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Solutions to Jaan Kalda s Problems in Kinematics Qilin Xue Tarun Agarwal Kushal
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Calculus Problem Solutions With MATLAB 1st Edition Dingyü Xue
where s ≡ 20ˆ x 20ˆ y and v ≡−800ˆ x +600ˆ y,whichrepresentstherelativevelocity.Aswithbefore,we wanttherelativevelocitytobeperpendiculartothedisplacement d.Onewayofdoingitismaximizing thedotproduct: |d × v| = |s × v + v × vt| = |s × v|
Letusalsomarkpoint G asthecentreof AF ;then, FC isboththemedianoftherighttrapezoid ABDF (andhence,parallelto AB andthe x axis),andthemedianofthetriangle ACF
Let x bethedistancetraveledbytheindividualballsand k bethedistancebetweenthetwoballs.Let theheightoftheballatpoint A be h1 andtheheightoftheballatpoint B be h2
Let t bethetimeittakestheballtohittheramp.Therefore,wefindthat
Now,wenotethatthetotaltime T =3t becausetheballtravelsadistance d tocollidewiththeramp, bouncesupadistance d tothevertexofitsparabolictrajectory,andthenfallsbackdownforthefinal distance d
Thismeansthatthedistancebetweenbothbouncingpoints s isfoundby
Solution2: Considerthefollowingdiagram:
Werotatetheplaneby α counterclockwisesuchthatgravitynowhasacceleration g cos α inthey-direction and g sin α inthex-direction.
Relativetothewater,theboyswimsahorizontaldistance a tan α.Thewaterduringthistimeflowsa distance wt = wa u cos α intheoppositedirection.Therefore,thehorizontaldistance x is:
Solution2(HuygensPrinciple):
Considerthesamesetupasbeforebymovingintotheframeoftheriver.Thistimehowever,thepath isreversed.Theboystartsrunningfrompoint O alongtheshoreandeventuallystartsswimmingto location A.ImaginetheboyemittingChernenkoradiationashemovesasshowninthediagram.The wavespeedis u whilethespeedoftheboyis w +v>u.Physically,theoutlinesofallthecirclesrepresent thesuperpositionofallthepointsinwhichtheboycanbeatafteratime t
DuetoHuygen’sPrinciple,wecanseethatthisformsawavefrontthatismovingtowards A ataspeedof u.Wecanletthiswavefrontevolveuntilapartofiteventuallyreachesthepoint A.Thepaththatthis partofthewavetakeswillrepresenttheoptimalpathoftheboy,thatis,perpendiculartothewavefront. Wecandeterminetheangle θ byconsideringtwoextremepathstheboycantake.
First,theboycanstartswimmingimmediatelyandreachadistance ut afteratime t.Duringthisperiod, theboycanalsorunadistance(w + v)t.Theangle θ isthusgivenby:
andthustheangle α =90◦ θ normaltotheshoreis
Thisisthesameanglefoundinthefirstsolutionandasaresultwecancopytheexactstepstodetermine x
pr 19. Wesplitup v intoit’sverticalandhorizontalcomponents.Fromherewecanseethateach parameter x,y and z asafunctionof t is
Byidea28,wecansettherightmostpointoftheroof(point F )tobethefocusoftheregion R ofall possibletrajectories.Optimally,thisparabolashouldpassthroughtheleftendoftheroof.
Then,wesetofcoordinatesof F tobe(0, 0),sothecoordinatesoftheleftendoftheroofare b2 (a c)2,a c ,wherewehavetakentheabsolutevalueofthex-coordinatetomakecalculationseasier.
Let θ =arctan a c b2 (a c)2 ,lettheinitiallaunchangle(tothehorizontal)be α,andlettheinitial velocityofthestonebe v0
Weknowbyidea33thattheinstantaneousaxisofrotation O oftheobjectexists. Let l1 and l2 bethedistancefrom O tothetopandbottomboards,respectively. Infact,wehavethat
Bythepropertiesoftheinstantaneousaxisofrotation,weknowthatallpointswithspeed |v1| lieona circlecenteredat O withradius l1,andallpointswithspeed |v2| lieonacirclecenteredat O withradius l2.
pr 28. Considerareferenceframemovingwithspeed u oppositetothedirectionofthecars.
Carsattheendwillbemovingwithspeed v + u,andthedistancebetweenthemwillbe vτ .
Carsatthefrontwillbemovingatspeed u (becausetheyarestopped)andhaveadistance l between them.
Nowwetakeratiosofspeedtolengthandequatethemtoget
Considerthediagramabove,where A istheengineofthelefttrain, B istheengineoftherighttrain, M isthemidpointof AB, P istheintersectionofthesmoketrails,and C isthatintersectionprojected ontoline AB.
Sincebothtrainstravelat v =50km/h, M iswherethetwotrainsmet.Inthetimeittookthetrains totravelfrom M to A and B,thewindcausedthesmoketodriftfrompoint M topoint P .
Letussetanarbitraryscaleof1cm=100km.
pr 29.
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display so marked a tendency to discover such coincidences of date that any statement of this kind cannot be regarded as reliable.
Diod. xi. 24.
Of all the great expedition, only twenty warships escaped from Himera, and these, over-laden with fugitives, perished in a storm on the way home. The news of the disaster was carried to Carthage by a few survivors who managed to reach the coast in a small boat. The consternation which it excited was naturally terrible; and for some time the Carthaginians lived in daily expectation of the appearance of Gelo’s fleet on the African coast.
In order, if possible, to ward off the fatal catastrophe which, under the circumstances, must have resulted from such an invasion, ambassadors were despatched to Syracuse with all speed to make the best terms they could. In point of fact, the alarm on this particular score was groundless. Gelo seems to have been content to leave well alone, and to reap the fruits of his victory in Sicily, without attempting conquest over-sea. It is obvious that, had he been otherwise inclined, the history of the world might have been changed by the destruction or permanent crippling of the Carthaginian power
The disposal of the large number of prisoners which had been taken was first provided for They were distributed among the Sicilian towns. Akragas got more than her due share, because the fugitives from Himera, fleeing inland to the mountains, had ultimately arrived in the territory of that city, where they were captured in large numbers. The magnificence of the temples and public works of that great town was largely due to the employment of these prisoners on their construction.176 That page of history which records Gelo’s reception of the Carthaginian embassy is obscure. The facts are sufficiently plain. He demanded extraordinarily moderate terms: a war subsidy of two thousand talents of silver, and the expenses of the construction of two temples. But why such moderation was observed by him at a time when he could without doubt have brought about the withdrawal of all the Punic settlements in Sicily, is not explained. Nor, in the silence of history, can any adequate motive for his action be suggested, unless he took the view that he would best
secure a lasting peace by such a policy. The Carthaginians attributed his treatment of them to the influence of his wife Demarete; and it is recorded to the credit of a people whose good points are not, from the force of circumstances, brought into prominence in Greek and Latin history, that they showed their gratitude to her by the free gift of one hundred talents of gold. Gelo, having exhausted sentiment in the late negotiations, exercised the persuasion of a husband, and appropriated the treasure to the establishment of that magnificent silver coinage which has excited the admiration of later ages.
Head. Hist. Num sub Syracuse.
Thus ended this brief but important chapter in Sicilian history. The Greek of Greece sought to ignore its significance; his posterity but half remembered it; and the great historian of the latter half of the century accepted the maimed tradition as he found it. But to the historical inquirer of the present day, who has all the evidence before him, this episode must appear not the least glorious part of the great struggle which saved western civilization.
H. viii. 126.
Among the troops who shared in the retreat of Xerxes’ army to the Hellespont, was a body of sixty thousand men selected from those which Mardonius had chosen. They were under the command of Artabazos, about whom and whose family Herodotus seems to have had special facilities for acquiring information. It may be suspected that this intimacy was due to the successive tenure in after-time of the Daskylian satrapy in Northen Asia Minor by Artabazos, his son, and grandson. The reason for his accompanying the march to the Hellespont was, so Herodotus says, that he might escort the king. It is more probable that the main motive lay in the organization of the new main line of communications along the North Ægean, with reference especially to commissariat. On his return from the Hellespont, he found the line threatened at one point by a rising against the Persian power, which had broken out in Pallene, the westernmost of the peninsulas of Chalkidike, and in the country immediately north of it, about the town of Olynthos. The desperate state of the king’s army in its passage by their territory had evidently
ARTABAZOS BESIEGES POTIDÆA.
given the citizens of this region the idea that the days of the Persian dominion in Europe were numbered, and that thus they might with safety throw off the yoke without further delay. The insurrection, though confined to this small region, threatened what was now the sole line of communications. It was imperative to crush it forthwith. This Artabazos set to work to do in the course of his return march to Thessaly. He laid siege to Potidæa, the chief town of Pallene, which stood on the narrow isthmus which connected the peninsula with the mainland, and, having walls from sea to sea, prevented all access to the peninsula itself to any force unaccompanied by a fleet. Its position was consequently one of great strength. Olynthos was by no means so strongly placed, but was of still greater importance to Artabazos, as more directly blocking the great highway from Asia. This latter town he took apparently without much trouble, and massacred its Bottiæan inhabitants at a lake hard by. He handed over the place to the Chalkidian Greeks, under the command of a native of Torone.
He then proceeded to blockade Potidæa on the side of the mainland, that towards the peninsula being inaccessible to him. The siege was marked by one of those attempted acts of treachery which too often blot the records of Greek courage. The commander of the contingent from one of the Pallenian towns, Skione, entered into communication with the Persian by means of written messages concealed in the feathers of an arrow which was shot to a place previously agreed upon. Unfortunately for the success of the plan, Artabazos on one occasion missed the mark, and hit one of the besieged in the shoulder. His friends gathering round him discovered the writing wrapped round the shaft, and carried it to the generals. The Skionian commander was, however, spared for the time being, lest the stigma of treachery should attach to his fellow-citizens.
The siege had lasted three months when an extraordinary ebb of the sea took place, rendering it possible for the besiegers to make their way on either side of the town towards Pallene. This phenomenon was not rare at Potidæa, so Herodotus says, but on this occasion it occurred on a larger scale than usual. It was probably due to one of those volcanic disturbances for which the
Ægean has been ever noted. Had the Persians taken immediate advantage of the opportunity thus offered, they might have got into the town, but, probably distrusting the nature of what must have seemed to them a very extraordinary occurrence, they were late in venturing upon the passage, and the returning flow came upon them when but two-thirds of the way across. Those who could not swim were drowned, and those who could were destroyed by the garrison, who put out in boats for that purpose. How many lives were lost history does not say, but the disaster was sufficiently great to make Artabazos throw up the siege. The capture of Olynthos had made the road fairly secure.
H. viii. 130.
After its hurried retreat from the European shore the Persian fleet had made its way to the Hellespont, where it had awaited the arrival of the retreating army, and had ferried it over to Asia. Nothing could show more clearly the futility of the alleged proposal of Themistocles to break down the Hellespont bridge. From Abydos it sailed to Kyme, where part of it wintered, while the remainder proceeded to Samos. On the appearance of spring the whole fleet assembled at the latter place, not, says Herodotus, with any intention of crossing the Ægean from thence, but to provide against possible revolt in Ionia. The position was well chosen for that purpose; but, more than this, the island lay at the eastern end of the shortest and most used passage of the Ægean, where an almost continuous line of islands stretches from Sunium to the Asian coast, affording protection against northern and southern gales. If the Greek fleet should sail to Asia, this was the route it would most probably take. Herodotus says they did not expect its coming, because there had been no pursuit after the retreat from Salamis. It may be apprehended that the Persian commanders were better able than Herodotus to gauge the significance of that fact, and that the expectations which the historian attributes to them are of his own suggestion.
GREEK COMMANDERS IN
479.
It does not appear as if there were any formed intention of resuming the offensive in the Western Ægean in order to give support to Mardonius whenever he should re-open the campaign,
H. viii. 130, ad fin.
though, if Herodotus is to be believed, plans of attack of some kind were discussed. Whatever they may have been, they were not put into immediate operation; and the appearance of the Greek fleet on the Asian coast later in the year completely altered the situation.
The approach of spring warned the Greeks that they must make preparations to meet the impending attack of Mardonius. With incomprehensible but characteristic dilatoriness, no immediate effort was made to collect the army, though a fleet of a hundred and ten ships gathered at Ægina under a new commander, the Spartan Leutychides. Moreover, Themistocles no longer commanded the Athenian contingent, his place being taken by Xanthippos. Possible reasons for this remarkable and important change have been already suggested. Of the actual reasons nothing is known.
There was, moreover, in this year, a change not merely in the personnel, but also in the system of command which prevailed during the previous year in the Athenian contingent. The Athenian army had played no part at Thermopylæ, and at Salamis it had acted, in so far as it did act, in immediate conjunction with the fleet. It had been, therefore, possible to place both arms of the service under the control of one supreme commander,—Themistocles. In 479, however, it was evident that the altered circumstances of the war would necessitate the employment by Athens of a considerable force on land, acting quite independently of the fleet. It would be impossible, therefore, for one man to command both; and a separate command on land was given to Aristides, another member of the College of Ten Strategi. He may or may not have been placed under the general control of Xanthippos. As events turned out, he must have exercised a practically independent command. An arrangement of this kind would, had the circumstances arisen but a few years earlier, have raised considerable constitutional difficulty; but between 490 and 480 the whole system of military and naval control had been completely remodelled.
At the time of Marathon, the supreme command was in the hands of one of the archons, with the title of Polemarch, and the ten strategi were subordinate to him, being merely the commanders of the
APPEAL FOR AND FROM IONIAN GREEKS.
contingents furnished by the ten Kleisthenic tribes, and also forming a council of war. In the course of the official year 487–486, the method of lot was introduced into the election of the nine archons, of whom the polemarch was one. The most thoroughgoing democrat at Athens, being, as a citizen, liable to service in war, would hardly fail to see the undesirability of entrusting his life to a general chosen by this method. That special form of fatalism would have few attractions for him. Thus the constitutional change with regard to the archonship necessitated some change in the arrangements of the military and naval commands. The polemarch was no longer commander-inchief. That office was vested in the members of the board of strategi, which henceforth had absolute control of military and naval affairs. As strategi, all of the ten were in a position of equality; and it is probable that each was allotted his own special department of administration, either on election, or by mutual arrangement between the members of the elected board. A board so constituted might work well in times of peace, but in time of war such a divided command could only lead to confusion and inefficiency. The people therefore reserved to itself the power of allotting special commands to strategi of its own choice, or even of appointing one member of the board a generalissimo (στρατηγός αὐτοκράτωρ).
It was under this constitutional arrangement that the mode of command adopted in 479 was possible.
It was while the fleet was at Ægina that the Greeks received the first direct appeal for aid from the Ionian Greeks. Doubtless the populations of the cities along the Asian coast were much stirred at this time by the disaster which had befallen the great expedition. That the Ionian contingent had shared in those disasters was a consideration which would affect but slightly the sentiments of the mass of the Ionian population; since, as has been already pointed out, that contingent represented merely the dominant philomedic minorities in the various Ionian towns. With the unbroken power of Persia to back them, those minorities could not be assailed with any hope of success; but now that that power was shaken, it might seem
H. viii. 132.
that the time had arrived for action. In Chios, at any rate, a plot was formed to murder the local tyrant Strattis. It miscarried, and six of the chief conspirators fled for their lives across the Ægean, where they made an appeal, first to Sparta, and then to the fleet at Ægina, to strike a blow for the liberty of their countrymen beyond the sea. Herodotus’ silence as to their reception at Sparta is eloquent; but his description of the effect of their appeal on the fleet is one of the most remarkable, and probably one of the most misinterpreted passages in his history, “The refugees, with difficulty, induced the fleet to go as far as Delos; all beyond was to the Greeks a land of danger, for they knew not even how it lay, and fancied it all to be full of the enemy’s troops. As for Samos, it seemed to them as far off as the Pillars of Hercules. So it befell that the Persians were afraid to sail westward of Samos, and the Greeks dare not go eastward of Delos, though the Chians entreated them so to do. So fear stood between them and protected them.”
This passage, even in its manifest rhetorical exaggeration, is interesting. The evident intention of the historian is to mark the fact that the mutual feelings of the two adversaries had entered upon a second stage.
He has spared no pains to draw a striking contrast between the exaggerated confidence prevailing on the Persian side up to the time of Salamis, and the corresponding lack of it among the Greeks. The balance of fear had been heavy against his countrymen. But now, at the opening of the campaign of 479, he is equally anxious to show that the scale had altered, and was now in equilibrium. With the dramatic instinct of the Greek, he wishes to indicate in one striking sentence that the turning-point in the tragedy has been reached. He was telling, as he well knew, the most exciting story in the history of the world up to his own time, and he may be pardoned, perhaps, if in his anxiety to emphasize its climax he has employed the language of exaggeration.
But when it becomes a question of determining the extent of the exaggeration, it may be suggested that there is perhaps less exaggeration in his statement than in the criticisms which have been passed upon it. May it not be that the eastern shore of the Ægean
THE SILENT ÆGEAN.
was to the European Greek of 480 a far less known region than might, without reflection, be assumed? Twenty years had passed since the outbreak of the Ionian revolt. Was not the attitude of Athens and Eretria in the first year of it peculiarly calculated to render communications between the two shores difficult and rare? The trade of the Ionian cities must have practically ceased during the seven years of the struggle; and, in any case, Persia, in her bitter resentment at the interference of the two states of European Greece, was not likely to encourage the visits of traders from the other side of the sea. Every avenue of trade in the Asian waters must have been unsafe to the Greek, not merely on account of the possible presence of the Persian fleet, but by reason of the swarm of privateers which the south coast of West Asia was ever ready to produce. And when the revolt was over, was it probable that the Persians would allow the Greek trader free access to information with regard to the plans of the expeditions of 492 and 490, or, amid the access of bitterness which arose from the failure of the latter year, with regard to the preparations made for a great revenge? If intercourse did continue, how does it arise that the Greeks were ignorant of the magnitude and real intent of the expedition of 480, up to within a few months of its arrival in Greece? The Ionian must have known long before. Why did he not tell the Greek trader, if that trader was a frequent visitor to his ports? After-ages do not realize the nature of the blow dealt to trade by a prolonged period of war, even if the active warlike operations be not continuous. To take examples from the history of England. Those who read the story of the Seven Years’ War mark with pride the absolute predominance which Great Britain had gained upon the seas by the year 1761. And yet, in that very year, eight hundred and twelve English trading ships were captured by the enemy,—no small fraction of the British trading fleet of those days. During the wars of the Napoleonic period when, after Trafalgar, Britain for many years commanded the sea, the English Channel, the greatest trade highway in the world, was almost as deserted as that Northern Ocean which Tacitus describes. Is it not possible, at least, that Herodotus has in his mind a state of things lasting for many years in the Ægean similar to that which
prevailed in the Channel in the first years of the nineteenth century? He may have exaggerated the feelings of the Greek sailors at this time; but who at the present day can say to what length of exaggeration he has gone?
H. viii. 131.
CHAPTER XI. THE CAMPAIGN OF PLATÆA.
W these events were occurring in Middle Greece, Mardonius, in the far North, was preparing to move. It is said that before starting he despatched an envoy to make inquiries of the oracles of Northern Greece, at Lebadeia, Abæ, and Mount Ptoon, on what subject Herodotus is unable to say with certainty—on the circumstances of the time, he is inclined to think.
H. viii. 136.
A much more important envoy was despatched to Athens in the person of Alexander, the son of Amyntas, a member of the royal house of Macedonia, who was connected with the Persians by family ties, and with the Athenians by his having held for them the position of Proxenos, or consular agent, in his own country.
It may fairly be doubted whether Herodotus got the tale of Alexander’s mission from an Athenian or from a Macedonian source, or whether he combined information derived from both. The reference to the character of the Athenian people has, on the one hand, a strong Attic flavour about it, H. viii. 137 et seqq. while the knowledge of the Macedonian royal family displayed here and elsewhere in his work suggests that Herodotus acquired his information on the spot in the course of a visit to that country.177
H. viii. 136.
From Sketch by E Lear ] PLAIN OF THEBES AND MOUNT KITHAERON.
1. Kithæron (about 15 miles).
2. Ridge between Parasopia and Plain of Thebes.
3. Thebes.
MARDONIUS AND ATHENS.
[To face page 436.
This tale might, consequently, be derived from Macedonia. This supposition is, however, rendered unlikely, owing to the excessively mistaken forecast which Alexander is described to have made of forthcoming events; and its Attic origin is the more probable. It is needless to say that that does not make for the veracity of a story whose evident intention is, like that of so many of the stories of this time, to bring into relief the self-denying patriotism of Athens. Yet, in spite of this, the story in itself is credible enough.
H. viii. 136.
Mardonius, so the tale runs, had made up his mind that if he could win over the Athenians to the Persian side he would thereby deprive the forces opposed to him of a people both numerous and brave, who were, moreover, mainly responsible for the disaster of the previous year. By this means he hoped to gain once more command of the sea, and expected to be infinitely superior to the enemy on land. This design, Herodotus thinks, was probably suggested to him by the oracles he had recently consulted.
The most remarkable reference, so far, is to the recovery of the command of the sea. No one could better estimate than Mardonius the full significance of the loss of that command. He must have known well that, unless it were recovered, he could at best obtain but a partial measure of success. Anything of the nature of a prolonged campaign to the southward of Bœotia would be, on the mere question of commissariat, impossible; and a brief campaign was not to be looked for. A foe which had been formidable with the courage of despair was likely to be more formidable when animated with the courage of a hope following despair He had, no doubt, accumulated during the winter in Thessaly as large a commissariat as possible; but it is beyond conception that he could have greatly increased the necessarily limited supplies obtainable locally by transport along that route of four hundred miles whose use had only been contemplated a month or two before, and whose organization must necessarily have been of the most hurried description. He must win Athens over, or modify his plans.
To her accordingly was offered a free pardon for the past on the part of the Great King, the enjoyment of her existing lands, and any accession of territory she liked. Nor did Alexander the envoy fail to point out to the Athenians the contrast between such a prospect and their actual state as the people who had suffered most from the war.
H. viii. 141.
The news of Alexander’s visit to Athens, and of its object, created considerable alarm at Sparta. An embassy was despatched with all speed to counteract the possible ill-effects of his proposals. This embassy was actually present when Alexander spoke; for the latter had been kept waiting for several days before he had been allowed to bring his business before the assembly. The astute Athenians had made up their minds to use Alexander as a lever wherewith to move the sluggish Sparta to action. They do not seem to have had any intention whatever of taking Mardonius’ message into consideration. When Alexander had done speaking, the Spartan ambassadors addressed the assembly. They urged that it would be gross desertion on the part of the Athenians to renounce their share in a war which had been provoked by them, and by them alone. Turning to more material matters, they
promised to alleviate the sufferings of the Athenians by undertaking the support of the non-effective part of the population.
The Athenian answer to Mardonius’ message was as firm as their determination: “So long as the sun runs his course in the heavens, we will never make terms with Xerxes.”
The answer to the Lacedæmonians as reported by Herodotus is, in sentiment and language alike, one of the finest passages in Greek prose.
“The fear of the Lacedæmonians lest we should make terms with the barbarians is, humanly speaking, very natural. And yet, knowing well, as you do, the spirit of Athens—that there is not in the wide world gold sufficient nor land so exceeding fair and good that we would accept it as the price of our own defection and of the enslavement of Hellas,—your fear, we think, does you but small credit. There are many powerful considerations which would forbid our so acting, even had we the will to do so. First and foremost is the burning and destruction of the images and temples of the gods, which we, so far from making terms with the doers of these deeds, must of necessity avenge to the full. Secondly, there is that tie of blood and language which binds the Greek world together, our common share in our religious foundations and sacrifices, our community of manners—things which it would disgrace the Athenians to betray. Know this, if you did not before know it, that so long as a single Athenian survives, we will never make terms with Xerxes. We admire your kindly thought for us, in that, homeless as we are, you are willing to support our families. That kindness on your part is complete, but we will endure as we are, without burdening you.
ATHENS AND SPARTA.
“But now, these things being so, send forth your army with all speed, for we imagine that the invasion of our land by the barbarian will not be long deferred, so soon as he hears our message refusing compliance with his demands. Ere, then, he enters Attica, there is time for us to meet him in Bœotia.”
And so the Spartan ambassadors went home.
The Athenians evidently hoped that they would be able to save their land from the devastation of the previous year by persuading the allies to meet the enemy in Bœotia.
Their hopes were natural, but they were not destined to be fulfilled; and, if by Bœotia the Bœotian plain was meant, it was fortunate they remained unfulfilled.
On receipt of the answer from Athens Mardonius started on his march from Thessaly without delay. The feudal families of that region had thoroughly espoused the Persian cause, and their attitude, as well as that of the Bœotians, shows that the dominant section in the two great territories of the North had definitely made up their minds that, whatever the fate of the South might be, those regions were to become part of the Persian Empire. The Theban advice to Mardonius to remain in Bœotian territory and seek to conquer Greece by corrupting the leading men of its various states, shows that the medization of the ruling powers in Bœotia was not merely a passive attitude. One thing, however, Mardonius had made up his mind to do—to capture Athens a second time. Herodotus attributes the intention to mere vanity, but any one or all of three practical reasons made its acquisition of importance to him. Its recapture might induce Xerxes from his base on the Asian coast to attempt to regain the command of the sea. Its possession might bring pressure to bear on the Athenian authorities, and aid his design of detaching that people from the forces of resistance. Finally, in case he intended to advance on the Isthmus, the possession of the Acropolis would protect his left flank. He occupied Athens without striking a blow, the population having been removed, as in the previous year, to Salamis. Having occupied it, he reopened the negotiations which Alexander had attempted but a short time before. The result was the same. The spirit of the people was shown by their stoning to death Lykides, a member of the council, for merely proposing that the message should be communicated to the Assembly. Even his wife and children were murdered in a similar way by the Athenian women at Salamis.
H. ix. 2.
H. ix. 6.
This second withdrawal to Salamis comes somewhat as a surprise in Herodotus’ narrative, for his
account of the visit of the Spartan embassy to Athens at the time of Alexander’s presence there makes it appear that an understanding had been arrived at by which Athens might be spared a second invasion. The explanation comes later. “So long as the Athenians expected that an army would come from Peloponnese to help them, they remained in Attica.” But when the presence of the enemy in Bœotia was announced, and it became impossible to hope that help from the South could arrive in time, they retired to Salamis, as they had done the year before. They also despatched an embassy to Sparta to protest against the delay
The strong appeal to patriotism made in their last communication to the Lacedæmonian embassy had failed to impress a people whose very institutions and training rendered them incapable of forming a real conception of the true spirit of a pan-Hellenic policy. Their stern discipline, moreover, was only too well calculated to render them mere tools of those set over them; and the delay in the present instance was probably due to the policy of an inner ring of the government at Sparta. The records of the time afford no certain clue to the motives lying behind that policy. It is possible that it aimed at forcing the hand of the Athenians, and compelling them to take part in the defence of the Isthmus.
ATHENIAN EMBASSY AT SPARTA.
H. ix. 7.
Sparta having failed to listen to persuasion, Athens had recourse, as on previous occasions, to threats. The Spartans were told that if Athens found herself deserted, she would seek her salvation in her own way; it was more than hinted that Mardonius’ offer might become a question of practical politics. The Spartan excuse for delay was similar to that urged for the desertion of Thermopylæ, the celebration of a festival. The story of the reception of the ambassadors is one of the strangest in the strange history of this time. They bitterly reproached the Lacedæmonians with their conduct. They put the very worst construction on the Spartan policy, which had, they said, inflicted on patriotism an amount of suffering which it dare not have inflicted on uncertain fidelity. It is probable that the reproach was, in so far as the Spartan authorities were concerned, well deserved. From the
language used by the Athenians it is evident that they believed that the Spartans had agreed to join in operations in Bœotia merely in order to keep Athens from medizing before the wall at the Isthmus was absolutely completed.178
That was the construction Athens put upon their conduct at this time; but it is probable that the more correct interpretation of their extraordinary policy is that by delaying they would be able to transfer the defence to the wall, and could, under any circumstances, rely on the devotion of Athens to the common cause.
Turning to the question of the future war policy, the Athenian ambassadors proposed that, as Bœotia had been lost, the enemy should be met in Attica; and they mentioned the Thriasian plain between Eleusis and Mount Ægaleos as admirably designed for a field of battle. [It must be remembered that this recommendation was made at a time when the Greeks were without experience of the effectiveness of the Persian cavalry on ground suited to its operations.]
The Ephors deferred their answer to the following day; from that to the next, and so on, until ten days had been wasted. They were waiting, says Herodotus, for the completion of the wall. They were, too, waiting, no doubt, until events in the North developed sufficiently to make it impossible for Athens to propose any other line of defence. This unsatisfactory state of things was brought to an end, so Herodotus says, by a warning addressed to the Ephors by Chileos, a Tegean, who had great influence in Sparta. He pointed out that if Athens joined the Persian, wall or no wall, the doors of the Peloponnese would be opened wide. Herodotus evidently supposed that until this moment such an idea had never occurred to the Spartan authorities, despite the experiences of Artemisium and Salamis in the previous year. In all probability, what really influenced these authorities was the fact that an able man, whose opinion they valued, was not so sure as they themselves were, that Athenian loyalty would endure much longer the severe test to which it was being put.
Their next act was a very strange one. Without saying a word to the ambassadors, they despatched under cover of night a force of five thousand Spartans, each of whom was accompanied by seven helots. There were, therefore, forty thousand in all. The number of light-armed helots is remarkable, certainly above the usual quota allotted to a force of five thousand heavy-armed.179
SECRET DESPATCH OF SPARTAN ARMY.
In constituting this force, the unusual number of light-armed in the army which it would have to meet would naturally be taken into consideration. The circumstances of population in the Spartan territories, moreover, were such that any unusual increase in the numbers employed on any expedition would be supplied by the increase in this branch of the service. The commander of this large force was Pausanias. Kleombrotos had been in command at the Isthmus in the previous year, but had died shortly after bringing back his army thence.180 It must have been prepared for departure for some time past No such force could start on short notice.181
The ambassadors, knowing nothing of this sudden march, and weary of the continual procrastination, were prepared to leave Sparta on the following morning. Before the deception was discovered the Athenian delegates actually stated that, in consequence of Sparta’s attitude, Athens would make terms with Persia, and, more than that, would accompany the Persians in their invasion. Truly the Spartan government policy had very nearly brought Greece to ruin.
The surprise of the indignant envoys may then be imagined when they were told in answer by the Ephors that they had every reason to believe that their army was, by that time, at Orestheion on its march against “the strangers,” as they called the barbarians. Orestheion was in the small plain of Asea, S.S.E. of the Arcadian plain, where one of the great roads from Sparta northward met the main road coming from Messenia to the Arcadian plain. The fact that they took this route is interesting, because it almost certainly indicates that they wished to avoid Argos, from which, as will be seen, a certain amount of trouble was to be expected.
Thus the truth came out; and the envoys started without delay in pursuit of this phantom army, accompanied by five thousand picked hoplites of the Periœki.
The truth about the attitude of Argos at this time is rendered uncertain by the fact that, after the war was over, the patriot Greeks regarded not merely those races which had medized, but also those who had not taken part with them, as having been enemies of their fatherland. That of itself would give rise to a number of traditions of doubtful credibility with respect to the attitude of such neutrals. Nevertheless, the attitude of Argos was highly suspicious, and there is no doubt that it was firmly believed in after-time that she had had traitorous relations with Persia.
H. ix. 12.
Herodotus asserts that the Argives sent a messenger about this time to Mardonius, who was in Athens, saying that they were unable to carry out the promise that they had made to him to stop the Spartan army on its march northwards. This tale is to a certain extent supported by the fact that the Spartans, instead of adopting the shorter route north by the Thyreatic plain and Argos, adopted the longer one indicated by the mention of Orestheion. Argos was, by its strategical position, ever a serious obstacle to Sparta’s communication with the north.
KITHÆRON AND PARNES.
Mardonius had, up to this time, refrained from damaging Athens and Attica, in the hope that the Athenians would change their minds, and accept his proposals; but, failing to persuade them to do so, and hearing of the advance of this army to the Isthmus, he set fire to Athens, and began to withdraw to Bœotia; “because,” says Herodotus, “Attica was not a country for cavalry, and if he were defeated in an engagement his only line of retreat was through strait places, so that a few men could stop him.” He determined, therefore, to retreat, and make Thebes his base of operations, as lying in a region eminently adapted to the use of cavalry. His evident fear was lest the Greek forces should work up through the Megarid and seize the difficult passes of the Kithæron-Parnes range in his rear.
As this range is of great importance in the campaign which was at this time about to open, it may be well to describe its nature, and to enumerate the passes by which it is pierced. It was regarded by the Greeks as an effective and important line of defence; and the difficulties which it presented to various armies which had occasion to traverse or to attempt to traverse it in the warfare of the fifth and fourth centuries before Christ, show that their estimate of its defensive possibilities was not a mistaken one. As its name implies, it is in reality composed of two short ranges, Kithæron on the west, and Parnes on the east. These are connected by an upland country known to the ancients by the name of Panakton, whose approaches on either side are, from a military point of view, of a very difficult character. The chain as a whole may be said to form a continuous barrier stretching from the head of the gulf of Corinth to the southern part of the Euripus. Both Kithæron and Parnes are sharply-edged, steep-sided ridges, whose highest points rise to a height of four thousand five hundred feet above sea-level, while the general elevation of each chain is about three thousand feet. Though not, as will be seen, of any great height, they offer comparatively few passages. There are six points at which the range may be traversed. Of these the western series, four in number, are of importance in reference to the battle of Platæa itself, while the two eastern passes afford alternative routes for an army retreating, like that of Mardonius, from Athens to Thebes.
At the extreme west of the range, where it sinks with sudden abruptness into the gulf of Corinth, it is turned rather than traversed by what is little better than a mountain track, which led from the Bœotian port of Kreusis to the Megarean town of Ægosthena. From Ægosthena a road led southwards to Pagæ, and so round the western bastions of Mount Geraneia to the Isthmus. It was also quite possible to reach Megara by a branch of this route.
Cf. Xen. Hell. v. 4; vi. 4.
The difficulties of this pass are such that it was rarely used for military purposes, and it seems to have played no part whatever in the operations of 479.
The second pass is that which the road from Platæa to Megara formerly traversed. It crosses Kithæron a little more than a mile
eastward of Platæa, entering a deep valley which runs into the chain from the north, and ascending steeply from the head of the valley to the summit of a col in the ridge. Its character forbids the supposition that it can ever have been used for wheeled vehicles, and its importance must have been mainly due to the fact that it is the only one of this series of passes, with the exception of the track by Ægosthena, by which land communication between Northern Greece and the Peloponnese could be maintained without entering Attic territory. The road south of it, towards Megara, traverses the troublesome hill region of the Northern Megarid.182 The fact that Platæa practically commanded the northern end of this pass rendered the town one of the most important strategic positions in Greece, both in the fifth and in the fourth centuries. It will be hereafter seen that this pass must have played an important part in the operations of the Greek army at Platæa.
The third pass is one by which the road from Platæa to Athens crossed the range. It is little more than a mile to the east of that last mentioned. Remains of the road are visible on the north side, entering a somewhat broad valley running into the hills. It must have always been an easy pass, and the ancient wheel-ruts worn in the rock show that it was used by wheeled vehicles.183 The road, after traversing it, turned east, and joined, near Eleutheræ, the road from Thebes to Eleusis by way of the pass of Dryoskephalæ. This pass also played an important part in the operations at Platæa.
PASSES
BETWEEN ATTICA AND BŒOTIA.
The fourth pass was well known under its Attic name of Dryoskephalæ, and though not traversed by the direct road between Thebes and Athens, must have been largely used by those going from one place to the other, owing to the route by way of it being more easy than the direct road by Phyle. From the Bœotian side, near the site of the ancient Erythræ, the ascent is steep; it must have always been necessary to make it by a series of zigzags. The summit once reached, the descent is gradual, down a long streamvalley which abuts on a small plain of Attica beneath the fortress of
