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of the original, and the reader who is able to study the New Testament in Greek will find that he is able thereby to solve many difficulties, and throw a clear light upon passages which previously had been quite beyond his comprehension.

ΧΕΝΟΡΗΟΝ.

Xenophon was a writer who fourished B.c. 400359. He was a pupil of the great philosopher Socrates, who once saved his life in battle. He was also a celebrated general; and the Anabasis, or expedition up the country (ara, up), is the account of a campaign in which he took a very prominent part. Xenophon lived at a time when the Greek language was at its best, when dialects were dying out, and Greece was beginning to have a uniform speech (κοινη διαλεκτος), in which the Attio was the principal element. The "Anabasis" has always had a great charm for all classes of readers, on account of its minuteness of detail, picturesque simplicity of style, and the air of reality and truth which pervades it. Its plainness and simplicity make it the most desirable work for beginners to take up. It is an account of an expedition undertaken by Cyrus the Younger to overthrow his brother, Artaxerxes, King of Persia, and of the retreat of the Greek troops after the death of Cyrus under the command of Xenophon himself. Cyrus collected a large army, composed principally of Greeks, and marched across Asia Minor towards Persia. The Greek soldiers, who at first did not know the object of the expedition, when they suspected that they were marching against Artaxerxes, were inclined to be mutinous, and resolved to ask Cyrus what were his real intentions. It is at this point that we take our first extract.

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XENOPHON.-"ANABASIS," Book I., Chap. 3. Ἔδοξε ταῦτα, καὶ ἄνδρας ἑλόμενοι σὺν Κλεάρχῳ πέμπουσιν, οἱ ἠρώτων Κῦρον τὰ δόξαντα τῇ στρατιᾷ. Ὁ δ ̓ ἀπεκρίνατο ὅτι ἀκούοι ̓Αβροκόμαν, ἐχθρὸν ἄνδρα, ἐπὶ τῷ Εὐφράτῃ ποταμῷ εἶναι, ἀπέχοντα δώδεκα σταθμούς· πρὸς τοῦτον οὖν ἔφη βούλεσθαι ἐλθεῖν: κἂν μὲν ᾗ ἐκεῖ, τὴν δίκην ἔφη χρῄζειν ἐπιθεῖναι αὐτῷ, “ ἂν δὲ? φεύγῃ, ἡμεῖς ἐκεῖ πρὸς ταῦτα βουλευσόμεθα.” Ακούσαντες δὲ ταῦτα οἱ αἱρετοὶ ἀναγγέλλουσι τοῖς στρατιώταις· τοῖς δὲ ὑποψία μένιο ἦν, ὅτι ἄγει πρὸς βασιλέα, ὅμως δὲ ἐδόκει ἕπεσθαι. Προσαιτοῦσι δὲ μισθόν· ὁ δὲ Κῦρος ὑπισχνεῖται ἡμιόλιον12 πᾶσι δώσειν οὗ πρότερον ἔφερον, ἀντὶ δαρεικοῦ τρία ἡμιδαρεικὰ τοῦ μηνὸς τῷ στρατιώτῃ ὅτι δὲ ἐπὶ βασιλέα ἄγει, οὐδὲ ἐνταῦθα ἤκουσεν οὐδεὶς ἔν γε τῷ φανερῷ.15

NOTES.

1. Ἔδοξε ταῦτα, these things seemed good, they determined on this course, viz., to ask Cyrus the object of the expedition. The neuter plural ταῦτα is followed by the singular verb ἔδοξε, according to the rule that a neuter plural in Greek takes a verb in the singular. 2. Ελόμενοι, 2 aor. mid., from αἱρέω.

3. Κλεάρχψ, a general of the Greek forces.

4. Ακούοι, opt. mood, because independent sentence following a prin

cipal sentence, of which the verb ἀπεκρίνατο is in an historic tense. 5. Κάν, contracted for καὶ ἐάν.

6. Δίκην ἐπιθεῖναι, to lay a penalty upon, to punish. So δίκην δοῦναι, το pay a penalty, to be punished. Compare the Latin penas sumere, panas

dare.

7. "Ην δέ. Here the construction changes from the oratio obliqua to the oratio recta, giving Cyrus' own words: "and if" (said he) "he fly"8. Αιρετοί, chosen by their comrades as spokesmen.

9. Τοῖς, the article used for the demonstrative pronoun τούτοις, το them. Note that the article originally was a demonstrative pronoun, and appears as such in Homer, etc. This old use of it is retained in expressions like the present one, and in ὁ μὲν ὁ δὲ, etc. 10. Μέν, on the one hand, followed by de, on the other.

11. Προσαιτοῦσι. Προς, when compounded with a verb, has the sense of addition. They ask additional pay.

12. Ημιόλιον . . . οὗ, half as much again as (ήμισυ, half, ὅλος, whole); οὗ genitive, because it is attracted into the case in which the demonstrative would be, if expressed. If put out at length, the sentence would run, ἡμιόλιον ἐκείνου ὅ πρότερον έφερον.

13. Δαρεικού, ο dareik, a Persian coin named after King Darius, as we speak of a napoleon, a sovereign, etc.

14. Τοῦ μηνός τῷ στρατιώτῃ. The article here has a distributive sense. To each soldier per month. Μηνός is genitive of time.

15. Εν γε τῷ φανερῷ, at least openly.

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δ ̓ οὐδὲν ἐνῆν. Θηρία δὲ παντοῖα, πλεῖστοι μὲν ὄνοι ἄγριοι, πολλοί δὲ στρουθοὶ οἱ μεγάλοι· ἐνῆσαν δὲ καὶ ὠτίδες καὶ δορκάδες ταῦτα δὲ τὰ θηρία οἱ ἱππεῖς ἐνίοτε ἐδίωκον. Καὶ οἱ μὲν ὄνοὶ, ἐπεί τις διώκοι, προδραμόντες ἕστασαν ἄν πολὺ γὰρ τῶν ἵππων ἔτρεχον θᾶττον· καὶ πάλιν, ἐπεὶ πλησιάζοιεν οἱ ἵπποι, ταὐτὸν ἐποίουν, καὶ οὐκ ἦν λαβεῖν, εἰ μὴ διαστάντες οἱ ἱππεῖς θηρῷεν διαδεχόμενοι τοῖς ἵπποις. Τὰ δὲ κρέα τῶν ἁλισκομένων ἦν παραπλήσια τοῖς ἐλαφείοις, ἁπαλώτερα δέ. Στρουθὸν δὲ οὐδεὶς ἔλαβεν· οἱ δὲ διώξαντες τῶν ἱππέων ταχὺ ἐπαύοντο· πολὺ γὰρ ἀπέσπα φεύγουσα, τοῖς μὲν ποσὶ δρόμῳ, ταῖς δὲ πτέρυξιν, αἴρουσα, 10 ὥσπερ ἱστίῳ χρωμένη. Τὰς δὲ ὠτίδας, ἄν τις ταχὺ ἀνιστῇ, ἔστι λαμβάνειν· πέτονται γὰρ βραχὺ, ὥσπερ πέρδικες, καὶ ταχὺ ἀπαγορεύουσι· τὰ δὲ κρέα αὐτῶν

ἥδιστα ἦν.

NOTES.

1. Ομαλόν (der. from ὁμοῦ, together), even, level. 2. ̓Αρώματα, εpices : hence our aroma, aromatic. 3. Στρουθοί, ostriches.

4. Δορκάδες, gazelles (δέρκω, to look), from the brilliancy of their eyes; ὠτίδες, bustards, so called from their large ears (ούς, ωτός, an ear). 5. Προδραμόντες ἔστασαν ἄν, having run forward, would stop short. "Αν gives a frequentative sense to the verb. β. Οὐκ ἦν, it was not ; sc. possible.

7. Διαδεχόμενοι. Δια in composition has a sense of division and alter nation. It means that they stood at different intervals, and thus caught them. 8. Οἱ δὲ . .. τῶν ἱππέων, those of the cavalry who pursued them. Caled the partitive genitive.

9. ̓Απέσπα. The nom. to this is στρουθός. 10. Αἴρουσα, raising them ; sc. πτέρυγας.

PARSING EXERCISE.

The student should parse προδραμόντες, ἕστασαν, θηρῷεν, ἀπέσπα, ἀνιστῇ.

The army of Cyrus met with Artaxerxes at Cunaxa, near Babylon, and a battle was fought in which Cyrus was slain by his brother, after which the chief Greek generals were treache rously killed by the Persians. Xenophon was left head of the helpless host, and he led them back through innumerable difficulties to Greece. When they came to the sea-shore, they broke out into transports of joy:

XENOPHON.-"ANABASIS," Book IV., Chap. 7.

Ἐπειδὴ δὲ βοὴ πλείων τε ἐγίγνετο καὶ ἐγγύτερον, καὶ οἱ ἀεὶ ἐπιόντες ἔθεον δρόμῳ ἐπὶ τοὺς ἀεὶ βοῶντας, καὶ πολλῷ μείζων ἐγίγνετο ἡ βοὴ, ὅσῳ δὴ πλείους ἐγίγνοντο, ἐδόκει δὴ μεῖζόν τις εἶναι τῷ Ξενοφῶντι. Καὶ ἀναβὰς ἐφ ̓ ἵππον καὶ Λύκιον καὶ τοὺς ἱππέας ἀναλαβὼν παρεβοήθει καὶ τάχα δὴ ἀκούουσι βοώντων τῶν στρατιωτῶν, “Θάλαττα ! θάλαττα!” καὶ παρεγγυώντων. Ενθα δὴ ἔθεον ἅπαντες καὶ οἱ ὀπισθοφύλακες, καὶ τὰ ὑποζύγια ἠλαύνετο καὶ οἱ ἵπποι. Ἐπεὶ δὲ ἀφίκοντο πάντες ἐπὶ τὸ ἄκρον, ἐνταῦθα δὴ περιέβαλλον ἀλλήλους καὶ στρατηγοὺς καὶ λοχαγοὺς δακρύοντες. Καὶ ἐξαπίνης, ὅτου δὴ παρεγγυήσαντος, οἱ στρατιῶται φέρουσι λίθους καὶ ποιοῦσι κολωνὸν μέγαν. Ἐνταῦθα ἀνετίθεσαν δερμάτων πλῆθος ὠμοβοίνων καὶ βακτηρίας καὶ τὰ αἰχμάλωτα γέρρα, καὶ ὁ ἡγεμὼν αὐτός τε κατέτεμνε τὰ γέρρα καὶ τοῖς ἄλλοις διεκελεύετο.

NOTES.

1. Εθεον δρόμῳ, were running with (at full) speed Dative of manner. 2. "Οσῳ δή, by exactly as much as they grew more ; exactly as their numbers increased the shouting increased.

to.

3. Μειζόν τι, something greater (than usual), something important. 4. Παρεβοήθει, he ran to give aid, or to the noise. Ilapa means motion Βοηθεῖν is to assist, being literally to rum; θέω, to a shout, fon. 5. Λοχαγούς, captains (άγω) of a cohort (λόγος).

6. Οτου δὴ παρεγγυήσαντος, some one or other having prompted the (genitive absolute).

7. Ωμοβοίνων, of raw on-hides (ώμος, ταω; βούς, οπ).

8. Αἰχμάλωτα, taken captive; lit., taken by the spear (αίχμη, ο spear άλωτος, taken).

9. Διεκελεύετο. Δία in composition has a distributive force. Sent orders round to the rest.

PNEUMATICS.-VI.

COMMON PRESSURE-GAUGE-SAFETY TUBE-ATMOSPHERIC RAILWAY-BLOWING MACHINES-VENTILATION OF MINES. IN our last lesson we found that if a gas be kept under a uni form pressure, and heat applied, it will increase in bulk of its volume at 0° for every degree the temperature is raised. Suppose, now, that the gas be confined so that it cannot increase in volume, we shall ând that as the temperature increases the elastic force will increase too, and in the same proportion as its

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If any gas be confined so that it cannot expand, and its temperature be raised from 32° to 212°, the elastic force will be increased by 0.366 of its original amount.

Sometimes the steam in an engine is exposed to a high temperature after it is first evolved, and is then said to be superheated. Its tension is increased by this, and thus it can accomplish more work, and at the same time " 'priming," or the condensation of the steam in the cylinders, is to a great extent prevented.

After what we have now seen respecting the change produced in the volume of a gas by variations in the temperature or pressure, we can very easily tell the specific gravity of a gas if we know the weight of any volume of it, and also its temperature and pressure. We have merely to ascertain the volume it would occupy at the standard temperature and pressure, and then compare its weight with that of the same volume of air. In the same way we can calculate the weight of any volume of gas, or the volume that a given weight of it would occupy.

We described in our last lesson a manometer for measuring high pressures like that produced in the boiler of an engine. This acted by the elastic force of compressed air: a spring is more commonly used, but it is somewhat liable to lose its elasticity, or to become injured by the moisture of the steam. These, however, only record high pressures, and not minor changes like those produced by alterations of temperature. We want, therefore, some means of measuring these, and for this purpose we employ a U-shaped tube, open at each end. The bend is filled with water if very low pressures are to be measured, and with mercury if to be used for those rather greater.

If the gas whose tension is to be ascertained is allowed to press on the liquid in one limb, it will depress it and raise that in the other, and the difference in level between the two will indicate the pressure. A sliding-scale is usually attached to show this difference. In this way we shall find that the pressure of the gas, as usually supplied to our houses, is seldom equal to two inches of water, a very small amount indeed when we remember that the pressure of the air will sustain a column of water over thirty feet high. It is, however, found to be quite sufficient to overcome the resistance caused by the friction of the gas against the pipes, and a greater pressure would only cause a greatly increased loss by leakage from the mains. This pressure is produced by weights placed upon the gasometer, and can in this way be regulated to a considerable extent. It is found, however, that considerable variations occur, it being greater just before the majority of people light it in their houses, and again in large towns about eleven o'clock, when many burners are turned off. These variations in pressure cause a loss in illuminating power, and several regulators have accordingly been devised to obviate this. The principle on which they act is merely that a conical valve is moved by the pressure so as to close to a greater or less extent the pipe along which the gas passes. There is a small but useful piece of apparatus, known as the safety-pipe (Fig. 17), which may be explained here, as it acts in a similar way to the pressure-gauge just mentioned. In many chemical experiments in the laboratory, as well as in the manufactory, a large amount of gas is evolved by the changes taking place within some closed vessel. If no escape be allowed for this, the Fig. 17. pressure may increase to such an extent as to burst the vessel; while, on the other hand, it is desirable not to allow the gas to be lost. A safety-pipe, similar to that shown in the annexed figure, is therefore introduced. This allows a portion of the gas to escape when the pressure reaches a certain limit. It is, in fact, a safety-valve of low pressure. A glass tube has a bulb B blown near the middle, and each end is then bent back upon itself. The upper end is also shaped into a funnel, which should be rather larger than the bulb. Water or mercury, according to the pressure required, is now poured into the funnel, so as to fill the bend and part of the bulb. If the pressure inside the vessel becomes too great, the liquid will be forced into the part c of the tube, and any excess of gas will then bubble up through

it, the funnel preventing the escape of the liquid. If, on the other hand, the pressure inside becomes less than that without, owing to the absorption or condensation of the gas, the pressure of the air will force the liquid into the bulb, and air will then bubble up through it. In this way the tube prevents the difference between the pressures from becoming dangerous, and at the same time, under ordinary pressure, excludes all air.

We have seen that power may be stored up in compressed air; hence it is sometimes employed to drive an engine in place of steam. Of course some power must be first employed to compress the air, and therefore in ordinary circumstances no advantage will be gained by the substitution, but in many special cases it may be and is employed. If steam has to be conveyed to any great distance, there is a considerable loss by condensation in the pipes, and in some places it is inconvenient or impracticable to have the boiler near the machine. In such cases, therefore, the steam may be employed in the compression of air, and by this the power may be transmitted to the place where it is required. A

In mining operations this is especially advantageous. narrow seam of coal, in which there is no room for an engine, has sometimes to be cut out by a machine, and even if the engine could be placed there, the steam and smoke would prevent a man being by it; such machines are therefore driven by compressed air. The same remarks apply to a narrow tunnel, as, for example, that which is now being driven through Mont Cenis; and here, too, compressed air is used instead of steam. There is also this further advantage attending the use of air, that the machine can be more easily moved, for a portion of the pipe may be made flexible, which cannot well be done with steam-piping.

The most important application of the pressure of air to driving machinery is seen in the atmospheric railway. At present this has not come into practical use, but it appears probable that the principle will ultimately be adopted in our underground railways, as it will effect a saving in working expenses as well as in construction, to say nothing of the much greater safety which would be ensured by its use, and the greater purity of the air in the tunnel.

The original plan proposed, and actually carried out on a short piece of line near Paris, was somewhat as follows:-A large iron tube, having all along the top an opening which was closed tightly by a flexible lid, was laid along the middle of the line. This tube was made uniform in size, and a pair of pistons, made to fit it, were fixed one to each end of a little carriage which travelled along in the tube. From the middle of this carriage rose an arm which projected through the slit, and was attached to the carriage on the line. A coulter-shaped piece of metal was placed on each side of the arm, so as to open the slit for it to pass along, and the aperture closed of itself as soon as the arm had passed. The pistons were also attached to short arms, so that the valve admitted no air in front of them. At each end of this tube was fixed a powerful double-acting airpump, and whenever it was required to start the train, the pump at the end to which it was going was set to work. It soon produced a vacuum in the tube, and the pressure of the air behind the piston was sufficient to drive the train. There were, however, many practical difficulties in the carrying out of this plan. The valves could not be got to close well, and hence there was a considerable leakage of air which greatly diminished the power. All the strain, too, was transmitted through the arm, and thus there was danger of breakage. From these and many similar causes the design was not carried out elsewhere.

More recently, however, an altogether different plan was tried with much greater success. In this the tube was built of brickwork, and made of such a diameter as to take in it an ordinary-sized railway carriage. A trial line, of nearly a mile in length, was constructed in the grounds of the Crystal Palace at Sydenham. The line was made with steeper gradients and sharper curves than any line yet worked, so as to give the system a full trial. The tunnel was carefully constructed, so as to be of uniform size, and one end of the carriage was made nearly to fit it, an aperture of a few inches being left all round. A brush fixed round the carriage nearly filled this, and was found to exclude the air sufficiently. The ends of the tunnel were closed by air-tight doors, and in a building near one end was fixed a large fan, constructed somewhat after the

plan of a centrifugal pump, and so arranged that by causing it to rotate in one direction it exhausted the tube, while on reversing it the air was condensed. The pipe leading from this entered the tunnel at a little distance from the end. The carriage being now placed just in the mouth of the tunnel at the further end, the engine was set to work, and, as soon as a slight amount of exhaustion was produced, the pressure outside forced it rapidly along. As the whole area of the carriage was exposed to the pressure, it was found that only a very small degree of rarefaction was required, a pressure of a few ounces to the inch being quite sufficient to impart to it a great velocity. As soon as the carriage had passed the portion of the tunnel where the exhaust-pipe entered, it ceased to be carried forward by the pressure of the air, but it had acquired an amount of momentum sufficient to propel it with considerable violence beyond the end of the tunnel. The doors at the end were, however, closed by powerful springs. The air, therefore, enclosed between them and the carriage became more and more compressed, until the pressure was sufficient to open the doors, and allow the carriage to run slowly out. The air acted, in fact, as a buffer, and brought the carriage to rest with scarcely any shock. When the carriage was to be sent back to the other end, the engine first exhausted the tube until the carriage passed the opening, the doors were then closed, the engine reversed, and then the air behind was condensed, and drove the carriage to the other end on the same principle as a boy drives a pea through his pea-shooter by the pressure of his breath.

The experiment appeared satisfactory, though no practical use has yet been made of it. The carriage, with passengers in it, could be started from one end, driven round the curves, and up and down the steep inclines, and yet stop at the other end, nearly a mile off, in the space of about one minute. The system appears to possess many advantages. Much greater inclines can be allowed, and all danger of the carriage running off the line on sharp curves is avoided. There is also much greater safety from accidents. Collision is impossible, for two carriages can never be travelling in opposite directions at the same time, nor can one overtake the other. The boiler, too, being away from the train, cannot injure the passengers if it explodes, and the only inconvenience then would be that the passengers would have to walk along the line to the nearest station. Further, as the trains would travel very rapidly, one line would, in most cases, be sufficient, and the additional expense incurred by the careful building of the tunnel would, in many places, be compensated for by the smaller amount of land required. The tunnel, too, unlike our present ones, would be well ventilated, as the air would be entirely changed each time a train passed through. There are, of course, many practical difficulties which might occur in the actual working, but the plan seems to promise well, and to be worthy of a thorough trial.

We must now notice the construction of a few common pneumatic machines, and perhaps the most important are those used for blowing. In furnaces for reducing and melting metals it is found impossible to cause a sufficient degree of heat to be produced unless a large additional quantity of air be forced into the fire, so as to quicken combustion. In mines, too, and underground passages ventilation must be carried on by artificial means, and for these and other purposes blowing machines are employed.

Fig. 18.

The most simple of these is the common household bellows, so familiar to all. In the lower of the two boards is a circular aperture, over which a piece of board is hinged, so as to act as a common clack valve. When the boards are separated, the air opens this valve, and enters, but as they are again pressed together this valve closes, and the air is then forced to escape by the nozzle. With this kind, however, only an intermittent current can be produced, for while the boards are being separated, air is drawn in at the nozzle as well as at the valve, though in a less degree. This was often found to be a serious disadvantage, and therefore two bellows, working alternately, were used in many furnaces. Double-acting bellows are, however, used now in nearly all forges, and these produce a uniform stream.

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enough for a blacksmith's forge, when the metal has only to be softened sufficiently to cause it to weld, they will not answer for a furnace for melting iron; and a fan, driven by steam, is usually employed in this case. The

Fig. 19.

air enters at the axle, and is thrown off by centrifugal force from the edges, and conducted along large tubes to the furnace. Another purpose for which these machines are employed is in the winnowing of corn. In former times, and in some places at the present day, the corn, when threshed, is thrown up in the air, and the wind carries away the chaff. The plan now adopted is to allow it to fall through a narrow slit, and cause a rapid current of air, produced by rotating fans, to remove the chaff. One great advantage of this plan is that the strength of the blast may be so regulated as not only to remove the chaff, but to separate also the small and shrivelled grains.

The pneumatic screw is another simple blowing machine, used for purposes of ventilation. It acts on exactly the same principle as the Archimedian screw, an axle with a spiral flange being made to rotate in a cylinder. This is placed at one end of the tube or shaft, and produces a powerful current, the direction of which depends upon the direction in which the screw revolves.

This machine is sometimes employed for the ventilation of mines, and is fixed above one of the shafts. A second shaft allows fresh air to pass down it, and replace that removed by the fan, and thus a constant current of air is kept up through the mine. The main galleries below are so arranged, by means of boarding and doors, that the fresh air must traverse the greater part of the mine before it can find its way to the "upcast" shaft, as it is termed. As the air will always find the most direct road, great care is required in the arrangements for effecting this.

In most mines in England blowing machines are now dis pensed with, and in their stead a large furnace is placed at the base of one of the shafts. This greatly rarefies the air above it, and thus renders it much lighter than that around. It ascends, therefore, and a fresh supply rushes down the second shaft to take its place, and in this way good ventilation may nearly always be obtained. The plan, too, is more simple than the use of fans, and less liable to get out of order. Sometimes the furnace is placed in a recess, part of the way up the shaft; sometimes, too, only one shaft is sunk, and divided by bratticing into three or more divisions, one for the pumps and working machinery, the other two for the "upcast" and "downcast." This plan is, however, very dangerous, and many of the fearful accidents we hear of in mines are to be attributed to its adoption.

Ventilation in our houses and public buildings is carried on in a similar way. It is much to be regretted, however, that the principles on which this should be arranged seem to be so little understood or carried into practice. If we hold a sheet of paper near a large fire, we shall soon see by the powerful draught that there is a strong current of air up the chimney, and cold air rushes in at the cracks of the doors and windows to supply its place. A good fire, therefore, adds greatly to the ventilation of a room. As, however, the heated air rises, it is an important thing to have some outlet for this, and an opening into the chimney near the top of the room will usually be effectual. In public buildings the foul air is usually carried off near the roof, and arrangements ought to be made by which fresh air can enter in a number of small streams at different places, instead of flowing in a large body through an open door, and thus creating a violent draught.

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IN judging of the various systems devised by the ancients to account for the grand mechanism of the heavens, we must bear in mind, and make allowance for, the very imperfect nature and construction of the instruments they possessed; and when this is done, instead of wondering at the errors they made, we shall often be surprised at the accuracy of their observations; some of these which still exist being sufficiently accurate to be at times of service to astronomers in the present day.

The simplest and probably the most ancient astronomical instrument consisted of a vertical pillar set upon an even surface, so that, by observing the shadow, the direction of the sun and its altitude at any period might be measured; by noticing, also, the direction in which the shortest shadow was cast by the pillar, they could ascertain the north and south points of the heavens. It is believed by many that the obelisks and stone pillars which were common among Eastern nations were constructed for some such purpose, and that they were frequently surmounted by a ball, in order that the position of the shadow might be more easily marked. Some of these obelisks were afterwards removed to Rome for the same purpose. These instruments were called gnomons.

The telescope, which has made such astounding revelations to men of modern times, and which has so greatly extended their knowledge of the universe, was quite unknown in early ages. Instruments for measuring time were also very imperfect, although, as will be seen further on, the importance of noticing the exact moment of the occurrence of any of the celestial phenomena is very great. Various forms of the sun-dial were in use, but these could only be of service when the sun was shining, and even then could not give very accurate indications. Other instruments were therefore planned, and the one most commonly employed was the clepsydra, or water-clock, in which the hour was shown by the amount of water that had passed through an aperture. Sand was afterwards used in the place of water, as its flow was found to be more regular and even. Rather strangely, we have come back very recently to a method of measuring minute intervals of time similar to this old plan. A vessel is provided with a small aperture from which a fine stream of mercury is issuing, and when it is required to note any brief interval-as, for instance, that occupied in the passage of a planet between two lines situated in the field of view of a telescope the mercury is diverted into a separate vessel at the moment of the disc of the planet coming into contact with the first line, and allowed to flow on until it has passed the second, when the stream is allowed to flow as at first. The amount of mercury in the vessel is then accurately weighed, and by comparing it with the amount which is known to flow out in a given interval-say, for instance, five seconds-the exact duration of the passage can be noted.

A few other rude instruments were also occasionally employed, but their construction was very imperfect, and we are not therefore surprised at the slow progress of the science. Among the Romans, too, science never found a congenial home; glory in war being the object of their ambition, rather than the peaceful yet glorious triumphs achieved by intellect. After the age of Ptolemy little progress appears to have been made, and even known truths were to a great extent forgotten. His system was indeed universally received for many centuries, more especially as it was supported by the authority of Aristotle; and fresh additions to it, in the shape of eccentrics and epicycles, were made; but few, if any, new discoveries appear to have been effected, and no noteworthy name appears on the pages of history.

After the fall of the Roman empire the science found a home among the Arabians, who, in the eighth century, seem to have devoted much attention to its study, and to have made considerable advances in it. By them the length of the solar year was calculated to within a very little of its true amount; the obliquity of the ecliptic was also measured; and at a place in the desert, near Palmyra, the length of a degree was ascertained with very creditable accuracy. The Ptolemaic system was, how ever, firmly received, though many of the more thoughtful and careful observers seem to have been far from satisfied with it,

VOL. IV.

and expressed their wonder at its manifest disproportions. Still such is the hold that preconceived notions obtain over the human mind, especially when those views are supported by priestly authority and made matters of religion, that for centuries no one seems to have referred to the old theory of Anaxagoras, or proposed any new one to clear up the difficulty. At length, however, about the year 1472, there was born one, Nicholas Copernicus, who, leaving all the speculations of former observers, inquired for himself into the motions of the celestial bodies. He first examined all the ancient observations he could find, and then commenced for himself a system of close and careful study of the heavens. He compared the actual places occupied by the sun and planets with those which, according to former theories, they ought to occupy, and thus obtained a better knowledge of their irregularities and variations than any astronomer before his time. He continued this course for many years, and at length arrived at the conclusion that Mercury and Venus revolved around the sun, instead of round the earth. He gradually extended his reasoning further, and at last started his celebrated theory, which regarded the sun as the centre of the system, with the earth and the other planets all revolving in regular order around it. By this grand idea all the complicated and bewildering schemes which had puzzled so many observers were at one stroke swept away. Instead of the cumbrous machinery of crystal spheres revolving one within the other, the utmost simplicity is seen to prevail; order and regularity take the place of almost inextricable confusion; and as the observer transfers his station of observation from the earth to the sun, the planets, which had previously appeared to wander on in ever-varying directions among the stars-now retracing their steps, and then, after an interval of rest, starting afresh-are seen to be steadily moving on in elliptic orbits around the central luminary of the system. The movements of the inferior planets Mercury and Venus, the reason why they were never seen very far removed from the sun, the retrograde motions of the planets, and their irregular movements, were all clearly explained by this grand yet simple theory.

We can with difficulty form an idea of the prejudice with which this scheme would be received; the earth was by it degraded from its central place, and reduced to the rank of one of the planets; and that which men had always been wont to regard as fixed and immovable, was now declared to be in rapid flight around the sun, and, at the same time, to be ever whirling round on its own axis. He himself foresaw the effects of this prejudice, and hence he seems to have been long before he fully accepted the theory, and then to have waited still longer before he ventured to make it public. His work on the subject, entitled "On the Revolution of the Heavenly Bodies," was finished in the year 1530, but he delayed publishing it for several years, although a few friends, to whom he had communicated and explained his views, at once adopted them and urged him to do so. At last, however, he gave his consent to its being printed, but his dedication almost takes the form of an apology for venturing to suggest such views, and his ideas were put forward rather in the shape of an hypothesis than of a definite system. We must not, however, suppose that Copernicus formed a complete system to account for all the motions of the planets; his life was too short for this task. His work was rather to indicate the true theory of the universe, leaving it for others to trace out more accurately the exact curves in which the planets moved, and to ascertain their various distances, sizes, and rates of motion. This work was taken up by Kepler, who has sometimes been called the "Legislator of the Heavens," as it was he who first laid down the laws and rules which govern the movements of the heavenly bodies. We shall notice more about this celebrated astronomer shortly, but must first look at the labours of another distinguished man who preceded him-Tycho Brahe. He was of Danish extraction, and was born very shortly after the death of Copernicus. It is said that his attention was first directed to the science of astronomy by an eclipse which happened at the time predicted, in the year 1560, and incited him to learn something of the wonderful science which enabled such predictions to be made. When at the University of Leipsic, much of his night was often devoted to observation of the stars, and thus he soon attained considerable proficiency; but there is one thing which tends rather to lower him in our estimation, and that is his partial rejection of the Copernican system, and the proposal of a new one, in which the earth occupied the

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central place, with the moon and sun revolving round it, while all the planets revolved round the sun.

The Copernican system, however, was, we must remember, at this time a mere theory unsupported by proof, and the main reason of Brahe's rejection of it was that, if the earth revolved in a large orbit, he thought the fixed stars ought to appear in a different position when seen from one extremity of the orbit to that which they occupied when seen from the other extremity; and not being able to observe this change, he concluded that the earth must be at rest. The principle of this argument was right, and in reality there is a minute difference in the appearance of the stars; it is, however, too minute to be observed, except by the most delicate instruments. The reason why it is not more clearly seen is that, great as is the diameter of the earth's orbit, the distance of even the nearest fixed star is so immensely greater that the change produced is scarcely visible. We may notice this same effect as we are carried rapidly along in a train; the objects situated near to the line of railway seem to move past us very rapidly, those further off have a less apparent speed, while lofty objects in the distance scarcely seem to move at all. Every minute changes the apparent position of those which are near, while it is only after the lapse of some little time that we perceive the motion of those at a distance; and, supposing the line of rails were perfectly straight, we might travel on for hours, and not be able to detect the slightest alteration in the apparent position of the sun. We see thus that the conclusion which Brahe arrived at was wrong, though his premises were right; and we shall find further on the great importance which is attached to this change of position, or "parallax," as it is called, all the distances of the heavenly bodies being determined by means of it.

His fame, however, as an astronomer rests upon the care and accuracy of his observations. A new star which appeared in the year 1572, and continued visible for about a year and a half, was specially observed by him, and he recorded a large number of very careful observations on the planets and stars, some of which are of great use for reference at the present time. To him, too, we are indebted for a catalogue of many of the fixed stars, which, though it contained a much smaller number than that of Hipparchus, was greatly superior to it in accuracy.

A table showing the allowance to be made in the apparent position of the heavenly bodies, on account of the effect produced by the refraction of the air, was also calculated by him. The nature of this refraction will be fully explained further on. We may mention, however, that it causes all bodies near the horizon to appear at a greater altitude than they really have attained; and hence, in important observations, allowance must be made for its action.

About the year 1575 Tycho Brahe attracted the attention of Frederick II. of Denmark, who gave him a small island on the Baltic, and an annual allowance. Here he built himself a large house and observatory, which he called Uraniborg, the "Castle of the Heavens," and in this he lived for years, occupied with his favourite science, and assisted by the best instruments which could be procured. After the king's death, some of those who were envious of his honours succeeded in depriving him of his allowance and his observatory. He did not, however, despair, for soon after he was received at Prague by the emperor, and an observatory erected for him and his pupils. Here he remained until his death, which happened a few years later. Among his pupils was Kepler, to whom we have already referred. He acquired from Brahe the habit of accurate observation, and was far more successful than his master in the theories which he formed. Naturally he was possessed of a quick and Hively imagination. He commenced with careful observation, and then formed his theories in accordance with the facts; and proceeding in this way, he soon made several important discoveries.

The task to which he now devoted his time and energies was to discover the nature of the paths described by the planets. Starting with the hypothesis of the sun being in the centre of the system, he began to watch attentively their places, and, to simplify matters, he confined himself at first to the motions of the planet Mars.

He calculated the place it ought to occupy according to the theory of its revolving in a circular orbit, and soon found that the place it really occupied in the sky differed considerably from that assigned to it. This theory was thus at once shown to be incorrect, and he had therefore to form a fresh one by the com

bination of several circular movements; and again he diligently calculated its position, till, just as he seemed to be on the verge of success, the planet once more wandered away from the path which he had assigned to it; and once more he had to commence his observations from the beginning. In this way he continued to try one hypothesis after another, submitting each to the test of most careful observation, till at length no fewer than nineteen different theories had been proposed, and the movements of the planets compared with those which were calculated by these theories; and yet the true solution of the problem was still unfound. His perseverance, however, never failed, and he toiled on, though eight long years had been occupied in the task. One important negative result he had, however, arrived at, and this was that, whatever was the nature of the curve the planets described, it was not a circle, nor a combination of circles. This was one great step towards the solution of the task. From the very earliest ages it had been assumed that, as the circle seemed the perfection of form, all the heavenly bodies must move in circles; but Kepler now cast off this trammel, and then applied himself afresh to his task.

In looking at the greatness of his work we must remember that the difficulty is much increased by the fact that our station of observation is itself in rapid motion. Could we view the planets from the sun, we should easily see their courses; but as we cannot do this, allowance has to be made in every calcu lation for the movement of our standpoint, and this motion was not then clearly understood.

Having discarded the theory of motion in circles, Kepler now proceeded to try other forms, testing them as before, and the first that occurred to him was the ellipse. The same series of calculations was accordingly gone through again, and this time the motion of the planet was found to agree with that assigned to it by the theory. The great problem of the heavens was now solved, and the joy with which Kepler enunciated the first of the laws which bear his name can scarcely be imagined. This law may be stated as follows:-The planets revolve around the sun in elliptical orbits, the sun being situated in one of the foci.

As this is one of the fundamental laws of astronomy, we must explain it rather more fully. In every circle there is a point called the centre, such that all straight lines drawn from it to the circumference are equal. No such point is to be found in an ellipse; but in the longest diameter two points can be found so situated that, if straight lines be drawn from one to any point in the circumference, and thence to the other, the sum of these lines will always be equal. These points are called the foci.

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Explanations of the practical methods by which the curve of an ellipse may be traced from any two points as foci, have already been given in Problem LVIII. of "Lessons in Geometry -"How to trace the curve of an ellipse by mechanical contrivances (see Vol. II., page 252); it is therefore unnecessary to repeat them here in detail. It will be needful, however, to call the reader's attention to what is termed the eccentricity" an ellipse, as it is a term that is constantly used in speaking of the orbits of the heavenly bodies. In Fig. 84 (Vol. II., page 252), G is the centre, and the fraction of which the numerator is GA and the denominator is a c—or, in other words, the propor tion between GA and G C, which is the half of the major axisis called the eccentricity. In the figure, however, this is repre sented very much greater than it is in orbits of any of the pla nets, and their paths therefore differ less from a circle. The consideration of the remaining two laws of Kepler must be deferred till our next lesson.

READINGS IN LATIN.—II.

VIRGIL.

VIRGIL was a Roman poet who was born in the year 70 B.C. and died 19 B.C. He flourished in the period which is known as the "golden age" of Latin poetry, of which he was one of the most brilliant ornaments. The works by which he is best known are (1) the Bucolics, a book of pastoral poetry, consisting of ten eclogues, as they are called; (2) the Georgics, four books of what is known as "didactic" poetry, containing instructions in the art of agriculture and similar occupations; and (3) the Eneid, an epic poem in twelve books, each of considerable length, the subject of which is the wanderings of the Trojan

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