χαριτας

Αγησίλαος περι ανδρειας και δικαιοσυνης ερωτηθεις, ποτερα βελτιων, Ουδεν ανδρειας, εφη, χρηζομεν, εαν παντες ώμεν δικαιοι. Ου μόνον δε το μη αποδιδοναι αδικον έκρινεν, αλλα και το μη πολυ μείζους τον μείζω δυναμενον. Δια το φιλοπονος ειναι, πᾶν μεν το παρον ἡδέως επινε, πᾶν δε το συντυχον ήδεως ησθιεν· εις δε το ασμένως κοιμηθῆναι πᾶς τοπος ην ἱκανος αυτῳ. Διδοντος δε αυτῷ παμπολλα δῶρα Τιθραυστου, ει απελθοι εκ της χώρας, απεκρινατο ὁ Αγησιλαος, ο Τιθραῦστα, νομίζεται παρ' ήμιν τῳ αρχοντι καλλίον είναι την στρατιαν η ἑαυτον πλουτίζειν, και παρα των πολεμιων λαφυρα μᾶλλον πειρᾶσθαι η δῶρα λαμβανειν. Αποθνήσκων δε τους φιλους εκέλευσε, Μηδεμιαν εικόνα ποιησασθαι· ει γαρ τι καλον εργον πεποίηκα, τουτο μοι μνημειον εστιν· ει δε μηδεν, ουδ' οἱ παντες ανδριάντες.

VOCABULARY AND REMARKS.

Το μη πολυ μείζους, supply αποδιδοναι
OvvTvxov, whatever he met with;

than those of that science.- ALFRED C. HILARY will find the work on Chemistry, published in Chambers's Educational Course, very good and cheap.

W. W. SNELLING will see one of his questions answered in the last paragraph. As to the other, we can only find room for a partial answer. The following is the order in which mathematics may be studied with advantage.

Arithmetic-Cassell's, Colenso, or De Morgan.
Algebra-Cassell's, Lund's Wood, or Colenso.

Euclid-Cassell's.

Optics-Griffin.

Airy's Tracts, etc. etc.

JAMES BURLEY: The scales appended to the maps in the POPULAR EDUCATOR explain themselves. The numbers affixed to different points of the line, show how many miles are represented by the lengths of the line between the zero point (or farthest point to the left) and the above points. A WOULD-BE PHOTOGRAPHER: The instrument in question is an ordinary camera-obscura, and may be obtained of Horne, Thornthwaite and Co., Newgate-street, or any optical instrument maker.

PERSEVERANTIA: Professor De Lolme's Manual will be found very useful, though not perhaps absolutely necessary. Dr. Beard's Latin Made Easy, is scarcely required by one who has his lessons in the POPULAR EDUCATOR. Andrews and Stoddard's Latin Grammar, is indispensable to a thorough knowledge of Latin. Dr. Beard's History of English Literature is not published separately. The Historical Educator is now complete in two volumes. You are mistaken in supposing that if a trader keeping his books by double entry, sold £30 worth of sugar for ready money, no notice would be taken of the transaction in the sugar account. Whether the money be An usher is an paid at once or at a future time, makes no diference. assistant teacher, and the qualifications for the office are obviously, knowledge, patience, good temper, and power of command, not to mention others. The advantage of matriculation is, that it enables you to take a degree. It is not necessary to know both French and German in order to matriculate at the University of London; either of the two is sufficient. inge the colleges or institutions in connection with the university. Private students cannot take degrees there without matriculating and joinWe cannot and room for lessons in civil law.

Αιζεται Problems. His solutions and occasional remarks do him great D. HORNBY has solved Problems 56 to 69 of the Second Centenary of credit.—THOS. BORCOCK has solved sixteen of the Second Centenary and

F. H. BIRTWHISTLE all of them, except only No. 35.

ERGATES may obtain the books he mentions at any bookseller's, either new or second-hand. There are several religious newspapers which are known to every body. The English Churchman, the Guardian, and the Record are the principal church weekly newspapers. EDWARD WOOD may get all the information he requires from any optician.

GULIELMUS TALBATUS: We cannot promise what you wish at present. ARITHMETIC: 81,000,000,000,000,000,000,000,000,000. To find the true discount of a given sum for a given time at a given rate, say-The amount of £100 for the given time at the given rate: £100: the interest of the given sum for the given time at the given rate: the discount required. In business discount is the same as interest.

W. M. WILLEY: We have been exceedingly gratified with your French communication, which does you infinite credit, considering how short a

Δίδοντος, offering to give ; λαφύρον, ου, το, booty, spoil. Avopiavres, all images would not (no image would) be a (permanent) memorial of me.

What are these parts (what is their mood, tense, person, etc.)? namely:

ερωτηθεις; χρηζομεν; αποδιδοναι; έκρινεν ; ησθιεν; κοιμη θῆναι; απελθοι; απεκρίνετο ; πειρᾶσθαι ; πεποιηκα. Decline the following:—ανδρειας; χαριτας; μείζους; τοπος; δῶρα ; εικονα ; μνημείον ; ανδριάντες.

ANSWERS TO CORRESPONDENTS.

We have received numerous expressions of gratitude for our past efforts in the cause of Popular Education, and regret at the prospect of their discontinuance in the present publication. Our correspondents may be assured that their communications will meet with all the consideration to which they are entitled. We hope still to promote the education of the people in other ways, and have repeatedly intimated our intention of giving articles on drawing early in the coming year.

C. R. The lessons on Chemistry are concluded. Electricity and galvanism will be discussed in our lessons in Physics.-Tav: The principles in physics, corresponding to axioms in Geometry or any other subject, are those which require no demonstration. For instance, it is an axiom that that the effect of a force is the same at whatever point in its line of action it be applied. Again, it is an axiom that two equal pressures applied at the extremities of equal arms of a lever balance each other, and that the pressure on the fulcrum is equal to their sum. Problems are capable of solution

labours have been so successful and so highly appreciated.

A NEW SUBSCRIBER's handwriting is good, but must be improved still further before he can hope to get into a merchant's office.

G. ARCHBOLD: Our Lessons in German will prepare you for translating German letters, provided you make yourself familiar with the German style of writing. It would also be desirable to get a work containing some German mercantile letters.

L. G. LAMBE: We find no promise given in the place you mention. ICONOCLASTES may get the works he wants from Paternoster Row. R. H. STY had better study the subjects he mentions in the order he has given them. His hand-writing is hardly good enough for a clerk's situation in these improved times.

JOHN TENNANT: We cannot engage to enter upon the subjects of which you speak.

T. H. SOUTHELL: The chief qualifications for a clerkship are superior handwriting, and quickness and accuracy in accounts. Our lessons in Bookkeeping ought to be amply sufficient, but they must be thoroughly mastered, and our correspondent must get a facility in working arithmetical questions correctly, besides improving his handwriting. H. K. L.: Our lessons in Chemistry are closed.

LITERARY NOTICES.

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A KEY TO CASSELL'S LESSONS IN LATIN. Containing Translations of all the Exercises. Price 1s. paper covers, or Is. 6d. cloth.

CASSELL'S CLASSICAL LIBRARY.-The First Volume of this Work, price 1s. 6d. cloth, consists of a LATIN READER, adapted to "Cassell's First Lessons in Latin."-Volume II. comprises LATIN EXERCISES, price 28. neat cloth.-Volume III. contains THE ACTS OF THE APOSTLES in the Original Greek, with copious Notes and a Lexicon, price 2s. 6d. neat cloth.

neutral line of which coincides very nearly with the equator. It is from this hypothesis that the name of the northern fluid has been given to that which predominates at the northern pole of the earth, and of southern fluid to that which predominates at the opposite pole. According to this supposition, the earth acts on the needles in the same way that a magnet does, the poles of the same name repel, those of the opposite name Fig. 365.

B

attract. Consequently, when a magnetised needle settles in the direction of north and south, the pole which points to the north contains the southern fluid, while that which points to the south contains the northern fluid. For this reason, the pole which points to the north is called the south pole, that which points to the south the north pole.

Magnetic Meridian-Declination.-It is well known that the astronomical meridian of a place is the plane which passes through the place and through the two terrestrial poles, and that the meridian is the intersection of the plane with the surface of the globe In the same way the magnetic meridian of a place is the plane, which at that place passes through the centre of the earth, and through the two poles of a magnetised needle in equilibrium on a vertical axis.

This being premised, as the magnetic meridian does not in general coincide with the astronomical meridian, the declination of the magnetised needle, in any place, is the angle made at that place by the magnetic meridian with the astronomical meridian, or, which comes to the same thing, the angle formed by the direction of the needle with the meridian. The declination of the needle is either eastern or western, according as the south pole of the needle is to the east or the west of the astronomical meridian. It is also called the variation of the compass.

Variations of the Declination.-The declination of the magnetic needle, which varies very much in different places, is western in Europe and Africa, eastern in Asia and America. It moreover has many variations even in the same place: some, which may be regarded as regular, are secular, annual, or diurnal; others which are irregular, are called perturbations.

Secular Variations.-At the same place, the declination varies at different times, but sometimes continues on the same side of the astronomical meridian, that is to say, to the east or west, for several centuries.

The declination for Paris has been noted since 1580. following are the variations which have taken place :

The

However, the annual variations are very little known, and appear to be irregular.

Diurnal Variations.-Besides the secular and annual variations, the declination undergoes diurnal variations, which are very slight, and only to be observed by the use of very long needles and exceedingly delicate instruments. In the climates of the north-west of Europe, the north pole of the needle advances every day from east to west, from the rising of the sun until about one o'clock p. m. It then makes a retrograde movement to the east, so as to arrive about ten o'clock at night very nearly at the point of departure in the morning. During the night the needle varies very little, but still does tend slightly towards the west.

Accidental Variations or Perturbations.-The declination of the magnetised needle is accidentally affected in its diurnal variations by many causes, such as the aurora borealis, volcanic eruptions, and thunder. The effect of the aurora borealis is felt at an enormous distance. Though only visible in the north of Europe, it sometimes acts upon the needle in these latitudes, so as to produce a variation of 20'. In the polar regions the needle oscillates sometimes to the extent of several degrees. Its irregular motion during the whole day which precedes the aurora borealis, announces the phenomena beforehand.

Declination Compass.-The declination compass is an instrument which is used to measure the magnetic declination of a place, when the astronomical meridian is known. It consists of a graduated horizontal circle, fig. 366, in the centre of which Fig. 366.

-22 22 -22 12

This table demonstrates that since 1580 the declination has varied in Paris more than 34°, and that the maximum of the western deviation took place in 1814. Since that time the needle has been returning to the east.

Annual Variations.-The annual variations were indicated by Cassini, who observed in 1784, that from the vernal equinox to the summer solstice, the needle in Paris retrograded towards the east, and that on the other hand it advanced towards the west during the other nine months. The maximuin of amplitude observed during the same year was 20.

Turning the Needle.-The applications of the declination compass which we have just indicated are only exact in proportion as the magnetic axis of the needle, that is to say, the right line which passes through the two poles, coincides with the axis of the needle itself, that is to say, with the right line which connects its two extremities. In general this condition is not fulfilled. This source of error is corrected by turning the needle. For this purpose, the needle is not fixed to the cap, but is simply rested on it, that it may be removed and turned round, and then placed again on the cap, so that the lower face becomes the upper face, and vice versa. Taking then the medium between the declination now marked by the needle, and that which it gave before, we have the exact declination.

In fact, if the right line ce represents the axis of the needle, and the right line ab its magnetic axis (fig. 367), the true declination is not denoted by the arc e N, which is too great, but by the arca N. Now if we turn the needle, the magnetic Fig. 367.

N

E

axis a b does not take the position a'b', but comes back exactly to its first direction, while the extremity e passing between the points a and N, describes an arc precisely as much too small as the first arc was too large. The medium between the two arcs observed gives the true declination.

Mariner's Compass.-The directing action of the earth on the magnetised needle has been put to a very important use in the mariner's compass, known also as the variation compass, or sea compass. It is a declination compass used to guide the progress of ships on the sea. Fig. 368 represents it enclosed, in a rectangular box, which is again placed in another large box called the binnacle, fixed to the after-deck of the ship. Fig. 369 is a transverse section. In these two cuts the same letters indicate the same parts of the instrument.

Fig. 368.

The needle ab (fig. 369), which is easily moveable on a pivot, is fixed to the lower surface of a sheet of talc, on which is drawn a star or mariner's card with thirty-two branches, indicating the eight points of the wind, the half and quarter points. In order that the compass may always preserve its horizontal position, in spite of the rolling and pitching of the ship, it is supported by two concentric moveable rings, one round the axis zz, the other round the axis cd, perpendicular to the first, fig. 368.

An opening м, covered with a plate of rough glass, is used to light the compass during the night. For this purpose a lamp placed outside the box, facing the glass pane, throws its light into the inside. The bottom n of the cylindrical box o, in which is the needle, is a pane of polished glass, that gives passage to the light to illuminate the sheet of talc t, which bears the mariner's card upon it, and which is transparent. A second pane of glass m covers the compass, and a pivot i, fixed in the centre of the pane, serves to fix a graduated dialplate A, which is only used for taking the bearings of coasts. To guide a ship by means of the compass, the navigator first finds on a naval chart what is the point of the wind the vessel must steer by to reach its destination. Then with his eye fixed on the compass, the helmsman turns the tiller of the rudder until the point fixed on and marked on the card, coincides with an imaginary line passing through the two points c and d, marked on the edge of the box, fig. 368, and which is parallel with the keel of the vessel. The variation, however, of the declination in different parts of the globe, compels navigators continually to correct the observations they make with the compass.

The inventor of the mariner's compass is not known, nor the precise date of its invention. Guyot de Provins, a French poet of the twelfth century, is the first author who speaks of the use of the magnet in navigation. The ancients, who had no knowledge of the compass, enjoyed no better guide than the sun or the polar star. They were obliged, therefore, to sail in sight of land, or to run the risk of losing their way when the sky was cloudy.

Fig. 369.

LESSONS IN MORAL SCIENCE.-No. III.

DICTATES OF CONSCIENCE?

THIS is one of the most perlexing questions in the science of morals. Many are of opinion that all that is necessary to render an action good is that the agent act agreeably to the dictates of his own conscience. This may be considered a vulgar opinion, usually taken up without much consideration. But there is an opinion, near akin to this, which has been advocated by some of the greatest men of the age; namely, that men are not responsible for their opinions or belief. It is thought that the adoption of this as a maxim is the only effectual method of putting an end to the bitter aniraosities and controversies among the advocates of different creeds.

It is not wonderful that they who make moral sense, in a

But as we have shown that conscience is the judgment of perfeet or infallible, it follows, therefore, that so far as there is the mind respecting duty, and as no man's knowledge is so far the conscience will be misguided. The question at error in the understanding in relation to matters of duty, just issue, therefore, is whether an action, wrong in itself, can be considered as a good and virtuous action if the agent believes that it is right. If the affirmative were true, then the discovery of truth would be of no value, for obviously upon this principle error is just as good as truth. But as soon would we believe that darkness is as good as light to direct us in the way which we wish travel. Again, this theory supposes that conscience; that, therefore, which is a sin in one man may be a man is under no law but his own opinion, or the dictates of