1. This is again an example of "want" vs "can". If you look at the actual numbers needed to take the last Peten holdouts, we are talking about under 2,000 soldiers. The problem was much that these were cities deep in the tropical jungle with no gold. The Spaniards were actually in the middle of taking out much of the place when Pizarro made the news with fabulous amounts of wealth being captured further south. Shockingly both the soldiers on the ground and the administration in Spain were more concerned with getting silver from the Andes than marginal (to Spanish eyes) agricultural land in central America. Even if we treble every Spanish number from the final battles, Spain at any time could have taken just about any of the holdouts. Like with China, this is conquest that is far more expensive (in the short term) than it is worth (in the short term). Hence why it was generally not even a tertiary front.
2. The American Revolution lacks any real impetus to switch from the American to the British side. No matter how much the Americans and the British ground each other down, no one seriously expected there to be death and killing on the home front. Put another way, the only military powers like to go home to kill the woman and children were already allied to the British. In contrast, when the Manchu invaded China if you keep fighting as a Ming general you run the very real risk of another horde, Japan or someone from southeast Asia coming in and taking your power and killing your family. Likewise, in the American Revolution collective punishment was a net plus for the Americans; Britain couldn't control the hinterland so mass reprisals mean that the rebels have a rally point for counter reprisals - against your loyalists. It is also fairly hard to claim to be the civilized Christian nation if you are killing civilized Christians. A further difference would be that the British were unable to sustain the victories like those seen in India (or later in China) that comes from having a decided artillery advantage. British victories were tactically significant, but they lacked any form of shock and awe - there is no sense of inevitability (particularly as the British supplied a regular dose of American victories). Another major problem is that the colonies had one of the highest agricultural surpluses in the known world per capita, this makes them wealthy, mostly freeholders, and well armed; when Chinese irregulars attack during the Opium war they are armed with spears that the Song said were obsolete - when American irregulars attack they might well be better armed than the British (given the high number of rifles used in the war). Lastly, the colonies had no possibility of a decapitation strike. Unlike in China, there was no centralized state. Taking Philadelphia, for instance, doesn't deprive the Americans of a bunch of mandarins necessary for tax collection, conscription, and judiciary services. Taking the capital of China would mean that a lot of empire wide management simply ceases to happen and with a bunch of peasants and serfs you end up with some very powerful symbolic gains.
On a more direct note, up until the French entered the War, the British were doing pretty well (albeit expensively) and might well have worn the Americans down to a negotiated peace. However, like in the case of China, France represents a real threat (so Britain cannot tie down the entire navy for naval support) before entry and a mass diversion of resources after the war. Ultimately, the war falters for the same reason China wasn't invaded - the intervention of competing European powers pretty much assures that it ends up being a losing cost:benefit outcome.
3. This is after the Napoleonic revolution and where army sizes drastically outstripped the ability of the land to feed them. If you look at the land actually held by the British, you find that there isn't a hope in hell of supplying the men off the ground. Likewise, rates of fire had crept up high (particularly with the Enfields) and bullets stopped being simple cast lead jobs. All of things that don't apply to EU era logistics start coming to the fore here. The total manpower deployed in Crimea is vastly beyond what could be fed if you ate everything edible off the lead. The weight of powder and manufacturer shot starts being a big logistical burden, and warfare changes. These changes will become even more obvious in the American Civil War, but the days of armies living off the land, buying/capturing bulk supplies from the enemy are pretty gone everywhere east of Persia.
As with the American revolution, you don't have an advantage of repetitive victories and you certainly don't have any other external threats facing the Russian commanders.
4. Sorry, but a war with machine guns and rail logistics is completely noncomparable. When I talk about logistics in the EU era I am talking about an era when a large body of well armed men can survive by pillaging the countryside for food, recasting lead for their ammunition, and using relatively small amounts of powder during brief quick engagements. By the Boer war, the logistical burden per soldier isn't remotely like that for the 17th century (indeed the logistical burden for a 17th century soldier is closer to that of a
Roman soldier than a khaki limey in the veldt).
1. That no major power could project and supply more than a few thousand troops (under 10k) to the far east until the Victorian era. As the mightiest naval power in 1775 could only land 60k men of a around 250-300k one month from home. The amount moved 6-10 months away to China would be even less.
As I have always maintained, this stems in large part because Britain would have to commit a lot of resources to move more. For a hypothetical Chinese invasion Britain would spend a huge portion of its budget for a decade building sealift (hence why I dropped all capital costs from my calculations) and that means it forgoes a lot of opportunities. When 1776 came around Britain hadn't even paid off the Seven Years War debt and that meant they were operating with far fewer hulls than would be the case if they could safely ignore the French. I have consistently said that any Chinese invasion would require nigh unto complete isolation from European power struggles - time to build the hulls, manpower to send the army away, and not having the
possibility of French moves looming over your head.
None of these limitations had anything to do with logistics. The British garrisoned New York with huge numbers and only when marching into the interior did those 60K. The fact is, what do you burn more of to go from New York to China? Sure you have more hull-time, more food, more pay ... but none of those are insurmountable - just cost ineffective. The only times I aware of a British expedition hitting logistical snags where either deep inland or when the French closed the Chesapeake.
2. The total conquest would probably take a long time and require a massive troop commitment. During the American revolution the ratio of combatant to hostile populace was about 1 to 20, while the Boer War saw ratios far under 1 to 10, not to mention other personnel. I believe any number over 1 to 100 is unfeasible. That would result in over about 150k men, around the amount of land troops that France and England struggled to supply in 1850, a mere three weeks from home.
Sorry, but no. During the second Battle of Canton we saw what the Chinese peasantry could bring to war - agricultural implements, fire hardened spears, and decrepit edged weapons. In Lexington we saw what American freeholders could bring to war - rifles and muskets. The force multiplier between the two was historically on the order of 50 or so. If we go to the Boer war, this get even crazier, the Boers did import a lot of explosives and machine guns. Given the chattal nature of Boer society, of course the populace was well armed and well versed in weapons use.
Both of these also occurred in situations where it was not possible to put down rebellions with wholesale slaughter. While many Boers died in confinement, the days of being able to torch their homes, their fields, and then leave them to simply die were gone. The very fact that you had camps instead of genocide shows that the constraints on occupying troops in this era were much stricter and inhibited rebellion suppression. In both the American Revolution and the Boer War you had committed peace parties that could and did use any "atrocity" to gain power in the commons. None of that is going to matter a whit in China a century earlier.
As far as Russia, sorry, but that wasn't even a war of conquest. Britain wanted to take Sevastpol to force Russia to make peace with the OE. One of the British war goals was
not to splinter the Russian state.
3. Winning nearly every battle and taking every major city does not always win a war. The American revolution held out despite a long string of defeats a naval blockade and most major cities lost. A committed china faced with the end of its civilization could manage similar feats. To ensure total victory you need to be able to commit substantial amounts troops as the British did in the Second Boer war and totally control the population.
Oh please. China would never have been facing "the end of its civilization". The Europeans invade, they either make a puppet emperor, or they depose the emperor. They find local power brokers who will collect the taxes and enforce the law (with European oversight) and the vast, vast majority of the population will live life pretty much exactly like before. I mean really, do you expect China to react that differently to a European invasion than to the Taiping rebellion? We saw the old Confucian texts banned. We saw the marriage laws changed. We saw mass eviction of landlords and a complete change in the mandarin class. Yet the place didn't devolve into an apocalyptic do or die scenario - it was a fairly normal peasant rebellion.
The real reason the US was virtually unique in being able to lose so many cities is that the vast, vast majority of its wealth wasn't located in the cities. If you look at per capita animal stock, the US had insane amounts - most of it inland. Of all countries on the earth at the time, the United States had the least wealth and power concentrated in the cities. In contrast, the exact opposite is true in China. In the hinterland there is very, very little wealth (outside the land itself). Taking the cities really does hammer the state apparatus (which was almost nonexistant in a lot of the colonies) and really does give the invader the block of the wealth and power. Peasant economies tend to be like that.
I would also like to put forward Kenneth E. Bouldings, Loss of Strength Gradient. He argued that the amount of a nation’s military power that could be brought to bear in any part of the world depended on geographic distance. The Loss of Strength Gradient demonstrated graphically that the farther away the target of aggression, the less strength could be made available.
Distance is more properly measured in time. In the modern (excluding ICBMs and transcontinental aircraft) and ancient eras, geographic distance and time to target were well related quantities. This changes right at the beginning of the EU era (though arguably earlier). Prior to the EU era, shipping large bodies of manpower isn't viable (with the Ming being an exception due to the treasure fleet) so most long distance campaigns (e.g. the Crusades) meant that you marched to the target and distance/time were pretty much equivalent. However, armies that were faster (e.g. the Mongols) suffered far less diminuation with distance. In the EU era, you finally see the development of mass bulk shipping which can move large armies great distances. This results in Oceanic distances being compressed (you might be able to cover 200 miles in a day on ship compared to 10 on land) when you measure by time. As noted by the previously quoted shipping rates, distances are also vastly cheaper to transverse thanks to better seafaring technology. The modern era loses this relative compression. While you can still move bulk manpower quickly on the ocean, now it becomes a non-trivial task to move food, ammunition, supplies (e.g. fuel), and equipment (e.g. artillery) in sufficient quantity. In the EU era, your tonnage was defined by the number of troops you carried, the mass of their weapons, and the food they'd consume until you reached the target - everything after that was had from forage, purchase, and capture. Post EU era your tonnage had all that, plus the weight of food at the target (varies by time on target), ammunition replacement (varies by engagement size, frequency, and length), fuel (is royal pain in the arse as you get rocketry equations), and everything spirals out quicker than tonnage can increase (which is saying something given that this is the steam revolution). On land you have a
huge compression. Not only do you have the widespread adoption of canals but you start getting rail. Rail means you move scads of manpower long distance faster than you can march them by far. Rail means you move from the energy density of horses and oats to coal (well over a factor of 100 more efficient). In a nutshell, the modern era means that distance at sea stops being a zero order problem and becomes a first/second order one while land stops being a second order problem and becomes a first order one.
Yeah going to China is harder than going to India regardless of the era ... but EU is pretty much the golden age of sea power (at least until the airplane and the ballistic missile). Going huge distances "just" requires a huge upfront investment in hulls (one few nations were willing to risk) and once you get to the target your soldiers don't need long logistical tails. Both before and after the EU era, technology changes that.