Where the Island lay decides which passes are possible at all. Polybius's Island is the land between the Rhône and a second river. If that river is the Isère, the army marched up the Isère and the candidate cols are those of the Maurienne and the Tarentaise: the Mont-Cenis, the Clapier and its Petit Mont-Cenis variant, the Petit St Bernard. If it is the Aygues at Orange or the Sorgue near Avignon, the army marched up the Drôme or the Durance and the candidates are the Montgenèvre, the Traversette and the Larche. No col is on both lists. So the first thing to settle is what the texts and the distances allow.

The river's name does not settle it. No manuscript of either author reads Isère: Polybius's manuscripts give Σκάρας or Σκώρας, Livy's sarar, bisarar or arar, and Isara is Cluverius's conjecture of 1624 in both texts (see the notes above). Holstenius's explanation, that ΟΙΣΑΡΑΣ was misread as ΟΣΚΑΡΑΣ, is plausible as palaeography, but it remains a conjecture. Conway's case for the Sorgue rests on Strabo's Σούλγας (4.1.11); Colin (1904) and Wilkinson (1911) had already put the Island between the Rhône and the Sorgue at L'Isle-sur-la-Sorgue, and Torr (1924) put it at the Durance. De Beer's Aygues has no ancient name to rest on at all. The river has to be found from the geography.

Polybius gives three measurements. The crossing was made "where the stream is single, about four days' march from the sea" (3.42.1). The Island was reached "on the fourth day" from the crossing (3.49.5). And the whole way from the crossing to the foot of the ascent was 1,400 stades (3.39.9), of which the last 800 were the ten days from the Island (3.50.1), which leaves 600 stades, 107 to 111 km, for the four days to the Island. Schweighäuser made that subtraction in 1789 and it has been the Isère party's main argument ever since. Measured along the valley floor on the route model, the distances are:

The 600 stades fit one combination only: a crossing near Roquemaure and an Island at the Isère, 111 km and 623 stades apart. That crossing is also the one about four days from the sea, since the delta mouth is some 90 km downstream of Roquemaure and about 55 km from Beaucaire. The Aygues fits four days of marching only if the army crossed at or below Beaucaire and then averaged 11 to 14 km a day on flat ground, and Beaucaire is two days from the sea, not four.

The same numbers can be turned round. Polybius's next stage runs 800 stades in ten days, 80 stades or about 14.5 km a day. At that rate four days is 320 stades, 57 km, which is the distance from Fourques to the Aygues. So one of Polybius's figures is wrong, or the four days from the crossing were long days and the ten days beyond the Island were short ones. The ten days were spent in flat country with an escort and no enemy, and 14.5 km a day is slow for that. I read the 600 stades as the more reliable figure, because it is the difference between two stated totals rather than a rate, and because Polybius's "four days from the sea" for the crossing points the same way. But the arithmetic is not clean, and the weighing in the model section counts the Island as a strong item and stops short of a decisive one.

Two other details favour the Isère. Polybius says the Island's third side was "mountains difficult to approach and to enter, almost inaccessible" (3.49.7): the Vercors and the Chartreuse close the Isère triangle in that way, while the small triangle between the Aygues and the Rhône has the low hills of the Baronnies behind it. And Polybius keeps the Island's people and the Allobroges apart. The prince of the Island escorts the Carthaginians "through the Gauls called Allobroges" (3.49.13), and the Allobrogian chieftains attack only when the escort has turned home at the foot of the ascent (3.50.2-3). Pliny's list of the Narbonese peoples runs inland from the coast "the Tricorii, and further in the Tritolli and the Vocontii and the Segovellauni, next the Allobroges" (Tricorium et intus Tritollorum Vocontiorumque et Segovellaunorum, mox Allobrogum, 3.34), and puts Valence "in the territory of the Cavares" and Vienne with the Allobroges (3.36). An Island in the Valence plain belongs to the Segovellauni or Cavares, with the Allobroges beginning across the Isère, which matches Polybius's distinction. An Island at Orange puts the Allobroges a hundred kilometres to the north, and de Beer had to make the "Allobroges" of the ambush a loose term for Alpine Gauls in general.

Livy points the other way. His Island is the same four camps from the crossing, but he makes the Allobroges live "near by" and makes the quarrelling brothers Allobroges, and then he sends the army "left into the Tricastini, along the outer edge of the Vocontii, into the Tricorii" and across the Durance (21.31.9). The Tricastini are at Saint-Paul-Trois-Châteaux, on the Rhône south of Montélimar. From an Island at the Isère that is a march back down the Rhône. From an Island at Orange it is a turn to the left, north, and then east up the Drôme, over the Col de Cabre or the Col de Grimone into the Gap basin, and down to the Durance: de Beer's route. Livy's itinerary is coherent from the southern Island and incoherent from the northern one. The question is whether it is Livy's itinerary at all. The names do not occur in Polybius, and Livy's sentence that after the Durance the army reached the Alps "by a mostly level road" (21.32.6) describes the Isère valley better than the Durance above Sisteron. The Oxford editors thought the reckoning of days excluded the Isère; the Clapier school from Perrin onwards has treated the Druentia passage as an intrusion from the annalistic tradition, and I could read Walbank's discussion of it only in snippets. I count it as a second tradition in its own right, of modest weight, and the model section runs the case in which it is trusted in full.

Ammianus (15.10.11) repeats Livy's peoples in Livy's order, "through the Tricasini and the far edge of the Vocontii to the passes of the Tricorii", and adds that Hannibal was guided by "natives from among the Taurini". He is a witness to the Livian tradition rather than to the route.

Polybius counts the days over the mountains too. From the foot of the ascent he gives nine days to the summit, two days there, a descent that begins on the next day and reaches the broken path, one day making it passable for horses and mules and three more for the elephants, and then three days to the plain (3.53.9, 3.54.4, 3.55.7-8, 3.56.1). The whole crossing is fifteen days (3.56.3), which the stages do not add up to, and the distance is "about 1,200 stades" (3.39.10). I tested each candidate against these figures on the Copernicus 90 m elevation model, with the route drawn as a least-cost valley-floor path between named places and the beginning of the ascent taken at the gate that each school itself uses: Aiguebelle for the Isère routes, Albertville for the Tarentaise, Sisteron for the Durance, Crest for the Drôme, Martigny for the Valais. The code and every intermediate number are in the files listed at the end of this page.

Three of the figures in the table tell the candidates apart and two do not. The 800 stades from the Island do not: along the Isère they end between Montmélian and Aiguebelle, where the Combe de Savoie shuts and the Maurienne begins, which is the first ascent of the Mont-Cenis and Clapier theories and equally the turn into the Tarentaise; from an Island at Orange, down the Rhône and up the Durance, they end 15 km short of Sisteron. Every school can claim the figure to within 10 or 15 per cent. The 1,200 stades for the crossing do not tell them apart either, and the reason is in the text: no line satisfies both of Polybius's totals. The Isère routes give 1,500 stades for the 1,400 from the crossing to the ascent and only 620 to 670 for the 1,200 of the crossing; the Durance routes give 1,140 and 940. The Drôme approaches that Livy's itinerary implies need 1,450 to 1,540 stades from Crest to the plain and 25 km a day for nine days over two intermediate cols, which is outside anything the narrative allows. One observation of my own, which I could not check against Walbank: 1,200 stades is exactly fifteen days at the 80 stades a day of the previous stage, so the figure may be a computation from the day-count rather than a measurement.

The nine days of ascent separate the candidates only a little. From the gates, the ascent averages 4 to 16 km a day for every candidate, slow but consistent with a battle on the first day, a captured town, a day's halt, a second ambush and a night on a rock. The four days of descent are more useful. Polybius's army came off the cliffs with its animals starving and reached the plain on the third day. From the Clapier the plain below 400 m is 25 km away, from the Traversette 28, from the Mont-Cenis 32: six to eight kilometres a day. From the Montgenèvre it is 51 km, from the Petit St Bernard 72 km to Pont-Saint-Martin, from the Larche 79 km to the Cuneo plain: thirteen to twenty kilometres a day downhill with a wrecked army. The difference is the length of the confined valley below each col, and it does not go away if the descent is measured to the first villages instead of to the plain.

The broken path separates the candidates most. Polybius says the descent was narrow and steep and that a stretch of about a stade and a half, some 270 m, had fallen away where the track ran along a precipice, an old break freshly enlarged (3.54.7); Hannibal "built up the cliff" (3.55.6). At 90 m resolution the elevation model can say where a ledge above a drop exists and where it does not. The Clapier has a 500 m stretch of the descent at 50 per cent one kilometre below the col, the Clarea headwall; the Traversette has 51 per cent half a kilometre below the col, on the east face above Pian del Re, losing 900 m in 2.7 km; the Grand St Bernard has 54 per cent at 1.8 km. The Mont-Cenis has its steep ground 13 km beyond the col, where the plateau drops through the Ramasse to Novalesa, after 13 km of near-level lake basin. The Montgenèvre, the Larche and the Petit St Bernard never exceed 23 to 29 per cent anywhere on their descents: there is nothing on them that a landslip could have made impassable to a mule. The model cannot say whether a particular ledge fell in 218 BC, only where the ground is of the kind Polybius describes.

Polybius sets Hannibal's speech at the camp on the pass and has him point out "the plains of the Po" (3.54.2-3). Livy moves it to the next morning and to "a certain promontory from which there was a far and wide view" (21.35.8). Advocates of every pass have claimed the view for their col, usually from personal experience on a clear day, and sceptics have called it a rhetorical commonplace. Whether a col sees the plain can be computed from the terrain model. For each col I cast rays every quarter of a degree out to 120 km over the elevation model, allowing for the curvature of the earth and standard refraction, and asked whether any ground of the Po plain, defined as land below 400 m east of 7.3°E and north of 44.4°N, was in sight. I then repeated the test at every 250 m of the first 10 km of the descent, from knolls 100 m and 300 m above each col, and from every cell within 1.5 km of the col and up to 300 m above it, the ground a general with a day to spare could walk to.

Only two cols see the plain at all. From the Traversette it lies in sight across a 63-degree sector from east-north-east to east-south-east, the nearest plain 26 km away at Revello and Saluzzo and the farthest 120 km at the edge of the model; it is in sight from every point of the first 2.25 km of the descent, and from the knolls beside the col across 22 to 26 per cent of the horizon. That matches both authors without special pleading. From the Clapier the col itself sees a two-degree sliver of plain 80 km away through the notch of the Val Clarea, beyond Turin; from one kilometre down the descent, on the lip of the Clarea headwall, it sees 5 per cent of the horizon, and from the ridge 1.4 km from the col, at 2,712 m, 8 per cent. That matches Livy's promontory on the first descent morning and gives Polybius a view to point at, though not a panorama. The Mont-Cenis sees nothing from the col, nothing from the first 10 km of the descent and a half-percent sliver from three cells on the ridge above; its famous prospect of the Susa valley is from the plateau's far rim, 12 km beyond the col. The Petit Mont-Cenis, the Montgenèvre, the Larche, the Petit St Bernard, the Grand St Bernard and the Col Agnel see no plain from the col, from any point of the first 10 km of descent, from the knolls, or from any of the 47 to 91 cells scanned around each of them.

The result is insensitive to the threshold for "plain" (raising it to 500 m adds the Cuneo terraces and the Canavese hills and opens no closed col), to the refraction constant, and to tree cover, which can only hide plain that the model shows. It does depend on the assumption that the observer stood within an hour's walk of the col, and it says nothing about weather. The Traversette has the view Polybius describes from the summit camp, the Clapier has the view Livy describes from a promontory on the first morning of the descent, and no other candidate has either.

Polybius dates the summit camp by "the setting of the Pleiades" (3.54.1), and Livy by the same star (21.35.6). For 218 BC at 45°N the true morning setting of Alcyone, the cluster's brightest star, falls on 29 October of the proleptic Julian calendar, and the first morning on which the cluster could be seen setting in the dawn falls between 4 and 9 November depending on the visibility threshold assumed, 6 November at the conventional 7.5 degrees. Two independent computations, Skyfield with the JPL DE406 ephemeris and PyEphem, agree to the day, and Columella's calendar of the first century AD, which has the Pleiades "begin to set at sunrise" on 20 to 21 October, "set" on 28 October and "set in the morning" on 8 November, agrees as closely as the 280 years and three degrees of latitude allow. So the army stood on the pass in the last days of October or the first week of November. The phrase is a farmer's calendar date, not a report of an observation made on the col, and its precision is about a week.

Polybius then says that on the descent the new snow of that year lay on "the snow that was there before and had lasted from the previous winter" (3.55.1), and Livy has "old untouched snow" under a shallow new fall (21.36.5). Whether last winter's snow survives to the end of October at a given col is a question about the snowline. In the modern climate the end-of-summer snowline of the French western Alps averages 3,035 m, ranging from 2,790 m in a cool year to 3,250 m in a hot one (Rabatel and colleagues 2013), and old snow survives in shaded hollows and avalanche cones a few hundred metres below it. Glacier records put 218 BC after the Iron Age advances had waned and within a century of a further advance around 100 BC, so the snowline was probably no higher than today's and may have been 100 to 250 m lower (Holzhauser, Magny and Zumbühl 2005; Le Roy, Ivy-Ochs and colleagues 2024). On those figures the Traversette, at 2,947 m, is at or above the snowline and old snow on its descent in late October is likely. The Clapier and the Grand St Bernard, at about 2,480 m, are 500 to 600 m below it and old snow on them is unlikely but possible in shade. The Petit St Bernard, the Petit Mont-Cenis and the Mont-Cenis, at 2,080 to 2,190 m, are 850 to 950 m below it, and the Larche and the Montgenèvre, at 1,990 and 1,854 m, more than a kilometre below it: old snow on those cols in late October would be exceptional in any climate the record allows. These bands are judgements rather than measurements; I found no station series of autumn snow patches for the southern French Alps. Two cautions on the text: Polybius puts the old snow on the descent below the summit rather than at the col, and his remark a few lines later that the heights of the Alps carry snow all year round (3.55.9) is a generalisation, so 3.55.1 may be a generalisation too. The model section runs that scenario.