How did armour change with the advent of the firearm?

Thanks to u/Bacarruda for linking the threads I was going to link! In addition to those two there is also this one. Those threads deal with the adaptations made to armour to make it bullet-resistant and the changing form of armour between 1500 and 1700, I'd like to talk about both the big picture and the small picture to address your question more specifically.

Let's start 'big' - the general development of armour after the introduction of firearms. Generally speaking, armour was not discarded quickly after firearms were developed. Indeed there is a hundred years between the first major battlefield use of handheld firearms in the Hussite Wars in the 1420's to the Battles of Biocca and Pavia in the 1520's (the early modern battles often cited as watershed victories of early modern firearms and firearm tactics). In that time armour did not diminish, but flourished, with full armour reaching new heights of quality, sophistication and beauty and mass-produced partial armours become more common than ever. For this hundred years, fully armoured men at arms (knights and those who fought like them) continued to be an important part of European battles, winning battles as late as Ravenna in 1512. And after Pavia, armour continues to be used, but it is after this point that we see full armours begin to decline (as can be measured by the decline of the armour industry in many cities starting in the 1530's and accelerating after the 1550s). But even so armour continued to be worn by large numbers of soldiers for over a hundred more years. One way of thinking of this is that the full armours of the men at arms declined in use and decreased their coverage, while the partial armours of light cavalry and infantry continued into the 17th century. By 1700, though, the most heavily armoured men are armed like the 'lightly armoured' men of 100 years before, in a helmet and cuirass, and these armours were worn only by specialists for specialized purposes. However, this form of armour continues for heavy cavalry and sieges through the 18th and 19th centuries, and is only discarded completely during WWI, when modern ballistic armour begins to be developed.

The upshot of this is that the adaptation of armour after the introduction of firearms was a very gradual process. Moreover, as I say in the linked threads, it wasn’t simply a matter of a new gadget, guns, being invented and then being made better (though that is a big part of the story), but also of changing battlefield tactics that allowed guns to be used more effectively and in larger numbers and changing ways of raising armies and producing armour and armaments. This is generally the case with technology - it is not a series of discrete ‘inventions’ that change the world, but complicated developments in the way we make and use these objects, and how they interact with other technology, that produces change. The history of technology isn’t a one-way street with technology influencing society, but a two-way street where society and culture (including battle tactics and the organization of armies in this case) affect how technology develops and is used while at the same time being affected by technology.

Looking more specifically at your question, the relationship between weapons and armour has long been a subject of study. Samuel Rush Meyrick, the Regency antiquarian that basically founded the study of armour as a thing in itself, wrote in the preface of his work ‘Ancient Armour’ nearly 200 years ago that Armour is shaped by arms - “Defensive arms clearly follow the character of the instruments of assault: hence our work and its plates, are, perhaps, fully as much occupied with the one as with the other." His turn of the century successor, Charles Ffoulkes, compared the development of armour to the arms race between naval guns and naval armour before and during the Dreadnought Era, when bigger guns were met by thicker armour and thicker armour was in turn met with bigger guns. This ‘arms race’ model is appealingly simple and deterministic, and has been very influential to the way we think about armour. We see a version of it in video games and pen and paper RPGs where better armour in the ‘late game’ or ‘higher levels’ is matched by better weapons. At this point it is conventional wisdom or even a kind of subconscious assumption as we study armour, something that we don’t even think to examine in terms of evidence.

But is it true? There is some truth to it, certainly. Especially in the early modern era you mention in your title, there is a direct relationship between thickening armour and improving firearms, until full armours become too heavy to wear and armour is discarded. We also see breastplates that have a strong ‘keel’ in the center, offering glancing surfaces to deflect bullets coming from the front. But in general the story of armour’s development is much more complicated. Armour is not just shaped by the ‘demand side’ of responding to new threats and offering better protection for its ‘end users’ (the people who wear it. It is also shaped by the ‘supply side’ - the technology of producing armour itself and its raw materials. Alan Williams has demonstrated the relationship between the size of blooms (that is, raw chunks of wrought iron or steel from smelting iron ore in a bloomery) and the introduction of plate armour. Basically, bigger plates of steel require larger blooms, and larger blooms become available in the 13th-15th centuries, when plate armour develops.

More than that, too often the story of how weapons spur the development of armour has priviledged those weapons that we think of as the instruments of progress over those we consider outmoded. For instance, you ask about the introduction of the longbow, but we might also ask about how armour developed to defend against the lance - a far more powerful weapon with much greater armour penetrating power. And it’s not like knights and their weapons were static - with the introduction of plate armour, fully armoured men at arms (knights and those who fought like them) began to bolt/staple a lance arrest (called a rest in English) to their breastplate to brace their lance against, improving the transfer of energy 3 fold or more according to Tobias Capwell’s tests. And indeed, if we enumerate the characteristics of say, a 15th century Italian armour that seem designed to defend against particular kinds of blows, we see a lot more defenses against lance strikes than against arrows, including: Stop ribs at the shoulder and the thigh to prevent blows skidding into the neck or groin Reinforcing pieces on the front in places where lances are likely to strike Prow-shaped wrappers over the visor to better deflect blows coming dead-on There are other adaptations, like a strongly crested or conical helmet shape, that seem adapted against blows falling from above in general. Now this isn’t to say that arrows weren’t a major concern! Around the turn of the 15th century we see the protection of the throat move from mail aventails (often with additional mail beneath in many places) to plate defenses of various kinds. Perhaps arrows had something to do with this. Perhaps lances did. And perhaps armourers were simply getting better and overcoming weaknesses that had always existed in their designs, refining their product to provide better protection to their customers.

Even this is only part of the story. In addition to what we are protecting against, we must consider what people in armour were -doing- because that also dictates the range of motion they will need, the amount of endurance they will need to have and thus the form and extant of their armour. These factors together with the weapons used against armour demand that we look at the whole ‘way of war’ in which the armour was used, as Tobias Capwell does in his studies of 15th century English armour. And this doesn’t factor in the supply side that I mentioned before or the vagaries of fashion!

So as always, it’s complicated. Weapons absolutely affected the form of armour. So did the type of fighting people did in armour, and the technology of creating raw materials, and the economics of equipping soldiers and the technical abilities of armourers and the dictates of fashion and social display.

I do realize I go on; I do so because I love this stuff, and I love to show the depth of it. I really believe that to understand medieval armour we must understand medieval society, technology, art and economics. But this isn’t so unique. Everything we make is a product of a thousand different factors that influence it and a reflection of all sorts of aspects of the world we live in. We can look at the device that I am using to type this and the device on which you are reading it in much the same way, and that’s one of the things that makes this so interesting. It’s all around us. Stuff is never just stuff.

TL/DR material culture is complicated and awesome

In addition to the very excellent answers to this that have been offered, I will look to directly address your question regarding the historical relationship between weapons and armor, at least during the medieval period in Europe.

This really starts with the armor that, IMO is the most underrated and had the longest service life throughout the medieval period.

Maille. Commonly known as chainmail because D&D and movies are a thing, maille armor is one of the more effective tools available to armor soldiers for over a thousand years.

Most of the evolution of armor during the medieval period is about making maille better and making it cover more of your body and putting padding under it to make it more effective still

A good chunk of the development of weaponry throughout this period is about penetrating or bypassing maille.

Axes, spears, lighter blunt weapons, and certain types of arrowhead, in addition to some sword designs, were all about finding ways to bypass or penetrate maille.

And then, advances in metallurgy begin to make it possible, starting in the early 14th century to add bits of metal plating to the maille.

And this continued until by the 15th century you could get, if you were rich enough, complete suits of plate that had maille in the gaps that would stop anything that was designed to penetrate only maille.

So, new and better weapons had to be developed. And were.

Polearms concentrated enough force to penetrate and damage people through plate, bodkin points on arrows could do damage if they found a gap.

Sword points were tapered to find gaps in plate. And maces and war hammers delivered blunt force trauma.

But, metallurgy continued to develop. And by the 16th century armor was so extensive that arrows would essentially bounce off and other weapons were, against the top level armor, not very much use either.

And this may have continued but for 2 major developments that were taking place.

The development and widespread use of hand-held gunpowder based weapons. Especially in the early days, these weapons functioned a lot like super powered crossbows. They COULD penetrate a lot of armor a quarrel wouldn't, and mass fire from them was terrifying.
The re-introduction of mass formation infantry, made up of commoners after the devastation of the black plague, as a counter to the earlier feudal era heavy cavalry dominated warfare.

When these 2 developments combined, you got mass fire infantry formations that began to spell the end of the heavy cavalry charge as THE defining military action, and began to see the rise of what becomes the rifleman.

The reason for this is simple. I can outfit 50-100 men with early firearms for the cost of 4-5 armored knights on horseback. Those knights were good to have. And cavalry continued to be a major part of warfare for centuries after, but as firearms became more powerful, armor was seen as less and less worth it.

Until by the development of the self-contained cartridge in the 19th century, firearms were too powerful to be stopped by any armor a person would typically want to wear on a battlefield due to weight constraints.