Broadsheet

This week we’re going to take a brief break from our series on hoplites (I, II, IIIa, IIIb) to address a broader question in how we understand the mechanics of warfare with contact weapons, which is the mechanics of the concept of a ‘battle pulse.’ This notion, that front lines in contact might occasionally withdraw to catch their breath, replace wounded men at the front or simply to relieve the psychological pressure of the fighting keeps coming up in the comments and is worth addressing on its own. Because while it is an important question for understanding any kind of contact warfare (because ‘pulse’ proponents insist on the pulse as being a general feature of contact warfare, not restricted to any particular culture), it is both very relevant to understanding hoplites, but also emerged as an extension of the argument about othismos that extended into Roman warfare.

There is something of an irony that we are briefly disengaging from our discussion of hoplites to discuss if hoplites briefly disnegaged from battle.

So our question here is, “was the fighting at the point of contact between two formations of heavy infantry a continuous run of fighting or did it proceed in pulses and bursts and if the latter, of what nature might they have been?” I should note that the normal expression here is to describe the sparring at the line of contact as a ‘series of duels’ but anyone who has watched or participated in experiments in contact-line fighting will immediately recognize they are not ever a ‘series of duels’ as any given combatant on the front moving into measure is entering measure of several enemies and so may attack or be attacked by any of them (and indeed, striking the fellow to the left or right of the fellow in front of you, catching them unawares, is often useful). So the line of contact is not a series of 1-on-1s but rather a rolling series of ‘several-on-severals’ with each man having his own set of ‘several,’ depending on the length of the weapons used.

Now before we rush in, I want to make a clarification of two terms I am going to use here that might otherwise be confusing. I am going to make a distinction here between ‘measure‘ and ‘contact.’ This is not some well-established distinction, so I am bending these terms a bit to make clear a different that I think matters. When I say measure here, I mean the reach of the contact weapons the men have, how far they can actually deliver a strike. That’s going to vary a bit based on the weapons they have, but it’s going to be around 1-2 meters.¹

When I say contact what I mean is a bit looser: two formations standing a few yards apart might be out of measure, but they are certainly in contact in that neither can maneuver freely and the men in the front of both must be focused on their enemies directly forward because anyone could dash into measure to strike at any time. For these units to move out of contact, I’d argue they need to back up a fair bit more, perhaps out to something like ‘javelin reach’ which with the heaviest of javelins might be around 20-25 meters. As we’re going to see, there’s a big difference between being just outside measure at perhaps 2 or 3 meters away and being at ‘javelin range’ at say, 15 meters away. But to be clear: measure here is the closer proximity, contact is the looser, more distant proximity.

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Whence the Pulse

We ought to begin with a brief history of the concept of the ‘battle pulse’ in ancient warfare and fortunately this can be quite brief.

As you will recall from our historiography on hoplites and Michael Taylor’s guest post on the book, John Keegan’s The Face of Battle (1976) had quite an impact. It inspired Victor Davis Hanson to essentially replicate the approach in writing Western Way of War, kicking off the modern period of hoplite debates, but it also had imitators in the study of the Roman army, most notably Adrian Goldsworthy. Now I think it is worth noting that is something of an important delay here: when Adrian Goldsworthy goes to write The Roman Army at War, 100 BC – AD 200 (1997), WWoW (1989) has been out for nearly a decade and while the full-throated heterodox vision of Myths and Realities hadn’t arrived yet, it was clearly coming. By this point, in particular, Peter Krentz, writing article after article, had punched some pretty significant holes in elements of orthodoxy, including the shoving-othismos. So when Goldsworthy (and Philip Saban, working at the same time) go to apply a Keegan-style Face of Battle approach to the Romans, they are doing so downstream of the hoplite debate.

And so in a sense you want to understand Goldsworthy and Sabin (and Zhmodikov, to whom we will come shortly) as essentially the extension of hoplite heterodoxy into the Roman sphere; you can see this, I think, quite clearly in their writing (and in turn they are relied upon and cited by more recent hoplite heterodox writers). Except, of course, the scholarship on Roman warfare never had anything remotely as rigid or implausible as the ‘strong’ orthodox hoplite model, so the modifications to our understanding of Roman battle that these fellows offer are more modest.²

The starting point of this burst (dare we say ‘pulse?’) of Roman-legion-heterodoxy is P. Sabin, “The Mechanics of Battle in the Second Punic War” BICS 67 (1996), followed very rapidly be the aforementioned A. Goldsworthy The Roman Army at War, 100 BC – AD 200 (1997) and then clarified and restated with Sabin, “The Face of Roman Battle” JRS 90 (2000). Essentially Sabin raises the question first, noting that our sources often describe Roman battles in the Middle and Late Republic as lasting several hours (typically one to three) and noting that neither the number of casualties described nor the limits of human endurance would be consistent with a continuous exchange of sword blows for three hours. Hence, Sabin figures, the Romans must have moved in and out of contact, which in turn also helps him make sense of how battles in the Second Punic War seemed so often involve a formation getting ‘pushed’ backwards (not literally, of course) significant distances to create pockets or holes without collapsing. I should note that Sabin doesn’t really get into how far out of contact these movements might be.

Goldsworthy then brings to this problem the work of S.L.A. Marshall in Men against Fire (1947).³ Marshall had argued that only a small portion of soldiers in WWII had actually used their weapons, an extension of Ardant du Picq’s should-be-more-famous maxim, “Man does not enter battle to fight, but for victory. He does everything that he can to avoid the first and obtain the second.”⁴ Goldsworthy sought to apply this insight to Roman combat and argued that likewise in the front line of a Roman legion, many men, indeed “the majority of soldiers” even in the front rank must have done essentially no meaningful fighting, mostly staying safe behind their shields.⁵ It seems worth noting that this insight is being applied by analogy – no one ever had a chance to study contact warfare in this way – and so while I think there is an insight here going back to Ardant du Picq, it is not clear to me that the straight-forward application of very modern evidence of combat participation with guns can be applied to combat with contact weapons without considerable hazards. Goldsworthy also imagines Roman maniples – the basic maneuver unit of the legion in battle – more as ‘clouds’ of men fighting (a kind of presaging of van Wees’ skirmishing hoplites) rather than a coherent mass with men having a specific, assigned place in the formation. Instead, braver individuals might hype up the whole group to make a big push into contact, bringing the ‘cloud’ of soldiers forward, but men were equally able to hang back in the ‘cloud’ because there isn’t much sense of an assigned place.

But how to keep that up for a few hours?

The solution was the ‘battle pulse.’ Sabin imagines Roman battle as a “natural stand-off punctuated by period and localized charges into contact.”⁶ In this vision entire Roman maniples might functionally withdraw to javelin range for extended periods to catch their breath, exchange some missiles and recover. This is, in theory, a separate process from the Roman triple acies having the second (principes) and third (triarii) ranks move forward to take over the fight.⁷

So to be clear, what is being described here when we talk about ‘battle pulses’ is an action on the front line that consists of pulses and lulls, where in the lulls, the two lines withdraw out of measure (well out of measure, by implication) to momentarily rest and reconstitute, before the ‘pulse’ when one side rushes back into contact, precipitating another round of fighting.

This vision of battle then acquired key support with A. Zhmodikov, “Roman Republican Heavy Infantrymen in Battle (IV-II Centuries B.C.)” Historia 49.1 (2000). Prior to Zhmodikov, the general model for Roman infantry combat was ‘volley-and-charge:’ the hastati and principes advanced and hurled their pila at the outset of an engagement before closing in for a decisive action with swords. Zhmodikov instead pulls together all of the evidence for javelin use and argues that pila remained in use over the whole battle. This was in the moment pretty important because it solved a problem that Goldsworthy and Sabin faced which is that our ancient sources on battles almost never describe anything resembling the extended pause between pulses: we get pushes in the sources but not very often do we hear ‘lulls’ described (in stark contrast to their frequency in sources for gunpowder warfare, I might note). When a force is described as moving backward, it is generally because they are routing or being pushed, not because they are mutually disengaging. Zhmodikov’s article thus promised to provide an evidentiary basis that the Goldsworthy-Sabin ‘pulse’ model otherwise lacked, albeit quite indirectly so (‘these guys throw lots of javelins, so there must be pauses’ is not the same as ‘the sources tell us there are pauses.’)

But note that Goldsworthy and Sabin are seeking to explain Roman combat evidence and to do that they have resorted to general arguments about human endurance and psychology because they do not have much direct source evidence for the lulls in their pulse model (by contrast, I’d argue, the pulse itself – the ‘push’ – is attested). Consequently, this is a theory developed to explain Roman warfare, which was because of the lack of direct testimony in the sources is instead posited as a general rule of combat (since the only argument available is one from human endurance and psychological capability), from where it then gets applied to hoplites and dismounted knights and Landsknechte and so on. So we have to discuss it in this Roman context, but with a key warning: Greeks are not Romans and the Roman tactical and broader institutional military systems were not very much like Greek ones. Or, as Ardant du Picq quips:

The Gaul, a fool in war, used barbarian tactics. After the first surprise, he was always beaten by the Greeks and Romans.
The Greek, a warrior, but also a politician, had tactics far superior to those of the Gauls and the Asiatics.
The Roman, a politician above all, with whom war was only a means, wanted perfect means. He had no illusions. He took into account human weakness and he discovered the legion.
But this is merely affirming what should be demonstrated.

(It is not, in fact, clear to me that ‘The Greek’ had superior tactics to ‘the Asiatics’ by which Ardant du Picq means the Persians. The Macedonians certainly did, but that’s a separate question).

What Pulse

So given that scholarship, why aren’t my discussions of hoplite tactics or, indeed, Roman tactics, full of discussions of pulses?

Because I don’t think they were full of pulses, or more correctly, I don’t think they were full of what I am going to call macro-pulses, but they did include lots of what I am going to call micro-pulses, because I think it is important to distinguish between the two.

In a micro-pulse, what we’re really describing is ‘withdrawing to measure’ – the combatants separate not a huge amount, but just a few steps outside of the reach of their weapons (striking distance here is termed ‘measure’ so moving ‘into measure’ means moving into an opponent’s striking range (to strike yourself) and so too ‘out of measure.’) I don’t think two opposing lines locked shields against each other and stayed in measure for minutes or hours on end. That doesn’t seem physically or psychologically possible. It would produce the casualty problem Sabin identifies and psychologically, as Ardant du Picq points to, men are going to want to pull out of reach of their opponents weapons and that psychological force is going to become swiftly overpowering. Anyone who watches combat sports or HEMA sparring, as an aside, can see this tendency for fighters to pull out of measure but remain ‘in contact’ (close enough to move back into measure at any moment) for themselves.

So I have no problem with the ‘micro-pulse,’ and indeed, I think they must have been continually happening down the line, with men or groups of men stepping forward into measure to deliver one or two strikes (and likely take a few in return) before backing out. And of course that pattern might also serve to conserve the men’s stamina, because the periods of really intense physical action – the throwing of blows or blocks – might be interspersed with longer periods of watching and smaller probing strikes. I admit, it would be really interesting to see how long a set of reasonable fit reenactors could keep up this kind of pulsing fight, never withdrawing much more than a few steps beyond measure. The key would be running the experiment as near to exhaustion as possible, because we ought to expect battle to push men to the very limits of endurance as they struggle to survive.⁸

The broader question then is the macro-pulse, where we imagine the lines truly break contact to the point where they are far enough apart that men cannot dash forward back into measure quickly. Now Goldsworthy-Sabin-Zhmodikov don’t, to my reading, draw a distinction between these two sorts of pulses, so it is hard to tell which they mean, but when they talk about extended javelin exchanges late in battles or lulls long enough to switch out wounded or fatigued men I read that as a macro-pulse (or more correctly a ‘macro-lull‘). To the degree that these authors actually intend what I’ve defined above as a micro-pulse, then I don’t think I have any disagreement with them on this point. But instead what they seem to imagine is a battle that consists primarily of macro-lulls, punctuated by micro-pulses, where formations spend a lot of time at ‘javelin reach’ of each other (so separated by perhaps 10 or 20 yards instead of 10 or 20 feet).

Critically, such a large disengagement requires the whole formation to move. A micro-pulse can work by having the front ranks simply accordion into the back ranks, closing the ‘vertical’ distance between them, but a macro-pulse requires the rear ranks to really back up and critically for men to keep backing up after contact is broken and thus there is no immediate pressure from the enemy (because the macro-pulse also requires the enemy not to advance back to the edge of measure). Indeed, Sabin seems to imagine it is in the context of these macro-pulses that the Roman changing out of battle lines occurs, so we are really backing up quite a bit.

Fundamentally, the macro-pulse exists in tension then (via Zhmodikov) with a volley-and-charge model (which has no trouble incorporating the ‘micro-pulse’ – no one has ever suggested Roman soldiers did anything like a shoving-othismos). The macro-pulse model also generally asserts more flexible physical formation, approaching ‘clouds’ or ‘mobs’ of soldiers, rather than a single formation with assigned places and it isn’t hard to see how that makes sense if this formation is supposed to pulse forward and backwards; by contrast the older vision of volley-and-charge assumes a regular, somewhat rigid formation, not infinitely rigid as we’ll see, but there is at least the notion of a block of men who are intended for the most part to maintain relative position. In essence, this macro-pulse model assumes that these fellows are doing something closer to what we might call ‘dense skirmishing’ in ‘clouds’ rather than formations spending most of their time well out of measure for contact weapons. You can see how this works as a continuation of the hoplite-as-skirmisher ‘strong’ heterodox vision.

To put it bluntly, I think micro-pulses happen and are in evidence in the sources, however I think macro-pulses – situations where the two lines truly disengage for a period without either routing– seem very fairly rare and the source evidence for them as frequent occurrences is actually quite thin.

The Lull In the Pulse

And it seems like from some quarters when I express this view there is a degree of incredulity that I would ‘go against the scholarship’ on an issue that is treated as ‘solved.’ Which is odd to me because it seems clear that significant parts of the Goldsworthy-Sabin-Zhmodikov thesis have been softened or even overturned.

An effort to find Goldsworthy’s pulses-and-lulls in the sources was mounted by Sam Koon, Infantry Combat in Livy’s Battle Narratives (2010).⁹ Koon set out to find the lulls though it is striking that the clearest example of a lull is also obviously exceptional: the two-part battle at Zama (202), where the ‘lull’ is very openly and visibly created by the recall of the hastati behind the next line and the re-ordering of the formation, rather than by a pulse-and-lull model; we’ll come back to this. And there is certainly some openness to this model. I am stuck, for instance by two chapters in The Oxford Handbook of Warfare in the Classical World (2013), eds. B. Campbell and Lawrence Tritle: Michael Sage’s chapter (“The Rise of Rome”) which accepts the Goldsworthy-Sabin-Zhmodikov model and Brian Campbell’s chapter (“Arming Romans”) which implicitly rejects it, asserting a volley-and-charge purpose for the pilum. But problems with the macro-pulse model emerged.

For one, some of the spacing and interval problems that Sabin brushed off as unsolveable (and thus avoids having to account for even flexible-but-real intervals and formations) have been revisited by MT. Taylor, “Roman Infantry Tactics in the Mid-Republic: A Reassessment” Historia 63 (2014) and to a significant degree resolved: there is a regular formation, it has both close-order and modestly-open-order standard intervals and we can also gauge to a significant degree the intervals between maniples. The units of the army (and the army itself) were accordions, not clouds of soldiers and men could – and in the sources do – close up to receive missiles or space out to fight in close combat (typically, we’ll get to this, they do the one and then the other). Most notably, the intervals between maniples are almost certainly – at points explicitly (Sall. Jug. 49.6) – where the light infantry (like the velites, but also any slingers or archers) are, which in turn exposes a real weakness in Zhmodikov, which is a near-total failure to distinguish between heavy infantry throwing their pila and the light infantry velites throwing their lighter javelins (hasta velitaris). The heavy infantry have just two pila, but the velites carry many javelins, which as you might imagine has implications for extended missile exchanges and intended function.

But crucially, Taylor’s approach fatally undermines the notion of the maniple as a ‘cloud’ of soldiers: these men have assigned spaces and semi-standard spacing with clear intervals between them. Polybius – who we must stress describes standard spacing in this army which he was an eyewitness to (18.30.6-8) – is not making it up. Instead, Taylor’s formation is not a cloud but an ‘accordion’ – the men have assigned spaces in which they are free to move around. Each man thus has some flexibility of position, but not infinitely so. That accordion nature can accommodate ‘micro-pulses’ but for a macro-pulse you have the problem above: it requires the rear ranks to back up quite a bit.

That point about distinguishing who is throwing the javelins in turn becomes the cornerstone of J.F. Slavik, “Pilum and Telum: The Roman Infantryman’s Style of Combat in the Middle Republic” CJ 113 (2018) which argues that the velites use showers of their light javelins -to enable the changing out of hastati to principes or triarii. Zhmodikov fails to distinguish the activity of the velites and so as a result his battles of “long exchange of throwing weapons”¹⁰ functionally collapses into the action not of Roman heavy infantry, but of Rome’s dedicated light infantry skirmishers, operating in those intervals noted above. I don’t know that Slavik’s philological argument – that we can distinguish what is being thrown and thus who is throwing it by the words used – is airtight, but in the cases where we are told explicitly what kind of soldiers are doing what, his argument holds much better: heavy infantry seem to volley-and-charge, while the velites and other lights may be skirmishing on a more extended basis in the intervals and covering the line-changes.

That said, whereas the heterodox/orthodox line on hoplites has tended to be a hard division into two camps, thinking on the Roman army, has tended much more towards synthesis, in part because the individual questions (role of the pilum, the extent of skirmishing, the presence of ‘pulses,’ the rigidity of the formation) are not treated as forming a coherent orthodox/heterodox, but rather ‘sliding’ values capable of moving independently. You can see this in general treatments, e.g. K.H. Milne, Inside the Roman Legions (2024), which clearly asserts a volley-and-charge model of pilum usage (163) and a clear sense of a “static front line” implying a regular formation (159, 162) with assigned places (166) but frequent micro-pulses (164, 167), but no macro-pulses except for the changing out of lines (167), with most fighting done with swords, not pila and supporting missiles to cover these movements by velites, not heavy infantry (168). It’s a blended position. At some point it is hard to say if that is either a very softened version of volley-and-charge or a softened version of Goldsworthy-Sabin-Zhmodikov, because we’ve more or less met in the middle.

So What of Battle Pulses?

So I do not think the scholarship at present requires me to adopt the complete Goldsworthy-Sabin-Zhmodikov model. And, as it is clear, I don’t entirely adopt that model, though I don’t think everything about it is wrong either.

In particular, I do not think macro-pulses, as I’ve defined them, were common, as distinct from the ‘micro-pulse,’ which I think must have been continuously happening, where the lines remain loosely ‘in contact’ (within maybe a few yards of measure) or the ‘line change’ (from hastati to principes to triarii), probably covered not by pila but by velites throwing their hastae velitares.

Now I am not going to reproduce Koon’s book going in the other direction in a blog post – and in any case, one of the authors above is already working on a monograph on Roman tactics which I shall not spoil here – but I want to give a few data-points as to why I lean this way.

The first is the soldier’s oath Livy reports before Cannae (Livy 22.38.4), “that they would not go away nor drop back from their posts [ex ordine] neither for flight or fear, unless to pick up or fetch a weapon, or to strike an enemy or to save a citizen.”¹¹ The word ordo in that sentence (ex ordine) means a row, a line, a series, a rank, an arrangement of things, but it is not a unit and it is certainly not a ‘cloud.’ It is an assigned place that the soldier is bound to. The oath, which Livy represents as customary and regular, makes no sense unless these soldiers have an assigned place in their unit to which they can swear not to leave nor even to shrink back from (non…recessuros, “not to withdraw from, shrink back from, fall back from, give ground”).

Meanwhile, we have a lot of evidence, I’d argue, as to the volley-and-charge nature of pilum use. We get lines like, “When he [the Roman commander] was leading the men-formed-up from the camp, scarcely before they cleared the rampart, the Romans threw their pila. The Spaniards ducked down against the javelins thrown by the enemies, then rose themselves to throw [their own] which when the Romans, clustered together as they are accustomed, had received with shields densely packed, then, with foot against foot and swords drawn, the matter was begun” (Livy 28.2.5-6), which is just a very clear statement of a volley-and-charge action, the throwing of pila by the Romans in the perfect (coniecerunt, ‘perfect’ meaning ‘completed’) tense: it happened (once) and then stopped.¹² Further examples of volley-and-charge in Livy are not hard to come by.¹³ Heck, Tacitus has a Roman general lay out the sequence in an order to his men: “with pila having been thrown then with shields and swords continue the butchery and slaughter” (Tac. Ann. 14.37).¹⁴

Most striking are the incidents where the Romans don’t throw their pila at all. Livy, for instance, has one general, the dictator Aullus Cornelius Cossus, tell his men to drop their pila and then note that the enemy (the Volsci who will have fought in the same manner as the Romans), “when they shall have thrown their missiles in vain” will have to come to close quarters where he expects the Roman line will triumph (Livy 6.12.8-9). Conversely, Q. Pubilius Philo’s troops are so eager on the attack that they drop their pila to engage directly with swords (Livy 9.13.2, cf. also 7.16.5-6, this happens more than once). Likewise, Julius Caesar reports in one battle that, “Thus our men, the signal having been given sharply made an attack on the enemies and they charged the enemies so suddenly and rapidly that a space for throwing pila at the enemy was not given. So throwing away their pila, at close-quarters they fought with gladii” (Caes. BGall. 1.52.3-4). It happens in Sallust too (Sall. Cat. 61.2).

If these guys think they are regularly going to back off out of close-combat to throw javelins for a bit, why do they drop their javelins (pila) the moment they come to close quarters? Surely, if having a ‘macro-lull’ was normal, they would want to save these weapons – at least in the back ranks – to be available in that event. Instead, the expectation is clearly not that the unit will back off after it has engaged nor that men in the rear ranks are throwing pila over the heads of the men in front of them (the danger of which is noted in some ancient sources, e.g. Onasander 17).

Now for the man in the front the answer is pretty obvious that pila are quite heavy and you can’t sword-fight while carrying them and a shield and so they have to go if youa re coming to close contact. But note that these lines don’t say “and then the front rank dropped their pila” but rather clearly whole units do. Which really only makes sense if these fellows imagine that once they are going into contact, they are not going to break contact for more missile-throwing or just to sit outside of contact.

We might also consider what we know about Pydna. Now this relies a fair bit on Plutarch and Plutarch is often not the best source on battles, but on Pydna he is working from some known sources (Scipio Nasica Corculum’s writings and likely the account of Polybius) and his vignettes are instructive. By the time the general, Lucius Aemilius Paullus is on the field – this was, you will recall, an unplanned engagement – the armies are already to close combat (Plut. Aem. 18.4) and we’re given a really physical description that the sarisae of the Macedonians were fixed in the shields of the Romans (19.1) so we know he intends us to understand these units are very much in contact (though we’d say that while the Macedonians are in measure, the Romans are not). Certainly no one has backed out of contact.

Then we get two interesting passages which I think we might say are something like micro-pulses: a Paelignian chucks his unit’s standard into the enemy to compel them to make a push (20.1-5) and after taking heavy losses, they’re pushed back but evidently still to some degree in contact (perhaps pursued) because – as Michael Taylor notes in his reconstruction of the battle – they continue to hold up the Macedonian agema which would otherwise flank the legion. Meanwhile we also get Marcus Cato (son of Cato the Elder), who loses his sword and has to gather up his friends to push forward to retrieve it (21.1-5). In both cases these are units that we have to understand are in contact, not back at javelin reach, where an individual is rallying men to push forward in an effort to force the enemy back: Marcus Cato’s effort succeeds, whereas the Paelignians are thrown back (but buy essential time for the main Roman force). Both of these events have to involve units that are outside of measure, but which do not seem – note the above line about pikes touching Roman shields – to be fully out of contact.

The battle is won, as Livy (44.41.6-9) and Plutarch (20.7-10) both note, by having the Roman maniples engage separately, exploiting disruptions in the phalanx as it advanced. What I find striking here is that our sources – both relying on the (lost) Polybian account of the battle – evidently think that this ‘engage at discretion’ order needed to be given as an order (Plut. Aem. 20.7-9); dropping well back out of contact was evidently not a thing units normally were not supposed to do on their own. If engaging at discretion like this was the standard way of fighting, there would be no point in Plutarch having Aemilius order it, or Livy noting the unusual nature of many separate engagements.

We can contrast what we’re told about the Battle of Zama, which gives us a very clear macro-scale battle lull, albeit an unusual one (Polyb. 15.13-14). Both armies are drawn up (after Roman fashion) in multiple battle lines; the first lines of the two armies, the Carthaginian mercenaries and the Roman hastati engage in a fierce close-combat fight, but separation doesn’t occur as a result of a macro-battle-pulse, it occurs because the mercenary line collapses after the failure of the Carthaginian second line to move up to support it (Polyb. 15.13.3-4; the impression is psychological collapse, as Polybius is noting the cheering and encouragement of the so-far entirely unengaged Roman second line as decisive). The mercenaries collapse into the main Carthaginian line, which does not admit them, leading to a mercenary-on-Carthaginian engagement in which the fleeing mercenaries are slaughtered by their employers (Polyb. 13.5-6), which in turn now leaves the field of gore and wreckage between the Romans and their enemies (Polyb. 14.1-2). Scipio doesn’t want to advance over that so – and this is the thing – “recalling those still pursuing of the hastati by trumpet” [emphasis mine] Scipio reforms his ranks (Polyb. 14.4).

What is significant to me here is that the disengagement of the hastati is not voluntary or automatic or natural, but in fact requires a trumpet signal: Scipio has to order an army-wide ‘pause’ in order to reorganize his units (really, he is ordering the ‘change out’ of the hastati as a way to halt their pursuit), which he can do in part because the peculiar situation where Hannibal (himself seemingly mimicking Roman tactics he has by this point so much experience with) has not yet committed his main line of infantry. This thus isn’t an organic ‘macro-lull’ so much as it is both armies attempting to the classic Roman hastati to principes line change, with the Romans doing it more successfully because their fussy tactical system creates lanes, whereas Hannibal needs his mercenaries to run all the way around his second (unbroken) line to get off of the field.

I think this episode should also give us some meaningful pause when trying to apply Roman tactical thinking outside of Roman contexts. The Roman system of maintaining multiple complete lines of heavy infantry, one in contact initially and two out of contact is, if not unique, certainly unusual. Likewise, a formation with wide, relatively regular intervals to enable the front battle line to be ‘changed out’ in a regular fashion is again, if not unique, highly unusual. Efforts to mimic that flexibility without the same complex and unusual tactical system often went badly, as with Hannibal’s mercenaries at Zama or, famously, the French dispositions at Agincourt, where an advanced cavalry force disrupted the two main lines of infantry attack¹⁵ as they advanced and then those lines, with no way to interchange, stacked up on each other to their ruin.

But it is also indicative of how unusual a ‘macro-lull’ was: this one only happens because Scipio Africanus gives an order to recall his front line as the enemy’s front ranks were breaking. Once again, the reason the armies end up separated after a ‘pulse’ of violence is not because that was the normal way these armies fought but because one general had specifically and somewhat unusually ordered it.

The other example of a large-scale macro-lull is equally instructive: Appian BC 3.68. Appian is describing an engagement between two veteran Roman legions at the Forum Gallorum (43 BC). Reading the passage, I think it is obvious we should not take the engagement as anything like typical: they fight in silence, no battle cries but also cries or shouts even as men were wounded and killed. Each man who falls is instantly replaced, every blow was supposedly on target. And in this context of a literary description of inhuman mechanical precision in battle, we’re told “when they were overcome by fatigue they drew apart from each other for a brief space to take breath, as in gymnastic games, and then rushed again to the encounter.” Immediately after that, we’re told the other soldiers present were taken by amazement at the sight and sound of it. It is a description that is clearly heavily embroidered, about a battle where Appian is writing nearly two centuries after the fact, about an army that is supposed to seem superhuman in its actions through the motif of presenting the soldiers as treating the battle like gymnastic games. I do not think we can draw secure conclusions about actual battlefield practice from such a passage alone.

After this, I should note, we swiftly begin running out of examples of clear ‘macro-lulls’ in Roman battles. Plenty of units being ‘pushed’ (discussed below) or collapsing under pressure or armies being flanked experiencing crowd collapse under continuous pressure (e.g. Cannae), but almost no examples of units engaging and then backing off and then moving back to re-engage.

The Roman Face of Battle And Implications for Hoplites

Summing all of this up, what do I think a Roman maniple engaging in pitched battle combat against heavy infantry looks like, given the evidence?

The attack begins with the volley of pila and it sure seems like usually any pila not thrown at this point are discarded, given how often we hear of pila being dropped without being thrown.¹⁶ We’ve already discussed the weapon and its performance and so need not belabor the point here.

The hastati follow this with a charge to contact with swords. A few things could happen at this point. One side could collapse, leading to rout and slaughter, of course. Alternately, both sides might stand firm: the Romans are heavily armored and have big shields and many of their opponents have big shields (if generally lighter armor) too, so a lot of strikes are going to not connect, or merely graze targets. Our ancient sources assume quite a lot of non-lethal, non-disabling wounding happening in these battles and we ought to believe them, given shields, armor, and movement. If both sides stay firm then after a few blows we might expect them to ‘accordion’ out to measure as men refuse to stay inside of the ‘killing zone’ a few feet wide running along the line, a ‘micro-lull’ in which the units are still in contact, but much of their front lines are not in measure.

On either side, the soldiers now need to move up to advance into measure in order to strike, but in this model they can do so with just a step or two. Because this is a formation with a regular order, the men in the front cannot simply drop back for fear – recall, they have sworn not to do so – and the eyes of their buddies are upon them, which is one of those things that can get men to fight when they might otherwise not, though one imagines many of the blows are very tentative and a high proportion of the total time here is spent watching and waiting. Sabin is right about that: it basically must be given the relatively low casualties in these periods and the fact that they might stretch on for many minutes even to an hour or more in some cases.

The men in the front are being cheered on by their fellows behind them and at least in the case of the Romans also urged forward by their centurions and it is this context where you get the micro-pulses: individuals or more likely groups of men push forward into measure for a concerted ‘push’ on the enemy line. They’re not literally shoving, of course, but simply moving aggressively into measure to attack – in the case of the Romans they have to move well into measure because they have swords and not spears, so they are relying on their heavy armor and big shield to absorb a strike from the enemy before they can reply. On the other hand, once they get through that range, they are significantly more lethal, better able to strike over or under an enemy’s shield and pierce armor. It’s a ‘high risk, high lethality’ tactical package that the Roman soldier carries, balanced with his heavier-than-typical armor and shield.

Now the enemy can do two things: they can hold firm against this ‘push’ or – seeing friends fall and feeling the danger – they can push back out of measure on their side, backing up to get space. This isn’t a rout yet, cohesion is not broken, they’re just going to back up into the empty space between them and the next man behind them and that man will then back up too to preserve space as the formation accordions in from the front, then accordions out again on the back. This probably isn’t a huge movement – it doesn’t need to be. A quick shuffle of a yard or two is enough to clear well out of measure. At which point the Romans can press again or stop at measure to stabilize.

Now what often happened, what Hannibal is counting on at Cannae, is that this process is going to repeat over and over again, steadily pushing a line backwards without breaking it. The Roman, after all, has the shorter range weapon – he must, on some level, advance or he has to endure ‘potshots’ from longer spears forever. And he can advance, trusting his large shield and heavy armor to absorb a blow or two from his enemy while he pushes into his own, shorter but more lethal measure. So when the enemy backs up, the Romans quickly – perhaps immediately – push right back into measure. A few more foes fall, the enemy backs up again. After all, his enemy lacks that heavy armor and big shield to be so confident in very close quarters and so will want to move away from the Roman with his deadly sword, back to spear’s reach. So long as cohesion holds, each localized ‘push’ is perhaps only gaining a few meters and neither side is breaking contact, but the line is bending and moving. Roman maniples can adapt well to that shifting line; the sarisa-phalanx cannot (thus Pydna).

In this sort of back and forth, I think we need to assume that wounded men (or utterly exhausted ones) can drop back through the ranks, but there’s clearly some shame in so doing, at least for the Romans (remember that oath). But there’s plenty of space with a Roman file width of c. 135cm. Heck, even at a conjectured hoplite phalanx’s 90cm, a hurt man could squeeze back – or be pulled back – by his comrades so long as the formation is hovering at the edge of measure rather than right up on the enemy. Cycling the front rank seems to have never been systematized, however, so I suspect the expectation is that many men in the front ranks will remain there through the whole fight if they’re not wounded.¹⁷

Because the line’s movement forward and back is driven mostly by psychology, it is a visible indicator of the more confident side – the side with confidence is pushing into measure, their opponents backing out. For many armies using contact weapons, there’s not much a general can do at this stage even if they see that their line is getting the worst of it, but Roman armies are unusually complex and so the Roman general has an option here if things don’t seem to be going well: he can sound that trumpet to recall the hastati. What I suspect happens here is that the men at the front are going to – still facing the enemy with shields up – quickly shuffle backwards (getting out of measure and moving to exit contact) while the velites (present in the gaps of the formation) shower javelins to give their opponents pause and then everyone breaks for the rear, passing through the intervals of the next line. The enemy cannot charge after them or they’ll run pell-mell into the well-ordered maniples of the principes and be butchered. Surely this must have entailed the loss of some of the hastati, but not many, I’d imagine, with the velites covering (and the velites, very lightly equipped, can easily flee an enemy’s heavy battle line).

The centurions rally the hastati in the safety of the space behind the principes, who now advance and the cycle repeats.

So micro-pulses but not macro-pulses: the lines once in contact don’t break that ‘loose’ contact except to flee, but they do ‘push’ and while there is no general pause in fighting, individually soldiers are not always swinging or being swung at.

What might that mean for a Greek hoplite phalanx? Well quite a few of these elements must substantially drop away. While the Greeks certainly have light infantry, as we’ve discussed they do not have integrated light infantry, nor the retreat lanes or tactical flexibility to use them in the way the Romans do; Greeks are not Romans. Equally, while the phalanx has a bunch of organizational units, it does not have a lot of maneuver units: the whole formation is supposed to move together. So the ability to maintain cohesion moving in and out of contact is going to be significantly less. And there is no way to change out entire battle lines, both because the phalanx is not built to do so and also because there is no second battle line waiting to rotate in any case.

But the other elements, I think, largely remain. No volley of pila (at least, not after the Archaic, but we must assume that earlier Archaic throwing spear fills a similar role to a pilum, a pre-charge volley weapon), but the hoplites charge to contact (as noted last time, either to measure or to impact). But they don’t start shoving, instead accordioning back out and then, as above, the micro-pulses: localized ‘pushes’ in sections of the line. In some cases, you might get the ‘pushing’ effect we see the Romans achieve although it is notable to me that it seems like hoplite armies achieve this effect less (though certainly not never!) and I suspect this is because everyone is working with a spear’s reach and thus a spear’s measure, so no one side is compelled (as the Romans are) to advance impetuously through an opponent’s measure, nor is one side (as Macedonians might) able to relentlessly push an enemy back from beyond their measure. But I don’t think the lines frequently disengaged in the Classical period, because we’re not told that they do so in any source I can think of and because the phalanx would be even less capable of doing a ‘macro-lull‘ than a Roman legion and it seems like the Roman legions almost never did them either.

The consequence of this model – micro-pulses but no macro-lulls – is to a degree to restore the role of heavy infantry as ‘shock’ based contact troops. These men – and I think this is true of hoplites as well – fight in formation, with assigned positions (or something very close to it) that they are expected to maintain for as long as they are able. Once they advance into contact, they do not expect to break contact until one side has won or lost the fight in that part of the line. But they do not stay permanently in measure swinging potentially lethal blows for an hour straight. Instead we might imagine an open space, roughly the width of measure (so a couple of meters), with men lunging or advancing forward to strike and then backing out. Every so often a concerted group of men will push into measure collectively. And sometimes their aggression causes the enemy to back up, leading to the ‘pushing’ effect we’re told about – which happens with no shoving.

But what they are not doing is backing out to go back to skirmishing. The reason so many javelin-wielding line infantry (archaic hoplites, Roman heavy infantry, Iberian and Celtiberian infantry) carry just one or two javelins is that they expect to hurl these immediately before contact to intensify the force of their onset and then not do any more throwing. If these units break contact, it is because they are routing or – in the Roman case only – because they have been recalled to reform behind the next line of heavy infantry. But heavy contact infantry are not skirmishers and so we should not try to extrapolate their behavior entirely from watching the fighting of Dani skirmishers in Papua New Guinea. Our sources resound with assertions and descriptions that heavy infantry worked differently on the battlefield than light infantry and that the two types were not interchangeable.

Hopefully that all clarifies my views on ‘pulses’ and ‘lulls.’ Micro-pulses? Yes. Macro-lulls? Only very rarely, in unusual circumstances.

Now as I write this, I am getting ready to fly out to attend the 2025 Prancing Pony Podcast Moot to deliver a keynote on the historical grounding of Tolkien’s view of war. Next week is also the week of Christmas. So there will be no post next week (the 26th), so we’ll be wrapping up our look at hoplites in the New Year.

This design pattern is common with paywalled subscription content sites, like email newsletters, to cut down on password sharing. Let’s say someone pays $10/month for a subscription-based newsletter. If they can sign in using an email/password combination, they might be willing to share their email/password combination for that particularly site with a few friends or colleagues, to give them access to the same paywalled content without paying for their own subscriptions. Same goes for sharing email/password combinations for streaming services like Netflix. Well, you can’t share a password if there is no password to share. If the only way to log in to a subscription-based account is via a magic link that expires within minutes, it’s a lot harder for person A to share their account with person B (let alone with persons C, D, E, and F...). Person B has to tell person A that they’re signing in again, then person A has to wait for the email to arrive, and then person B needs to wait for person A to copy and paste the “magic” link, and hope it arrives before it expires. This pattern adds a significant convenience cost to account sharing — but it also makes signing in more annoying for honest users who aren’t sharing their account. ↩︎
Proponents of “magic links” argue that they’re beneficial for technically befuddled users who don’t use a password manager. That’s a good argument for offering “magic links” as an option, but it’s not a good argument for making them the exclusive way to sign in to a site or service. Good password managers are built into modern OSes and web browsers. Those of us who use them should not be punished with a significantly worse experience just because some users do not. When “magic links” are offered as an alternative to a saved password or passkey, there’s a path for all users. When “magic links” are the exclusive method for signing in, all users get the slowest experience.

(And yes, Passport, the subscription system behind Dithering and the rest of Ben Thompson’s Stratechery media empire, exclusively uses “magic links” for sign-in. I don’t like it, but, in Passports’s defense, once you’re signed in, Passport keeps you signed in for a very long time. Other CMSes tend to expire sign-ins far too quickly, which makes for a particularly frustrating experience with “magic links” because you need to keep using them every few weeks.) ↩︎︎

Bell Labs, as we’ve noted before, was for years America’s premier industrial research lab. Not only did Bell Labs invent much of the technology that powers the modern world — the transistor, the solar PV cell, the first communication satellite — but it made numerous scientific breakthroughs, accumulating more Nobel Prizes than any other industrial research lab.

I’m generally skeptical of efforts to create a “modern Bell Labs,” as I think much of what made Bell Labs work was historically contingent. But I nevertheless think there’s value in understanding what exactly made Bell Labs so good, and how we might apply those lessons to modern organizations.

One way of understanding what made Bell Labs tick is to look at its early history, before it became America’s premier industrial lab. To that end, let’s take a look at how Bell Labs won its first Nobel Prize.

The prize was awarded to physicist Clinton Davisson in 1937 for demonstrating the existence of electron diffraction — the fact that, in some circumstances, electrons act like waves rather than particles. This discovery was based on research done by Davisson that began in 1920, just a few years after Theodore Vail (the first general manager of AT&T) returned to the company and set it on a more technology-focused trajectory, and before Bell Labs as a formal organization even existed.

Clinton Davisson and Western Electric

Clinton Davisson was born in Illinois in 1881. While he displayed an aptitude for math and science from an early age, he had a somewhat fitful journey into physics. When Davisson graduated high school in 1902, he attended the University of Chicago, but after a year was forced to drop out due to lack of funds. One of his professors, Robert Millikan (who would later win the Nobel Prize for discovering the charge of the electron with his oil drop experiment), arranged for Davisson to work at Purdue University as an assistant instructor in physics. Davisson returned to University of Chicago later that year, only to leave again to work as a part-time instructor at Princeton. Davisson finally graduated from University of Chicago with his bachelors in 1908, and received his PhD from Princeton in 1911.

After graduating from Princeton, Davisson got a job as an instructor of physics at Carnegie Institute of Technology (today known as Carnegie Mellon). While at Carnegie, most of Davisson’s time was occupied by teaching; over the next six years he managed to perform a few experiments (one on X-rays reflected off of tungsten, another on the energy emitted by hydrogen spectral lines), but achieved no publishable results. Davisson’s only publications at Carnegie were one theoretical article (on Niels Bohr’s recently-invented model of the atom) and two short theoretical notes (on gravitation and electrical action, and a theoretical model of the electron). Including his work at Princeton, by 1917 Davisson had only published six papers.

In 1917, Davisson took a summer job at Western Electric, the manufacturing arm of AT&T, to assist with manufacturing vacuum tubes for the military during WWI. At the time, vacuum tubes used a filament coated in platinum oxide, but platinum was in short supply due to the war; Davisson worked to help develop a nickel oxide coated filament. Davisson, who was mostly interested in scientific investigations rather than development work, was apparently not particularly thrilled with this assignment — Mervin Kelly, former president of Bell Labs, noted in a biography of Davisson that “the needs of the situation forced upon him somewhat of an engineering role for which he had little appetite” — but he nevertheless did it well. The temporary assignment soon became permanent, and by 1918 Davisson was in charge of four different groups of engineers at Western Electric, managing all aspects of the new nickel oxide filament’s development.

Following the end of the war, Davisson planned to return to Carnegie, where he had been offered a promotion to assistant professor. However, Davisson’s boss, Harold Arnold (who would become Bell Labs’ first director of research) asked Davisson to stay at Western Electric. Davisson had little to no interest in management, or in engineering-type work, though he had performed those tasks when they were required of him — his overwhelming interest was in scientific investigations, to achieve “complete and exact knowledge of the physical phenomena under study.” Arnold seems to have enticed Davisson to stay by offering him the opportunity to pursue fundamental scientific research at Western Electric, a rare occurrence at industrial labs at the time, and for most of his time at AT&T, Davisson would have the luxury of following his own research interests, aided by a small team of physicists and lab assistants.

Davisson, nickel, and electrons

Davisson’s first post-war assignment was to bombard vacuum tube filaments with positive ions, to see how it affected electron emissions. This research assignment was the product of a patent dispute over the vacuum tube between Western Electric and General Electric. The dispute began in 1915 when Harold Arnold filed a patent on an improved vacuum tube, to provoke an interference with an existing General Electric vacuum tube patent which Western Electric believed was illegitimate. The dispute, which took 16 years to resolve (it was ultimately decided in Western Electric’s favor by the Supreme Court in 1931), hinged on extremely technical aspects of vacuum tube operation, and whether certain improvements were novel enough to be patented. Because of the highly technical basis of the various patent claims, Arnold felt it was valuable to gain a better physical understanding of how, specifically, vacuum tubes behaved. To assist on this assignment, Davisson was joined by Lester Germer, a young physicist.

An early vacuum tube. Electrical current flows between the filament (cathode) and the plate (anode) By changing the voltage at the grid between the two, the flow of current can be controlled. Via Wikipedia.

Ultimately, Davisson and Germer found that ion bombardment had virtually no impact on the electron emission behavior of tube filaments. After these ion bombardment experiments were concluded, Germer continued to work on studying the electron emission of filaments, while a new physicist, CH Kunsman (who had joined in June 1920) took over as Davisson’s primary collaborator. Davisson and Kunsman then began using their experimental apparatus to bombard vacuum tube grids and plates with electrons instead of positive ions. During these experiments, Davisson and Kunsman stumbled across an unexpected phenomenon: that some electrons bounced off their targets “elastically” (with roughly as much energy as they had collided with).

Davisson thought that these elastically scattered electrons might prove valuable as a research tool. Just a few years before, in 1911, a research team led by Ernest Rutherford had discovered that matter in an atom was concentrated in a tiny, dense “nucleus” at its center, by bombarding a thin gold foil with alpha particles (helium atoms shorn of their electrons) and observing how they were scattered. Davisson thought that a similar experiment, using elastically scattered electrons instead of alpha particles, might shed light on the electron structure of atoms. At the time it was generally agreed that the atomic nucleus was surrounded by electrons which inhabited discrete “shells” — specific orbits that electrons were allowed to occupy — but little was known about how those shells were arranged.

In 1921, Davisson and Kunsman began their experiments using elastically scattered electrons. By bombarding a piece of nickel with electrons, and recording the angles at which they bounced off, they hoped to learn about the structure of the electron shells surrounding the nickel atoms.

Arrangement of Davisson and Kunsman’s electron experiment. Via Gehrenbeck 1974.

Initially, this line of research appeared promising. Davisson and Kunsman were able to develop a formula that related the scattering angle to a hypothesized structure of the electron shells (though they only made a qualitative comparison between their formula and their experimental results), and they published a short paper on their work later that year. The duo then continued this line of study with other metals, examining the scattering behavior of copper, aluminum, platinum, and magnesium, and publishing papers on their results in 1922 and 1923. However, these investigations ultimately failed to pan out, teaching them little about the behavior of atomic electron shells.

These disappointing outcomes apparently dulled the team’s enthusiasm for the electron scattering studies; when Kunsman departed Western Electric in November of 1923, the scattering experiments ceased.

Experimental serendipity

A breakthrough in this line of research came a little over a year later, following the return of Lester Germer, who had been on a leave of absence from Western Electric since 1923 due to health concerns and a nervous breakdown. When Germer returned in July of 1924, he resumed work on the electron scattering experiments.

These experiments had to be performed in a high vacuum, which required occasionally pumping air out of the large tube which contained the experimental apparatus. In early 1925, following one such repumping, a bottle of liquid air broke, cracking a charcoal “trap” that was used to help maintain the vacuum within the tube and covering the target — a highly polished piece of nickel — in a layer of solid oxide. Instead of simply replacing the target, Davisson and Germer decided to repair it, putting it through several rounds of intense heating and then removing a thin layer of material from the top.

Initially, when the scattering experiments were resumed with the bombardment of the repaired piece of nickel, the results were similar to what had been obtained prior to the accident. However, a few weeks later, Davisson and Germer began to observe electron scattering behavior which was very different from what had been seen prior to the accident and subsequent repair.

Electron scattering behavior before and after the lab accident and target repair. Via Gehrenbeck 1974.

Upon close examination of the target piece of nickel, it was found that the repair had changed the character of its surface. Prior to the accident the nickel, like most pieces of metal, consisted of numerous tiny intersecting crystals — regular arrangements of atoms — which were fused together. But following the accident and repair, the number of crystal grains had been reduced by “several orders of magnitude”, resulting in just a few large crystal facets. Davisson had originally theorized that the atomic structure of the target — how the electron shells were arranged — would affect how electrons were scattered. But now it appeared that instead it was the crystal structure — how the individual atoms were arranged — which determined how electrons were scattered. Eventually, they found that the unexpected scattering results were due to the electrons bouncing off a single crystal of nickel.

Grain boundaries in a piece of metal. Individual crystals with different orientations are fused together. Via Wikipedia.

Pursuing this unexpected phenomena, Davisson and Germer eventually obtained a large single crystal of nickel (grown by a member of Bell Labs’ staff) to use as a target, and began to bombard it with electrons at different angles in 1926. However, the results appeared underwhelming. Davisson later noted that:

We were surprised and disappointed to find that it was indistinguishable from what would have been observed had the target been one of ordinary polycrystalline nickel— a simple curve with never a bump or spur from one end to the other. The Br and C-azimuths were explored with the same result.

New target bombarded with electrons at different angles. Via Gehrenbeck 1974.

A year of experimental effort had apparently led to nothing.

While these experiments were taking place, another notable event occurred. In 1925 the research activities of AT&T were reorganized and combined under a single roof: Bell Telephone Laboratories.

Wave particle duality

While Davisson, Kunsman and Germer were bouncing electrons off of various materials, a revolution was brewing in the field of physics. In 1905 Albert Einstein, to explain certain experimental results — namely, the way electrons were ejected from the surface of metal when exposed to light, known as the photoelectric effect — posited that light might impart energy via discrete packets, or “quanta”, of energy. Light, long thought to consist of waves, might in some cases behave like particles. This hypothesis was strengthened by experimental results from the American physicist Arthur Compton in 1922, who fired X-rays at various elements to see how they scattered. Compton found that the wavelengths of the X-rays increased when scattered by the target, which implied that the X-rays were transmitting their energy as a series of particle collisions.

Around the time Compton was performing his experiments demonstrating that light waves sometimes acted like particles, a French physicist, Louis de Broglie, was hypothesizing that, conversely, particles of matter might sometimes act like waves. De Broglie advanced this theory in his 1924 doctoral thesis, and suggested that it could be experimentally verified by studying the scattering behavior of electrons by crystals. If electrons — atomic particles that carried negative charge — acted like waves, the regular structure of the crystal would act somewhat like a series of closely-spaced mirrors, reflecting the electrons in such a way to produce a tell-tale interference pattern (a phenomenon known as Bragg diffraction).

Bragg diffraction of X-rays on a crystal. For particular wavelengths, the waves will be reflected off the rows of atoms such that the wave peaks will reinforce each other. Via Davisson 1927.

Most physicists did not think much of de Broglie’s theory, but some — including Einstein — found it compelling. One such supporter was German physicist Max Born, who discussed de Broglie’s ideas with his colleagues, including a young German graduate student named Walter Elsasser. Elsasser, who had seen Davisson and Kunsman’s 1923 paper on electron scattering, thought its results provided some evidence of de Broglie’s wave theory of matter, and published a short paper on this idea in 1925.

Elsasser then attempted to verify the theory with his own electron scattering experiments. But such experiments were difficult, as they required creating high-vacuum conditions that few labs were equipped for. After several months of attempts, Elsasser gave up (even though Einstein told him that he was “sitting on a gold mine.”) Several attempts by other physicists to show electron diffraction were either similarly abandoned due to technical difficulties, or produced inconclusive results.

Davisson, de Broglie and electron waves

In July of 1926, a few months after beginning the single crystal scattering experiments, Davisson went on vacation with his wife to England. While there, he attended a meeting of the British Association of the Advancement of Science, possibly so that he could classify the trip as “work related” and have it reimbursed by Bell Labs. At the meeting, Davisson saw a presentation by Max Born on the wave theory matter, which by now had been further developed by Erwin Schrödinger. Davisson at the time was unfamiliar with this theory, and was surprised to learn that his own previous electron scattering research was being used to support it. Davisson discussed his research with Born and others, and showed them unpublished data from his recent single crystal experiments that he had brought with him. Though the recent data didn’t appear to reveal much, the European physicists convinced Davisson that he nevertheless may be on the right track, and on his journey back to the US, Davisson began working his way through understanding Schrödinger’s papers.

When Davisson returned to the US, he and Germer first looked closely for the predicted electron diffraction pattern in their existing experimental data, but failed to find it. Undaunted, Davisson and Germer decided that a more “thorough search” was called for. They began by closely examining their experimental apparatus. Upon inspection, it was discovered that the crystal target had been rotated slightly, and that the opening in the Faraday box used to gather scattered electrons was shifted from where it was believed to be. When a correction was applied to previous experimental data to account for this, there appeared to be “extremely good” correspondence between the data and what the wave theory predicted.

Davisson and Germer then began a new series of single crystal electron scattering experiments, looking for beams of scattered electrons where the wave theory predicted they should be. On January 6th, 1927, they found what appeared to be confirmatory evidence, a telltale “peak” of electrons collected at a particular speed, which (per de Broglie’s wavelength formula) corresponded to a particular wavelength. This peak was not quite where the theory predicted it would be (the theory predicted one at 78 volts, while the peak was found, somewhat accidently, at 65 volts), but it was nevertheless evidence of a beam of diffracted electrons. Subsequent experiments found more peaks predicted by the theory.

Davisson and Germer published a paper with their results in Nature in April 1927. It included their electron scattering data, as well as scattering data collected when X-rays (which had known wavelengths and were known to diffract through crystals) were fired at the single crystal target. They found that if the wavelength of the electrons was calculated, and a (at the time unexplained) 0.7 adjustment factor was applied, the electron peaks corresponded with the peaks observed in the X-ray data. The paper concluded by noting that their results were “highly suggestive…of the ideas underlying the theory of wave mechanics”.

Intensity of reflected X-rays at various wavelengths (top), and intensity of reflected electrons at various speeds (bottom). Via Davisson 1927.

Davisson and Germer followed up this work with more experiments, looking for more predicted electron peaks and trying to explain peaks that were observed but not predicted by the theory, or that were predicted but not found. Many of these anomalous results were found to be caused by gas on the surface of the crystal or trapped within it. Others (such as the 0.7 adjustment factor) could be explained by the electrons refracting when they entered the crystal, altering the angle of their path through it. A follow-up paper, submitted to Physical Review in August, included even more predicted electron peaks, as well as explanations for several anomalous ones, though several other unexplained discrepancies between the theory and the data remained. Subsequent experiments by other physicists would later confirm Davisson and Germer’s results, that electrons were diffracted through crystals in accordance with the wave theory of matter.

Davisson and Germer followed up this work with experiments investigating whether electrons exhibited other wave-like behavior, including refraction, reflection and polarization, publishing 16 papers from 1928 to 1932, further strengthening the theory that electrons behaved as waves. Germer would continue studying electron diffraction into the 1940s, while Davisson shifted his efforts into “electron optics” — how differently shaped openings could act as lenses for electrons. In 1937, Clinton Davisson was awarded the Nobel Prize in physics for the 1927 experiments which demonstrated the wave nature of the electron. (He shared the prize with G.P. Thomson who had, independently, also demonstrated the wave nature of the electron by scattering electrons through thin films of metal.)

Conclusion

Overall, what strikes me about this scientific discovery is how messy everything is. At a high level, the discovery seems like what we might expect for the scientific process: there’s an unexplained observation (Davisson and Germer’s surprising scattering results on the repaired piece of nickel), followed by a hypothesis that could explain those observations (de Broglie’s independently developed wave theory of matter), followed by an experiment to demonstrate the new hypothesis (Davisson and Germer’s 1927 scattering experiments). But when you zoom in, the path looks incredibly circuitous, full of false starts, disappointing results, and discrepancies between theory and experiment. Davisson’s research is kicked off by the unexpected discovery of elastically scattered electrons, but the resulting line of research to explore the electron structure of atoms is disappointing; so disappointing, in fact, that it’s abandoned for nearly a year. When it’s resumed, another unexpected event — the lab accident that results in a highly modified nickel target — leads to a new line of research, investigating the influence of crystal structure on electron scattering behavior. But this line of research also initially doesn’t seem very promising, yielding disappointing results at first. It’s only a third unplanned event — Davisson learning about the wave theory of matter from European physicists, which his earlier scattering experiments (done for totally different reasons!) seem to provide weak evidence for — that puts Davisson and Germer on the correct track.

Armed with this new theory, Davisson and Germer were eventually able to use their experimental apparatus to demonstrate that the data fit the theory’s prediction (electrons diffracting through a crystal), but this process was also messy. The data collected didn’t straightforwardly correspond with the theory’s predictions. The initial peak of electrons was found at 65 volts, not the predicted 78 volts, and the same experiments yielded a much larger peak at 30 volts that had to be strategically ignored. There were numerous other discrepancies from the theory: various beams of electrons where they shouldn’t be, a 0.7 “correction” factory that needed to be applied. Resolving these discrepancies took time and effort.

What’s more, the experiments were incredibly difficult to perform. Davisson and Germer succeeded in demonstrating electron diffraction where others had failed because their lab, unlike many others, had facilities for producing very high vacuums. But creating these conditions was difficult: the apparatus frequently broke, and slight misalignments in various pieces of equipment could, and did, distort the data.

Other takeaways from this discovery:

The importance of technology, and particularly new observational tools, for scientific discovery. The discovery couldn’t have been made without the ability to create a high vacuum, and Davisson’s line of research was kicked off by the discovery of elastically scattered electrons, which Davisson suspected could be used as a research tool.
The importance of serendipity and the unexpected for making scientific discoveries. The unexpected discovery of elastically scattered electrons, the accidental modification of the nickel target, Davisson’s chance exposure to the wave theory of matter, and the accidental discovery of the 65 volt electron peak all played a role in Davisson’s demonstration of electron diffraction.
It can be hard to predict how a line of research will evolve. Davisson began by studying the behavior of vacuum tube filaments, which led him to elastically scattered electron experiments, which led him to studying the effect of crystal structure of electron scattering, which (eventually) led him to electron diffraction. Except for the initial vacuum tube filament studies, none of these research directions was planned, and were only possible because Davisson had somewhat free rein to research what he liked.
It’s understandable why this sort of research is rare in a corporate setting. Davisson’s discovery was the product of a years-long line of research, which probably wasn’t particularly cheap. (It doesn’t seem to have taken a huge amount of personnel, but the equipment was almost certainly expensive, as evidenced by the fact that few other labs possessed it.) It didn’t result in any new products or services for AT&T. It was probably ultimately valuable to AT&T for the prestige factor of the Nobel Prize, but the prize wasn’t awarded until 17 years after the research began (and of course, most research efforts won’t be awarded Nobel Prizes). For an organization which needs to earn a profit, it’s not hard to see why funding this sort of work seems like a bad bet.

What does Davisson’s discovery tell us about Bell Labs? Davisson’s line of research was initially pursued because it was believed that there was value in a deep, physical understanding in how vacuum tubes and electronic devices behaved. This was apparently believed strongly enough that Western Electric allowed Davisson to pursue these sorts of scientific investigations, without worrying about whether they would result in practical applications, something that was (and is) rare in corporate settings.

It’s interesting to contrast this discovery with the discovery of the transistor. In some ways the efforts are similar. Both were research programs rooted in a deep understanding of electronic components, and both yielded Nobel Prizes in physics. But while Davisson’s research was pursued without regard to any particular practical application (and didn’t result in any, at least for AT&T), the transistor effort was part of a specific program to create a solid state amplifier. Bell Labs’ later ‘basic’ research efforts were much larger than those in the 1920s, but they also seem to have put more effort into nudging their researchers into working on important problems of practical significance.