ascertain its embouchure. After encountering many and great dangers, they reached the sea by the central or principal branch of the Niger, which is the river called Nun, and which disembogues itself into the Atlantic Ocean, between the Bight of Benin and the Bight of Biafra. The source of this river, as determined by Laing, is at the foot of Mount Loma, in the Kong Mountains. From this point to Timbuctoo its course was known; but the brothers Lander made it known from Boussa to the ocean, and so solved a part of the geographical problem which had so long existed without a satisfactory solution. LESSONS IN ARITHMETIC.-XXI. CONCRETE OR COMMERCIAL ARITHMETIC. 1. WE have hitherto been concerned with what are called abstract numbers-that is to say, numbers abstracted from their connection with any special thing, object, or magnitude; and we have established all the principles connected with them which are necessary to be known by the student of elementary arithmetic. We now proceed to apply these principles to concrete numbers-that is to say, to numbers which indicate some actual magnitude, object, or thing-as, for instance, time, money, length, etc. Theoretically, we are already in possession of principles which enable us to perform any calculation with reference to any concrete number. Take length, for instance. Suppose that we fix upon a certain length, and call it a mile. By means of this mile we could measure any other length whatever. For by fractions or decimals we could express any part or parts of a mile whatsoever; we could add, subtract, multiply, or divide any number of miles or parts of a mile, etc. etc. But it is manifest that, although this could be done, great inconvenience would arise from the cumbrous nature of the operations. In treating, for instance, of fractional parts of a mile, it would be often very difficult to realise the length indicated. What idea would most people have of of a mile? But if they were told that this length is very nearly indeed equal to a foot, they would form a very clear conception of the length. Hence, in measuring all magnitudes, the method of subdivision has been employed. Certain magnitudes have been fixed upon and named, and then these again divided and subdivided, and names given to the divisions, as convenience best suggested. Quantities expressed in this way by means of different subdivisions are called compound quantities. Thus, a sum of money, expressed in pounds, shillings, and pence, is a compound quantity. The names of the various subdivisions are generally called denominations. 2. Accurate Standard or Unit. On proceeding to measure any magnitude or quantity, it is evident that it is of the utmost importance to come to an exact definition of some one fixed magnitude of the same kind, with which we may compare all such magnitudes. Such a fixed magnitude is called a standard. When this has been done, then the standard can be subdivided, or multiples of it can be taken, as we please, and names given to the subdivisions or multiples. The subdivisions which are employed in England in the coinage and weights and measures are, as might be expected, not founded upon one carefully prepared and philosophical system, but have gradually grown up during long centuries, having often been suggested by special convenience or local usage. The subject has of late received much attention, and the possibility and advantage of establishing a uniform decimal system of coinage, weights, and measures, have been discussed with considerable warmth. On July 29th, 1864, an Act of Parliament was passed to render permissive the use of a decimal system of weights and measures called the "Metric System." Contracts and transactions, therefore, based on this system are now legal. We shall, however, return to this subject hereafter. We proceed now to treat of the subdivisions of various concrete quantities which are now generally in use. MEASURES OF TIME. 3. The time of the revolution of the earth in its orbit can be shown by the calculations of astronomical science to be an uuvarying quantity, or, at any rate, to be subject to no appreci able variation for an immense number of centuries. Now, it is found that this time is 365·24224 (i.e., about 365-25, or 3654) mean solar days, a solar day being the interval which elapses between noon and noon-that is, between the times when the sun is successively highest in the heavens.* The year is made to consist of 365 days-i.e., about 1 of a day less than the time of the revolution of the earth in its orbit. To every fourth year (Bissextile or leap year, as it is called) one day is added, and thus at the end of every four years the earth is again very nearly in the same part of its orbit as it was at the beginning of them. We say very nearly, because the earth actually revolves round the sun in 365-24224 days, which is less than 365 days by 00776 of a day. This error in excess amounts to a day in about 128 years-i.e., to very nearly 3 days in 4 centuries. Hence, to make our reckoning still more accurate, we omit 3 days in 4 centuries; and this is done by making the year which completes every century not a leap year, except such centuries as are divisible by 4. Thus A.D. 1700, 1800, and 1900 are not leap years, but A.D. 2000-i.e., the year completing the twentieth century-is a leap year. The establishment of the leap year is due to Julius Cæsar; that of the omission of the leap year three times in 400 years to amounted to ten days, caused the ten days which followed Pope Gregory XIII., who, in the year A.D. 1582, when the error October 4th to be omitted in the reckoning. October 5th con sequently was called October 15th. This latter system, the New Style, as it is called, was not adopted in England until A.D. 1752, when the difference between this and the old mode of reckoning amounted to about eleven days. The difference between the Old and New Style amounts Christmas Day and Lady Day, for instance-Old Style, would at present to about twelve days. Thus any fixed dayoccur twelve days later than our present Christmas and Lady Day. Russia is now the only country in Europe which retains the Old Style. Having, then, thus established a fixed invariable standard whereby to measure time, we are enabled to make any further subdivisions for convenience. Any number of seconds are written either thus-35′′, 23′′, or 35 sec., 23 sec. It is better, however, in indicating time, to use the abbrevia tions sec. and min. for seconds and minutes, inasmuch as the same names and the marks and" are used for certain divisions of the circle (Art. 18). The Calendar months into which the year is divided do not each contain the same number of days. The number in cach month, however, may be remembered by the following lines: Thirty days have September, But leap year comes one year in four, MEASURES OF LENGTH. 4. Having determined, as above explained, an exact measure of time, we are enabled, curious as it may appear, to deduce from it a fixed and invariable measure of length. We might, of course, take any object-a piece of metal, say-and, giving to its length a particular name, thus obtain a means of measuring all other magnitudes. But this object, whatever it might be, and however carefully preserved, would be liable to be lost, to alteration from decay, variation of temperature, etc. It is therefore very desirable to have some invariable and independent times in the year rather longer, and at others rather shorter, than its A solar day is not actually of unvarying duration, but is at some average length. It is this average length of the solar day which is called the mean solar day, and is divided into 24 hours. means to which we can always have recourse, to give us an exactly accurate standard of length with which to compare all other lengths. Now, the interval of time called a second being invariable, it is found that a pendulum which, in the latitude of Greenwich, under certain conditions, oscillates in one second, is of a certain length. It is further proved, from mechanical and mathematical principles, that this length must always be exactly the same whenever the experiment is tried under exactly the same conditions. This accurate and scientific method, however, as might be expected, was not the way in which a measure of length was first determined. A certain measure called a yard having been established, and this yard divided into 36 equal parts, called inches, it was found that the length of the pendulum oscillating in one second of time at Greenwich contained 39-1393 such inches. We thus see that we have a means of recovering and correcting, at any time, the measure of the yard. The actual standard yard was fixed, by Act of Parliament passed 1835, to be "the straight line or distance between the centre of the two points in the gold studs in the straight brass rod now in the custody of the Clerk of the House of Commons, whereon the words 'Standard Yard, 1760,' are engraved." The Act further states that in the latitude of London the pendulum vibrating seconds of mean time in vacuo at the level of the sea is 39 1393 inches. This standard, however, was, in fact, destroyed in 1834, at the fire of the House of Commons, before the Act passed. The Astronomical Society, however, had carefully prepared a standard yard, which is calculated to differ from the old one by not more thanth of an inch. We cannot here touch upon the ingenious and refined processes by which measurements are made when extreme accuracy is required, as, for instance, in determining a new standard length from the old one, or in finding to what amount of variation a given measured length is subject, from unavoidable external causes. The reader may consult the article Standard in the "Penny Cyclopædia," which will give him a good general idea of the subject. SUBDIVISIONS OF LENGTH, OR LINEAR MEASURE. 5. The smallest measure is a barleycorn, or one-third of an inch; so called because, originally, the inch was obtained by placing together lengthwise three barleycorns taken from the centre of the ear. Little more, however, than the name of this subdivision remains, measurements being generally conducted in decimal or fractional parts of an inch. LESSONS IN BOOKKEEPING.-V. THE Bill-Book generally consists of two distinct parts; the one contains the Bills Receivable, that is, the Bills which have been given to a merchant instead of cash, and of which he is to receive payment at certain periods; and the other contains the Bills Payable, that is, the Bills which he has given to others instead of cash, and which he must pay at certain periods. Instead of entering these in separate parts of the same Book, they may be entered in separate Books; the one being called the Bills Receivable Book, and the other the Bills Payable Book. When a Merchant receives Bills in lieu of money from persons who are indebted to him, it may be done in two ways; first, he may either draw a bill on the person who owes him the amount of it; or he may have a bill indorsed over to him, either from the person who drew it for the same amount on another, or from the person through whose hands it passed in a similar manner. When a Merchant accepts Bills, that is, agrees to pay them, they may be either drawn upon him by persons to whom he is indebted, or by persons who have consigned goods to him for sale on their account; or they may be drawn upon him by persons who consider him as the agent of a principal (another merchant) with whom he keeps an Account Current. The Bills Receivable Book contains the particulars of Bills Receivable (that is, for which cash is to be received), which become a merchant's property in the manner which we have described in the preceding paragraph. These particulars are recorded in columns ruled and titled for the purpose; and in the system which we intend laying before our students, they are entered in the following order :-1st. The date when received; 2nd. The person from whom, or on whose account received; 3rd. The number affixed by the Merchant on the bill; 4th. The person on whom the Bill is drawn; 5th. The date when the Bill is due ; 6th. The amount or sum for which it is drawn; 7th. The manner in which it is disposed of; and 8th. The date when it is disposed of. Besides these particulars, the following are frequently added in business :-9th. The name of the drawer of the Bill; 10th. The date when and the place where it is drawn; 11th. The period or time for which it is drawn; and 12th. The persons to whom, and drawn upon others and endorsed over to a Merchant, they are the place where it is made payable. When Bills Receivable are called Remittances; when they are drawn by the Merchant himself, they are called Drafts. The Bills Payable Book contains the particulars of Bills Payable (that is, for which cash is to be paid), which a Merchant has accepted, and which are therefore called his Acceptances. These particulars are also recorded in columns ruled and titled for the purpose; these are, in this system, entered in the following order :-1st. The date when the Bill is accepted; 2nd. The person by whom and on whose account it is drawn; 3rd. The number which the Merchant affixes to the Bill; 4th. The person to whom it is made payable; 5th. The date when it falls due; 6th. The amount or sum for which the bill is drawn; and 7th. The date when it is paid. Other particulars besides this are 1 deg. or 1°. entered in the Bills Payable Book, similar to those which we have enumerated under the head of Bills Receivable; but as 1 r. or p. = 1 inch = 1 foot written 1 in. = 1 yard 1 yd. = 1 rod, perch, or pole = 1 furlong 1 fur. = 1 mile 1 m. 11. = 1 league = 1 degree* 1 great circle of the globe. Other measures of length are sometimes used, having reference to special descriptions of magnitudes. For instance, 12 lines make 1 inch; 4 inches make 1 hand; 9 inches 1 span; 18 inches 1 cubit; 6 feet 1 fathom. In measuring roads and land, a chain 22 yards or 4 rods long is used, called, from its inventor, Gunter's chain. It is divided into 100 links, each of which therefore contains of a rod, or 7·92 inches. CLOTH MEASURE. many of them seem to be unnecessary, except in very particular cases, we have not burdened our system with these, being satisfied that the general principles of Bookkeeping are most readily acquired when the attention of the student is not attracted by too many things at once. When those particulars only are entered in both Bill Books which are deemed to be indispensably necessary, it is usual to have a column in each of them headed with the words Remarks, and intended for the insertion of any additional particulars relating to a Bill which In the measurement of cloth, linen, etc., the following lengths may seem to be very requisite to be known; such as the amount are sometimes used : of foreign money for which foreign bills are drawn, with the rate of exchange between the moneys of the different countries where the bills were drawn, etc. Such a column prevents the necessity of entering these particulars separately as memoranda in the Day-Book. The following are the forms or specimens of certain bills of exchange, both inland and foreign. Inland bills of exchange are written orders for the payment of money, drawn by a merchant residing in one place of a country, on a merchant or banker residing in the same place, or in another place of the same country, in favour of a third person, for value received in some shape or the other. These bills are either in the form of a Draft or a Promissory Note. and sixpence, for value received. (due July 17th). London, 14th April, 1863. Three months after date we promise to pay to Mr. Abel Smith, or order, Three hundred and six pounds, ten shillings, HOWARD, SON, & Co. Foreign bills of exchange are written orders for the payment of money drawn by a merchant residing in a particular place of one country, on a merchant or banker residing in a particular place of another country, in favour of a third person for value received, as before mentioned. These bills are, of course, of two kinds, when the moneys of the two countries are different. FIRST FORM OF A FOREIGN BILL OF EXCHANGE. London, 21st May, 1863. £600, at 13m. 12s. bco. per £ stg. Three months after date, pay this our first of exchange (second and third of same tenor and date unpaid) to the order of Messrs. Brown & Co., Six hundred pounds sterling, at the exchange of thirteen marks twelve shillings banco per pound sterling, value of the same, which place to account as advised. J. & R. MORLEY. Messrs. Lichtenstein and Co., THE DAY-BOOK, JOURNAL, ETC. The next book which falls under our consideration is the DayBook, which, as we formerly remarked, might be more properly denominated Goods-book, as it contains the particulars of the purchases and sales of Goods on credit; but this term is too limited, if, as is generally done, it is made to contain the particulars of all other transactions which do not strictly belong to the Cash-Book or the Bill-Book. In mercantile houses, where the particulars of important transactions are numerous and minute, as in the case of the entries of invoices of the shipments of Goods, and the sales of consignments, it is usual to make only an abstract of these particulars, and to refer to the InvoiceBook and the Sales-Book for those which are necessarily omitted. In like manner, when the particulars of Insurances on Goods, Speculations in inland or foreign produce, or Adventures to or from foreign countries, become too numerous or cumbersome to be entered at length in the Day-Book, references must be made to those Books which are specially kept for these purposes. In transactions where Goods are sold for Cash, the particulars must still be entered in the usual manner in the DayBook, just as if they had taken place on credit; and the particulars of the transactions relating to the money paid for the Goods must also be entered in the Cash-Book. Were this not done, the accounts both of Property and Persons could not be kept in a proper manner, and nothing but confusion and error would ensue. We cannot, however, stop here to explain the reason of this or of many other things which we have said in these lessons, otherwise we should never have done; but the reason will be sure to suggest itself to the attentive student. In home or inland transactions, where Goods are purchased by a Merchant on Commission as an Agent for another party, it is usual to enter in the Day-Book only the gross amount or sum on which the Commission is calculated, and the Incidental Expenses attending the Purchase and the Transmission of the Goods to the Principal, or party for whom the Merchant is Agent, without entering into the more minute details. This will be exemplified in the system relating to Inland Trade. The method of keeping the Day-Book which we shall adopt in our Lessons, is a modification or rather an improvement of the principle of Check Entries by means of Double money columns, invented by Mr. Jones. This method consists in having Dr. and Cr. money Columns in the Day-Book, and putting in the one column the net sum to be carried to account in a line with the names of the Debtor and Creditor in any entry; and in the other column the cost of the Goods, etc., in a line with their quantity and price. In the former column are also entered the Discounts, Commissions, and other deductions from the cost; and in the latter column are entered all Charges, Incidental Expenses, etc., forming additions to the cost. It is found that when the two columns are added up at the bottom of every page, and at the end of every month, their amounts always exactly agree, unless some error has been committed. Hence, if this process is carried on from page to page, such error cannot remain undetected longer than the time required to finish the page in which it occurs. The same method of checking erroneous entries is adopted in the Journal, where it is even of more importance than in the Day-Book. Hence, as both the Debtor and Creditor are mentioned in each entry, the amounts of the sums entered in both columns, whether taken page after page, or month after month, are sure to agree, if no mistake has been made in entering them; if there has, as we said before, it will be detected as soon as the Bookkeeper reaches the bottom of the page. But this advantage, although great in keeping the Journal free from error, is not the only one gained by the adoption of this method. For the Ledger itself being a periodical transcript of the Journal, the amounts of all the sums entered in the Dr. and Cr. columns of the Ledger during any given period, must exactly agree with the amounts of the sums entered in the columns of the same name in the Journal. In this way a regular and complete system of Checking Entries in Bookkeeping is obtained; the liability to commit error in posting is very much diminished, if not altogether removed; and the speedy detection of error is rendered almost certain in the hands of an intelligent Bookkeeper. Moreover, the process of balancing the Books at the year's end is thus made an operation of comparative ease, accuracy, and certainty. It being now clearly understood by the student that the Journal is not in business what its name implies, a mere record of daily occurrences, but a collection of all the entries of the transactions of any concern for a given period, which are intended to be carried to account in the Ledger, it becomes necessary to explain how this part of Bookkeeping is performed. The Journal is made up from the Daily or Subsidiary Books which have been already described; and the process of making up-that is, of copying the entries from these books into the Journal-is called Journalising. In the system of transactions about to be laid before our students, this process is performed at the end of each month. Instead of Journalising, therefore, it should be denominated Monthly Posting or Sub-Ledgerising. The first book which is journalised is the Cash-Book. In doing this, you make Cash Account Dr. to Sundries for all the Receipts of money during the month, and you then specify the names of all the Accounts on which Cash has been received, taking care to collect all the sums received on the same account in any case into one amount, for the sake of abridging the entries in the Ledger. If, however, Cash has been received on only one Account, then make Cash Account Dr. to that Account. Next, you make Sundries Dr. to Cash Account, for all the Payments of money during the month, and specify the names of all the Accounts on which Cash has been paid, collecting all the sums paid on the same account into one amount, as before; and if cash has been paid on only one Account, make that Account Dr. to Cash Account. In making up these cntries for the Journal, short loans which are settled within the month are to be omitted; if not settled within the month, they must be extended in the proper columns, treated as regular transactions, and carried to account in the Ledger; all balances of Cash are to be omitted in Journalising, because they are not real transactions, but only operations employed to check the accuracy of the Cash Account. LESSONS IN ARCHITECTURE.-II. BUILDINGS IN UNHEWN STONE. WE will now proceed to trace briefly but distinctly the progress of architecture amongst the different nations of antiquity, for the purpose of reaching our own times in chronological order. Before entering into details, we may point out the particular features which characterise the grand periods of the art, and the different systems in which its resources were developed in order to satisfy the numerous demands of the civilisation in which it originated. Architecture, like all the productions of the human mind, The simplicity of the first erections for religious purposes may be seen in the construction of the altars of early times. The first sacrifices, which the Bible and ancient tradition trace up to the earliest times, were made upon consecrated heaps of stones, which were collected upon high places. These first altars, called BETH-EL (the House of God), were erected in Chaldea, in Judea, and in Egypt. They were built, according to the Scriptures, of stones without cement, if the places where they were raised afforded proper materials. In other places they were constructed of turf and earth, where the plain country presented no solid materials. Such erections or mounds are found in Asia Minor and in India; at Heliopolis, celebrated for the worship of the DRUIDICAL REMAINS ON THE PLAIN OF CARNAC, IN THE DEPARTMENT OF MORBIHAN, FRANCE., presents at first only simple rudiments, quite in accordance with | sun, and the great sidereal divinity of the Syrians. Lucian primitive manners. From the earliest ages we find three great divisions established amongst all nations: first, private buildings; econdly, religious edifices; and thirdly, military constructions of a defensive character. The first care of a people, as we remarked before, would be to construct individual habitations; but being at first hunters and shepherds, they would be necessarily wanderers, and their dwellings would be tents constructed of the skins of animals, or cottages made of branches of trees. When they dwelt on the borders of rivers they would employ reeds; Asia and Egypt present us with examples of this kind. In some exceptional cases they dwelt in caverns, or in shallow excavations. The cottages were usually circular; piles of stones and earth, arranged in a circle, constituted their foundation. This form is found amongst all nations; that of the square, requiring more complicated combinations, was not adopted at first. 24-N.E. describes a throne or altar to the sun composed of four great stones arranged in the form of a table. At Ortosia, in Syria, there is an edifice of this kind raised in an open enclosure, and built of stones in a square form. Strabo relates that, travelling in Egypt, he saw his road covered with temples devoted to the god Mercury, which were composed of two unhewn stones, which supported a third, resembling the cromlechs which are to be seen in some parts of England. Artemidorus, quoted by Strabo, mentions that in Africa, near Carthage, the god Melkart (Moloch), or the Phoenician Hercules, was worshipped in a similar manner three or four stones being placed one upon another in the form of a rude altar or table. This simple manner of building applied to primitive altars, and to the sacred enclosures which surrounded them, after having been developed, as we have seen, in Asia and Africa, extended into Europe from the borders of the Black Sea and the Caucasus, Mon frère partit hier pour Paris. My brother left yesterday for Paris. a conqueror. 2. The student will bear in mind that the past indefinite [Sect. 41] may be used for the past definite. The past definite, however, may never be used for the indefinite. tion the indefinite is preferred to the definite, as the latter would appear too formal [§ 117 (3)]: In conversa 3. The past definite may generally be rendered in English by the perfect. The past definite can never be rendered in English by the participle present of the verb preceded by was. J'allai à l'église hier matin. I went or did go to church yesterday morning. 4. TERMINATIONS OF THE PAST DEFINITE OF THE FOUR CONJUGATIONS. See Sect. 22, and § 60. -is where M. Dubois, of Neufchatel, saw a great number, even to This simple and primitive style of architecture appears to have been originally universal, if it was not simultaneous with the progress of civilisation, which marched from east to west; and has left monuments and edifices so varied as to occasion them to be classified, and have names given to each class. These names are borrowed from the old Celtic tongue, or language of the Druids. Thus, erections of the first class, which consisted of long stones, erect and isolated (standing singly) like obelisks, were called Peulvans, or Menhirs. Buildings of the second class, consisting of a huge unhewn stone, supported on two or more rough stones set on end on the earth, are called Cromlechs by British archæologists and Dolmens by French antiquarians. The third class consists of Uncovered Alleys, of upright stones, placed in rows like trees, and occupying a very considerable area, like those of the plain of Carnac, in the department of Morbihan, part of the old province of Brittany, in France. While in the fourth class these long rows of stones assume a circular or elliptical form, and support stones placed on them horizontally so as to form a lintel or architrave. The military constructions of early times appear to have been mounds or artificial hills, at the summit of which there was a shallow excavation, of which the edges formed a rampart. It is certain that in countries where hills naturally occurred they were fortified in the same way as those which were raised by art. These natural fortifications are still to be seen in the neighbourhood of Athens and the Piræus, and they were of immense service in the wars of Greek independence. Mankind in a savage or wandering state having no instruments for raising the earth or digging ditches, made fortified enclosures with heaped stones, having a double slope. The entrances to these fortresses were defended by artificial hills, placed inside near the gates. LESSONS IN FRENCH.-XXIV. 1. The past definite may be called the narrative or historical tense of the French. It is used to express an action entirely past, definite and complete in itself. The time may or may not be specified, but every portion of it must be elapsed. Tu chant -ai fin Nous cherch -âmes Vous port -âtes carried aim -èrent loved, liked finished -îmes sais -îtes d -ûtes perd -îtes lost -irent -ûmes entend 1. Le banquier reçut-il beaucoup d'argent la semaine dernière ? 2. Il en reçut beaucoup. 3. Aussitôt que vous aperçûtes votre frère, ne lui parlâtes-vous pas ? 4. Dès que je l'aperçus, je lui parlai. 5. Avez-vous déjà porté vos habillements neufs ? 6. Je ne les ai pas encore portés. 7. Quand il vous donna de l'argent hier, le remerciâtes-vous ? 8. Je le remerciai et je le priai de vous remercier. 9. Avez-vous trouvé vos livres? 10. Je ne les ai pas encore trouvés. 11. Lorsque vous vîntes nous voir ne finîtes-vous pas vos affaires avec mon père? 12. Je les finis alors et je le payai. 13. N'avez-vous pas vu votre sœur aînée pendant votre séjour à Lyon ? 14. Je ne l'ai pas vue. 15. Ne vous couchâtes-vous pas trop tôt hier au soir? 16. Je me couchai tard. 17. A quelle heure vous êtes-vous levé ce matin? 18. Je me suis levé à cinq heures; je me lève ordinairement de bonne heure. 19. Ne cherchâtesvous pas à vous échapper de votre prison l'année dernière ? 20. Je n'ai jamais cherché à m'échapper. 21. Avez-vous vendu vos propriétés ? 22. Je ne les ai pas vendues. 23. Qu'avezvous donné au soldat? 24. Je ne lui ai rien donné. 25. Pendant son séjour à B., nous lui donnâmes tout ce qu'il voulut. EXERCISE 98. 1. What did you receive last week? 2. We received fifty francs from your friend, and twenty-five from your brother. |