycle was so called Meton, its inventor, B.C. 432. It consists of a period of nineteen years, or, more accurately, of 6,940 days, at the end of which time the new moons fall on the same days of the year, and the eclipses return in the same order. The word cycle means the revolution of a certain period of time, which finishes and recommences perpetually. Those used in chronology are three in number, viz.-the cycle of the sun, the cycle of the moon, or metonic cycle, and the cycle of indiction. The first, or solar cycle, consists of twentyeight years, after which period the dominical letters return in the same order; that is, the first day of the month falls on the same day of the week. The number of the year in the metonic cycle is shown by "the golden number," as it is called. The cycle of indiction, or Roman indiction, is an arbitrary, not astronomical period, supposed to have been introduced by Constantine the Great, but its origin and purpose are alike uncertain. 53-Girondists. P. M.-In 1791 the department of La Gironde sent to the legislative Assembly, amongst its representatives, three men of eloquence and talent, who became the leaders of a celebrated political party during the Revolution; hence the members of the party came to be named Girondins, or Girondists. Its principles were republican. The party was powerful, but not always consistent, during the continuance of that Assembly; and in the following year, 1792, Louis XVI. chose his republican ministers from it. After the September massacres, its members, for the most part, became favourable to the Constitutionalists. In the Convention, the Girondists at first commanded a majority, but on the king's trial they were much divided; and being pressed by the violence of the sections of Paris, they were at length expelled the Assembly. Thirty-four of them were outlawed; and in October, 1793, twenty-two of their leaders were guillotined; others put an end to themselves. Madame Roland, wife of a minister of that name, was one of the distinguished members of the Gironde party, and was executed when the party fell. She was authoress of a celebrated composition entitled the Appel au Peuple. 54-Domesday Book. L. E. T.-This book is a register of the lands of England, framed by order of William the Conqueror. It was sometimes termed Rotulus Witonia, and was the book from which judgment was to be given upon the value, tenures, and services of the lands therein described. The original is comprised in two volumes, one a large folio, the other a quarto. The first begins with Kent and ends with Lincolnshire, and is written on three hundred and eighty-two double pages of vellum, in one and the same hand, in small but plain characters, each page having a double column. It contains thirty-one counties. After Lincolnshire the claims arising in the three Ridings of Yorkshire are taken notice of and settled; then follow the claims in Lincolnshire, and the determination of the jury upon them; lastly, there is a recapitulation of every wapentake or hundred in the three Ridings of Yorkshire, of the towns in each hundred, what number of carncates and ox-gangs are in every town, and the names of the owners placed in very small characters above them. The second volume, in quarto, is written upon four hundred and fifty double pages of vellum, but in single column, and in a large fair character, and contains the counties of Essex, Norfolk, and Suffolk. In these counties the liberi homines are ranked separate; there is also a title of invasiones super regem. The two volumes are preserved, with other records of the Exchequer, in the Chapter House at Westminster; and at the end of the 2nd is the following memorial, in capital letters, of the time of its completion:-" Anno Millesimo Octogesimo Sexto ab incarnatione Domini, vigesimo vero regni Willielmi facta est ista descriptio, non solum per nostres iomitatus, sed etiam per alios." From internal evidence, there can be no doubt that the same year, 1086, is assignable as the date of the 1st volume. 55-Critical Philosophy. M. M. H.-This name has come to be exclusively applied to the system of philosophy which owed its existence to Immanuel Kant, a professor of logic and metaphysics in the University of Königsberg, in the latter half of the 18th century. The promulgation of his doctrine produced an important era in the history of philosophy. At the time when Kant commenced his teaching, the philosophical world was divided between the French followers of Locke on the one hand, and the rationalists who were disciples of Wolf and Leibnitz. The former resolved all our mental powers into modifications of sense, while the latter rested their arguments upon abstract conceptions in the understanding. Kant opposed both schools. He divides the speculative part of our nature into three provinces-sense, understanding, and reason. He holds that our perception of the outward world is merely representative. To render human experience possible, two ground-forms, under which all sensi |