thing of the practice. As a general rule, perhaps, to divide your time almost equally between the two branches would be unobjectionable. Under any circumstances much depends upon yourself. On your admission as solicitor, you will have a furter infliction of stamp-duty, but this will be regulated by the particular courts in which you desire to qualify as a practitioner. You may put down £40 under this head. At present there is a further annual duty, payable for renewal of certificate-on country solicitors, £8; on those in London, £12 per annum. For the first three years of practice, half these sums. If you will accept a piece of gratuitous advice, assuming that you are Young, are desirous of having a thorough knowledge of the law, and your resources are not large, you will endeavour to enter a respectable office as an assistant, at a nominal, or even, at first, no remuneration. Be industrious; endeavour to understand everything you see and do; and when the services you have rendered to your employer sert to justify it, apply to him for your articles, and if he be a gentleman he will meet you with that liberality your services have deserved; but if he be not, then, of course, you will not desire to stay with him, but will seek some more desirable engagement. It is no disgrace to the profession that many of its brightest ornaments have thus entered its ranks. Why should you not make another?-C. W., Jun. 08. Mental Arithmetic.-Allow me to direct the attention of C. Y., and others who participate in his desire, to the following valuable remarks on mental arithmetic by Professor De Morgan:There are two sorts of mental arithmetic. The first consists in the actual performance of rules in a manner different from that which is asual on the paper, and more fitted to the mode in which computation and mental retention are to go together. It should never be forgotten that the retention is the thing to be principally considered. The second consists in the substitution of easier rules in particular cases, rules framed according to the particular numbers to be used. In this second case the easier rule is as much the proper rule for the paper process as for the metal one; but, as capable of being mentally performed, which the common rule is not, it gets the character of belonging to mental arithmetic. As an example of the first sort, take the addition of 8 and 47: in doing this mentally, the 80 and 40 should be added first, and 120 retained; the 5 and 7 should be then added, and 120 and 12 put together. Or else, 85 and 40 should be first added in thought, giving 125, and 7 then added, giving 132. This process put down on the paper would require more writing than the common one. As an example of the second kind, take the rule for calculating the price of a pound from that of a hundred-weight; or two-pence and one-seventh for every pound sterling in the price of a hundredweight. Thus £14 per cwt. is instantly 28+2, or 30 pence per lb. ; £18 10s. per ewt. is 37+21, or 3. per lb. This process is as much of an breviation on the paper as it is in the mind. The first sort of mental arithmetic has been but Hale studied; and it would seem as if what there is of it in the schools referred to were the result of the pupil's own thought applied to a clear perception of the meaning of what he is about. In all probability, the method which is most easy to que mind will not be so to another. That young pupils can, when instructed in an intelligent manner, frame processes for themselves, many teachers know: the following is the evidence of Mr. Wood, in his "Account of the Edinburgh Sessional School," though it would have been more satisfactory if the time previously given to the subject had been stated:-"They will multiply such a line of figures as 768 59 28 16 5 4 8 7938764 by 7, 8, or any other figure, in less than the sixth part of a minute. From such a line they will subtract another of the same length in the ordinary way in about seven seconds; and if allowed to perform the operation from left to right, while the question is under dictation (though it should be dictated with a rapidity which would not permit ourselves to take down merely the original figures), they will present the whole operation, both question and answer, in scarcely one second from the time of announcing the last figure. In addition, they will sum up seven lines of eight figures each, in the ordinary way, in less than one-third of a minute; and if allowed to perform the operation while the question is dictating, in about three seconds. All other calculations they perform with proportional celerity. These modes of working during dictation (when allowed) are suggestions of their own, in their zeal to surpass each other, and not taught by the master." We turn to the second sort of mental arithmetic : that in which the processes are only mental as being more easy, and therefore being better on paper than the usual ones, as well as possible without it. Of all the aids to abbreviated computation, there is nothing like the ready knowledge of decimal fractions; and of all the advantages of decimal fractions, none is so conspicuous in commercial arithmetic as the use of the decimal parts of a pound. It will be worth while to recapitulate and extend this mode of operation, which sets the advantage of a decimal coinage in a strong light: showing that it is better, as our coinage stands, to learn a rule by which to go out of it into decimals, and working the question in decimals, to return the answer into ordinary denominations, than to remain in those ordinary denominations, and work the question by them. For the first three places of decimals, the rule is as follows:-Allow 1 in the first place for every pair of shillings, and fill the second and third places with one for every farthing above the shil50 for the odd shilling if there be one. lings, and one more for sixpence, together with 4s. 4d. is £218; 4s. 73d. is £232; 5s. 44d. is £268; 5s. 7d. is £-282: 17s. 11d. is £898. Thus For the fourth and fifth places of decimals, fill them with 4 for every farthing above the last sixpence, and I more for every 24 in the result (or, if found more easy, for every three halfpence in the farthings used). Thus for 4d. the fourth and fifth places are (18x4 or) 72+3 or 75; for 74d., 28+1 or 29: for 8d.. 33; for 114d., 95. For all decimal places after the fifth, let the number of farthings above the last three halfpence be a numerator, let 6 be a denominator, and use the figures in this fraction reduced to a decimal. These can be formed in the head, and will soon be remembered, namely: It is not often, perhaps, that more than five decimals are wanted, and three will most frequently be sufficient; but those rules are valuable by which, in case of need, approximation can be extended. A very little practice would enable any one to use the preceding rules so as to write down at once, to any extent required, any decimal of a pound; instead of £176 13s. 103d., for instance, to put down £176 6947916666, &c. Considering the very great facilities afforded by this rule, which are more than those who have not tried it have any idea of, it would be worth while to save trouble yet further by learning the multiples of 4 up to 23 x 1 or 92, and those of 14d. up to one shilling. The inverse rule, to turn a decimal of a pound into money, is as follows:-A pair of shillings for every unit in the first place; a shilling for 50 (if so much) in the second and third places; a farthing for every unit left in the second and third places, after abatement of 1, if what is left be 25 or upwards. Thus £477 is 9s. 64d., and £217 is 4s. 4 d. The labour of questions in commercial arithmetic is much more than halved by the use of the preceding rule, and the risk of error reduced in proportion. It is not easy to make those believe this who have grown up in the use of the ordinary methods. We shall point out a few of the advantages attending the transformation, in rendering questions capable of being solved mentally, with ease and dispatch. The two great modes of estimating fractions of a sum, namely, the number of shillings, &c., in the pound, and the per centage which the part is of the whole, can be reduced to one another, or either mode compared with the other, almost instantaneously. Suppose, for example, it is required to know how much per cent. of his debts he can pay whose assets are 8s. 73d. in the pound. The regular book arithmetician would proceed as follows: of business has its own cases, which need only be learned by those who are to attend to that business. In the books of arithmetic there is the fault of presuming that every person is to learn every variety of commercial rule by rote; compound interest and the determination of the price of a mixture from that of the materials are supposed to be equally necessary to all, though the subdivision of business makes it as certain as any thing which can be predicated of two rules of arithmetic, that no one who requires one of the above rules will require the other. A mistake of the same kind is very likely to be committed in teaching rules of abbreviation. The time is not yet come for a very extensive use of tables in mercantile affairs; nor can it come until a decimal coinage is established. When the present coinage has become matter of history, it will not be the least amusing anecdote connected with it, that the great financiers of the nation were so much afraid of the fractions of their own money, that they preferred to lose eight pounds out of three hundred in the collection of a tax, that it might be exactly seven pence in the pound, rather than let it be three per cent. It is obvious enough that the income tax was meant for the nearest approximation to three per cent. which would give an exact number of pence in the pound; and it was supposed, for example, that in calculating the tax on £587, the first of the following calculations being the easier would be substituted for the second or more difficult:587 587 The one who is used to shorten his rules will say that 8s. is 40 per cent., and 8s. 6d. 42 per cent., and will perhaps rest satisfied with that approximation. But the method we advocate enables us to write down at once 432 as the fraction which 88. 73d. is of a pound, and thence to name 43,3 per cent. as the proportion required. If still greater precision be demanded, the advantage is still greater; for 43229 gives £43 4s. 7d. per cent. 10 With regard to most rules of abbreviation there is this to be said, that however convenient they may be, each in its place, they will be so seldom required that they will be forgotten: so that, when an occasion for the use of any one of them arises, one person will have finished the question in the ordinary mode, while another is recovering the abbreviated rule. It is only with respect to processes which are sure to be often wanted that such rules are therefore worth their trouble: each kind Answer £17 12s. 2d. But, in truth, had the rule for procuring the deci mal parts of a pound been well known, it would have been easier to do the second than the first, as follows: 587 3 1761 17-610= £17 12s. 2d. If any person not much accustomed to computation, and feeling its difficulty, should endeavour to mend his habits by the practice of the foregoing recommendations, we warn him that he will have his period of difficulty, during which he will not be able to see that he gains anything. He has to acquire what he probably never aimed at before, quick and ready habits of doing a few simple things. Without resolute determination he will do nothing; if he feel that he is not of the nature of those who face difficulties and conquer them, he had better not proceed to the trial. There is no use in disguising the fact that persons of ordinary memories never become good computers without hard work and steady perseverance; but, on the other hand, it must be allowed that long vestigation of Truth? 7. Give examples of their united action. MATHEMATICAL CLASS. Design of Class. It may be well to state at the outset that this class is especially designed for the benefit of young men and others who are desirous of obtaining a knowledge of mathematics, but who have not the advantage of a living teacher. If, therefore, the exercises and solutions are found to be of a character so simple as to yield comparatively hale pleasure or profit to the advanced mathematician, he will have the kindness to bear in mind that the class has not been opened for his especial benefit. The plan which the teacher of this class intends to pursue is as follows: 1. To prepare, from time to time, a number of questions in Arithmetic, Algebra, Geometry, and Mechanics, which involve important principles. 2. To receive from the members of his class solutions to the questions; which solutions, if urreet, and provided they come within certain rules of correspondence (given on the wrapper of the present number), will be acknowledged. 3. To publish, from time to time, the best solufions which he may receive, with such notes as he may think calculated to render the solution more perspicuous. 4. It will be his privilege annually to award certificates of merit, printed on beautifully embossed sards, in gilt frames, to the three best in each of the following divisions:- 1. Arithmetic and Algebra. 2. Geometry. 1. Mechanics. In order that members may be the better able to judge of their own proficiency as compared with that of other members, the teacher proposes, when acknowledging correspondence on wrappers, to connect the numbers of the proposi tions which each person is successful in solving with his initials. QUESTIONS FOR SOLUTION.-I. Arithmetic and Algebra. the 1. There are said to be 1,500,000 tons of iron smelted per annum in Great Britain; the specific gravity of cast iron is 7-248. Required the side of a cube that would contain that quantity. 2. There is a rectangular field, the length of which is 950 links, and the breadth 870 links; included, however, in this admeasurement is a ditch which equals one-twentieth of the whole, and extends half round the field. Required its width. 3. A certain man found gold coins of the respective values of 278. and 21s. each. Now, for every two that he found of the greater value he found three of the lesser value; and the entire worth of what he found was 641. 7s. How many did he find of each? 4. A general distributed to 9 captains, 12 lieutenants, and 135 common soldiers, the sum of 1,7991. 17s. To every lieutenant he gave twice as much as to a private soldier, and to every captain three times as much as to a lieutenant. much did each receive? Geometry. How Lotices of Books. The Diffusion of Knowledge. By Thomas gain a subsistence, or to appear fashionable and young men in connexion with the "Dundee Literary Societies' Union;" and it is well worthy of that publicity which, by the aid of the printing press, has been given to it. The venerable lecturer discourses upon the progress of literature and science in past ages, and takes a gloomy, though we believe truthful, view of their position in the present. He next dwells upon the means to be used to raise the great mass of society from their present state of intellectual degradation, and discourses in a suggestive strain upon seminaries for the instruction of infants, intellectual schools, mechanics' institutions, and young men's societies for mutual improvement. We commend the following extract to the attention of those who fancy that the education of the people is accomplished, or that there is no necessity for great earnestness in this matter: "There is perhaps no country in the world, excepting Switzerland and the States of America, where the body of the people are better educated or more intelligent than in Scotland; yet we need not go far, either in the city or in the country, to be convinced that the most absurd and superstitious notions, and the grossest ignorance respecting many important subjects intimately connected with human happiness, still prevail among the great majority of the population. Of two millions and a half of inhabitants which constitute the population of this part of Great Britain, there are not, perhaps, 30,000, or the eightieth part of the whole, whose knowledge extends to any subject of importance beyond the range of their daily avocations. With respect to the remaining 2,470,000, it may perhaps be said with propriety, that of the figure and magnitude of the world they live in-of the seas, rivers, continents, and islands, which diversify its surface, and the various tribes of men and animals by which it is inhabited-of the nature and properties of the atmosphere which surrounds them-of the discoveries which have been made respecting light, heat, electricity, and magnetism-of the general laws which regulate the economy of nature-of the various combinations and effects of chemical and mechanical powers-of the motions and magnitudes of the planetary and the starry orbs-of the principles of legitimate reasoning-of just conceptions of the attributes and moral government of the Supreme Being-of the genuine principles of moral action, and of many other subjects interesting to a rational and immortal being, they are almost as entirely ignorant as the wandering Tartar, or the untutored Indian. polite. And if this rule be admitted, I am afraid that a goodly number even of lawyers, physicians, clergymen, teachers, nay, even some authors and professors in universities and academies, would rational inquirers after truth. Admitting this statement, it will follow that there is not one individual out of 400 of the human race that passes his life as a rational intelligent being, employing his faculties in those trains of thought and active exercises which are worthy of an intellectual nature. For, in so far as the attention of mankind is absorbed, merely in making provision for animal subsistence, and in gratifying the sensual appetites of their nature, they can be considered as little superior in dignity to the lower orders of animated existence." be struck off from the list of lovers of science and The doctor does not close with these gloomy statements, but gives wing to his imagination, and presents at least a dazzling prospect of future glory. He says: "I behold in the prospect of future ages the most important changes in the improvement both of the intellectual and of the physical world. I behold the surface of the earth, at no distant period, adorned with vegetable and architectural beauties; our deserts transformed into fruitful fields; our marshes drained; our gardens producing the fruits of every clime; our highways broad and spacious, and at the distance of every quarter of a mile furnished with seats and bowers for the shelter and refreshment of the passing traveller; our abominable lanes and closes-the seats of physical and moral pollution-overturned, and laid open to the light of heaven; and our narrow streets expanding into spacious squares, cheered with the solar beams and with rural prospects, and ventilated with the refreshing breeze; our densely crowded cities almost completely demolished, and new cities arising from their ruins, on noble and expansive plans, corresponding to the expansive state of the human mind. "I behold the climates of the earth meliorated by the hand of genius and industry, by the cutting down of forests, the draining of marshes, and the universal cultivation of the soil; the thunder-bolts of heaven wielded by the philo sophic sage, and the forked lightnings, directed by the hand of art, to play in harmless coruscations in the region of the clouds. I behold locomotive engines, steam carriages, and air balloons brought to perfection, transporting multitudes of human beings from one city to another, from one nation to another, and from one continent to another, with a degree of velocity which has never yet been attempted. I behold the "Of 800,000,000 of human beings which people savage restored to the dignity of his intellectual the globe we inhabit, there are not, perhaps, nature, no longer roaming the desert wild and 2,000,000 whose minds are truly enlightened as uncultivated like the beasts of prey, throwing they ought to be, who prosecute rational pursuits aside his warlike bows and his battle axes, directfor their own sake, or from a pure love of science, ing his faculties to the improvement of his species, independently of the knowledge requisite for their and to the most sublime investigations. I behold respective professions and employments; for we men of all nations and kindreds cultivating a must exclude from the rank of rational inquirers harmonious and friendly intercourse-the tribes after knowledge all those who have acquired a of New Holland, Borneo, Sumatra, and Madasmattering of learning with no other view than togascar, visiting the British Isles with the produc tions of their respective countries, and holding literary correspondence with the directors of our philosophical and missionary associations on all the subjects of christian and scientific investigatna. study of any of the more rigid and abstract works on the subject, would be of much service. As such we can recommend it to our readers. A logic in the sense of a systematic and classified series of directions upon "the right use of reason," and the conduct of the understanding," it certainly is; but in the more strict and legitimate signification of the term, viz., an exposition of the form and manner of all true thinking, it certainly is not. To such of our readers as have studied the series of papers on the "Art of Reasoning" which have appeared in this periodical, the examples contained in this work will form an agreeable and useful praxis upon the accuracy of the rules laid down for their guidance. "I behold the scenery of the heavens more fally explored, and new prospects opened into the region of the stars; the geography of the moon brought to perfection, and traces of the existence and operations of its inhabitants exhibited to view; the nature of comets ascertained; the causes of the various phenomena which appear en the surfaces of the planets explained; the construction of the sun, and the nature of its spots determined; and the sublime scenes connected with new and variable stars, double and treble stars, and the thousands of nebulæ dispersedthroughout the regions of boundless space, more fully displayed. "I behold the ministers of religion expatiating amidst thousands of intelligent worshippers on This is one of the books suited to the wants of higher themes and more diversified subjects than the times; learned, acute, philosophical, and pothose to which they are now necessarily re-pular in its style, it is a treatise which demands stricted, not confining their attention to a few fragments of the christian system, and a few points of religious contemplation, but taking the whole of divine revelation for their text-book, and deriving their illustrations of it from the records of history, and from all the diversified scenes of the universe. Logie for the Million; a Familiar Exposition of Reason and Faith; their Claims and Conflicts. the attention of every sincere inquirer into the truth of Christianity, We recommend every reader to purchase and study this most excellent little tractate. It deals in a most lucid and masterly manner with most of the prominent kinds of modern unbelief, especially with the self-styled rational, i. e., the mythic school of theologians. "In fine, I behold the human soul thus The following beautiful little apologue will illus. elevated and refined, and endowed with multifa-trate the position which the author adapts:-"We ricus knowledge, dropping its earthly tabernacle should represent Reason and Faith as twin-born; in the dust, and in another and a happier region the one, in form and features the image of manly of existence, prosecuting similar investigations on beauty,-the other, of feminine grace and gentlea more ample scale, contemplating the economy ness; but to each of whom is allotted a sad privaof other worlds, exploring the wonders of divine tion. While the bright eyes of Reason are full of visdom and omnipotence throughout the im- piercing and restless intelligence, his ear is closed ensity of creation, rising nearer and nearer to to sound; and while Faith has an ear of exquisite the divinity, expatiating amidst objects of beauty delicacy, on her sightless orbs, as she lifts them and beneficence, and beholding new scenes of towards heaven, the sunbeam plays in vain. Hand grandeur and felicity rising to view in boundless in hand the brother and sister in all mutual love perspective, while ages, numerous as the drops of pursue their way through a world on which, like ocean, are rolling on." ours, day breaks and night falls alternately; by day, the eyes of Reason are the guide of Faith, and by night, the ear of Faith is the guide of Reason. As is wont with those who suffer under such privations, respectively, Reason is apt to be eager, impetuous, impatient of that instruction which his infirmity will not permit him readily to We have never been favourable to writing down apprehend; while Faith, gentle and docile, is to the people, and we are always inclined to look ever willing to listen to the voice by which alone with an eye of suspicion at the shoals of “make-Truth and Wisdom can effectually reach her."enes" which issue from the press. We have no fath in the possibility of acquiring knowledge except through hard labour, diligent attention, and resolute perseverance. "Lightly come, lightly go, is as true in education as in other every-day Teatters. Were we inclined to admit of any exception to this rule, the work before us would receive our suffrage. It is not a regularly digested and scientific treatise on the subject, nor is it even a popularized view of the science, but a series of original and selected remarks upon a few of the calef species of argumentation. Should any one wishful of gaining a clear, perspicuous, and accarate view of the objects of the science of reasing take up this book, he will be grievously disappointed; but to any one who has acquired a knowledge of the methods and forms of logic, the work will be found valuable. It is a very large collectanea of the very best specimens of argumentative literature; and as a sequel to the Pp. 2, 3. Little Henry's Holiday at the Great Exhibition. The Great Exhibition is now closed, but its congregated wonders will long remain the topic of frequent fire-side conversations, and its chefs d'œuvres will become as "familiar as household words." The young who were privileged to visit it will delight to be able to talk of it intelligently; and those who did not see it will be glad to get a good description of its contents. To both of these classes the little book before us will be very acceptable; and we shall be disappointed if children of a larger growth" do not read it with avidity and profit. It has already been highly honoured, her Majesty having directed it to be placed in the hands of the youthful members of the royal family. |