Why were crossbows not used in the 19th century?

A great question and there is your reason.  Gunpowder may well have been weak, but a slug or even a charge of nails would do great damage in close quarters and obviously they were able to hang onto this against its recoil.

The cross bow is operating at medium range and this would be closer targeting armor.  It would also be excellent in support of pike-men against heavy cavalry.

Except with the English, the long bow was not often deployed, and its advantage was in range.  It could imposes rapid plunging fire on a charging body of men.  I actually do not think that the long bow was ever fully exploited.  In combination with a pair of horses, the second carrying a bundle of arrows, you have the capacity to close on a group and hurt them at a substantial distance that would be comparable to Mongol ability who used a smaller but stronger bow....
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Why were crossbows not used in the 19th century, even though they could be reloaded way faster than the infantry guns of that period?

Cesar Contreras

https://www.quora.com/ 

A lot of good answers here, so let me tell you a history lesson on the first army that came to this conclusion: the Spanish Tercios. 

It was the XVI century and the Great Captain, Gonzalo Fernández de Córdoba, was tasked by Fernando and Isabel, the Catholic Kings of the newly formed Kingdom of Spain, with the mission to go to Italy and defeat the superior French forces seeking to conquer Naples and the rest of the Peninsula. This was no easy task, for the French had numbers on their side and their fearsome heavy cavalry, the best of Europe and queen of the battlefields. So how to beat them? 

In his first try, as a matter of fact, the French sent Swiss pikemen and heavy cavalry and the Captain was defeated as he had nothing but light troops, though the war was won thanks to his great audacity and guerrilla tactics. 

Back at home, and hurt in his pride more than anything, the Captain devised a new organization for his army with the infantry on center stage and the other corps assisting them. He placed a large number of pikemen front and center (4 squares to be precise), very akin to the Swiss, but he then backed them up with sword and buckler men and crossbowmen. He too was one of the first commanders to believe in the use of firearms and so kept an artillery division that not only had cannons, but also lighter hand cannons. And onward he went when the second Italian war broke out, to face the mighty French and their fearsome cavalry. 

Some astounding victories later, the Great Captain realized the damage the hand cannons were capable of delivering, specially against the heavily armored opponents he was facing, and so he quickly began to add more and more arquebuses and muskets to his lines. First to go were the crossbows, who had not proven good enough to deter the enemy pikemen and heavy cavalry forces (yes, the rate of fire may be good, but when firing upon massed ranks of armored pikemen or cavalry, they were poor deterrents), and next the sword and buckler men were too replaced by the heavier mosquets because the Spanish realized they could deliver real damage to the enemy lines without exposing themselves from their pike lines, which were their shield against the heavy cavalry. The Spanish then would proceed to break the Swiss at Bicocca with hardly any losses, crush the French cavalry and capture their King at Pavia and move on to victory in a hundred battlefields across more than a hundred years.