Alexander's technicians had not stopped at stone-throwers; stronger and taller siege-towers than ever before were waiting to be assembled, leaving space for archers and battering rams on as many as twenty different levels, up to a height of 180 feet; they were an extraordinary feat of carpentry, for their axles were made of oak, their planking of fir and their wooden towers were coated with lime and hung with sheepskins to keep off enemy missiles. There were improved grappling irons, though Alexander's head engineer disputed their merits; there was also a borer on wheels whose long iron-tipped pole was poked into mud-brick walling by a newly improved method. Wide drawbridges fell from each storey of the towers, down which more troops could pour than on usual designs; rams were mounted on a superior form of 'tortoise' 48 feet square, beneath which they were worked by ropes and a roller, while animal skins and a three-storey tower protected them, its top level carrying catapults, the bottom two holding buckets of water to put out any flames. But without exceptional leadership no number of new machines would bring Tyre down. Men as well as mules would have to heave these gigantic towers into position, and encouragement rested with Alexander, cut off by half a mile of water from the point at which conventional siegecraft could begin. 'Genius,' Napoleon once remarked, 'is the inexplicable measure of a great commander.' Before Tyre, Alexander's generalship had been good rather than great; with a characteristic leap forward to meet a challenge, he was now to show for the first time that genius which singles him out in military history. Before settling down to besiege, he sent heralds to offer Tyre peace in return for surrender. The Tyrians seized and killed them, hurling their bodies off the city walls in full view of the enemy. 'A truce must not be broken or a herald killed; a man who has surrendered to a superior must not be abused': the Tyrians had flouted an unwritten law of Greek warfare.

In reply, Alexander's first plan was bold. If he could not sail to Tyre, he would build a mole across the waves and walk there. For the mole, he had a successful precedent. In 398 Dionysius I had taken the city of Motya in north-west Sicily after rebuilding its sunken causeway across a whole mile of sea. Tyre was only half that distance away and though no previous earthwork survived as a foundation, most of the sea cliannel was so shallow that its mud could be used to bind the stonework together. It would be interesting to know how, if at all, Alexander had estimated the depth of the sea, as a hundred yards or so short of the island the water deepens suddenly. But even at that distance, Alexander's causeway would have served its purpose; his siege-towers would still overtop the wall, allowing his archers to shoot down on to the defenders, while his new stone throwers could batter the fortifications. Fortunately the forests of the Lebanon were a nearby source of timber, whereas Old Tyre, fast being demolished, provided the necessary stone; any further transport of building materials would have been impossibly slow, especially in the absence of the fleet. Ancient Greece knew no efficient carthorse collar and had never even devised a wheelbarrow.

Through the shallows the work proceeded apace, watched by Alexander who, said his officers, 'explained each step in person, encouraging some with a kind word, lightening the labours of others who had worked conspicuously well with a gift of money'. The people of Tyre were sceptical, harassing the builders from their warships and jeering at Alexander for daring to rival the God of the Sea. But the mole drew nearer, Poseidon notwithstanding, and the Tyrians soon took to pelting it with arrows from their arrow-catapults: in reply, Alexander hung up leather hides to protect his men and ordered two tall siege-towers to be erected to that he could shoot back. The Tynans, themselves engineers with a respectable history, replied with a show of technical cunning.

In the secrecy of the city harbour they built up a transport ship to hold as much dry timber, shavings and torchwood as possible, adding pitch, sulphur and other inflammable material. The idea of a fireship was not new, but to each of its two masts near the prow they lashed two beams and hung up cauldrons filled with fuel; when the beams burnt, the cauldrons would tip and fan the fire, like the famous firepots which Rhodes would popularize over a century later. After ballasting the stern so that the prow was well clear of the water the crews waited for a favourable wind and then arranged for triremes to tow them towards the mole. Within range, they set light to the cargo, dived for safety and left the ship to blow straight into Alexander's siege-towers. The triremes bombarded any Macedonian defenders, and skiffs put in to the mole elsewhere and destroyed all available catapults. Victim of a most intelligent manoeuvre, Alexander ordered new machinery to be built and the mole to be widened to some 200 feet in order to hold more siege-towers. Personally, he departed to Sidon on the happy news that the Phoenician fleet was at last returning home from Persian service; they might well be compelled to join him now that they had heard how their bases had surrendered, and as his hewers of wood in the Lebanon cedar forests were being harassed by natives, the Shield Bearers and Agrianians came too, prepared for a short sharp exercise.

On reaching Sidon, Alexander was more than compensated for the slow and disastrous progress of his mole. The kings of Byblos and Arad had returned to put in his power the ships with which they had deserted from the Persian admirals. Sidon did likewise, pleased by her change of king, and Rhodes sent nine warships, a precious gesture from an island whose entrepreneurial skills were becoming indispensable to the trade of the south-east Mediterranean. A hundred warships in all had joined him, enough to cripple the Persians' fleet at the start of their sailing season and to vindicate his long-term policy of taking the sea-ports one by one. It did not seem too disturbing when a fifty-oared pinnace arrived from Antipater with an urgent message in its captain's keeping; across enemy seas and against a March wind, the journey must have been dramatic and it would not have been undertaken for a triviality. As the captain had been the hero of the surprise of the ten Persian triremes in the Cyclades the previous autumn, his message probably concerned the evident attempts of the Spartan king Agis to rebel with Persian naval and monetary support. Alexander was already aware of Spartan discontent and none too worried that the Greek allies would abet it; the Persian ships were now a dying threat, so he left Sidon for ten days and menaced the tribesmen of the Lebanon cedar forests in order to safeguard his timber-cutters, sparing himself nothing in the process, as is plain from a delightful incident.

Lysimachus, Alexander's favourite boyhood tutor, had insisted on joining the march to the woods but as darkness fell, cold and unfamiliar in the mountains, he was lagging far behind the professional soldiers. Rather than abandon him to the enemy, Alexander fell back by his side and together, pupil and tutor soon found themselves cut off from all but a few of their troops. The night was growing chilly and they had no supplies to light a fire; in the distance, Alexander saw the enemy camp fires and 'trusting in his own agility - for, as always, he consoled his Macedonians by sharing their hardships in person', he set off to fetch his men a light. Reaching the camp fire, he surprised and stabbed two enemy guards with his dagger, snatched a torch from the embers and brought it back to warm his followers. Having scared off enemy reprisals, tutor, pupil and friends spent the night by their own blazing fire. In the search for Alexander's personality, this story must not be discounted; Chares its teller was Alexander's Master of Ceremonies, who would hear it told at dinners by his king, and any exaggerations may come not from his own imagination but from fellow-guests at table. Serious concern for his soldiers, a personal daring which in a lesser man would be a foolish waste of life: it was only proper that the new Achilles should have risked himself in the manner of his hero for the tutor who had first given him his Homeric nickname.