I'm a finance guy, not a historian, so my sources may need further sourcing. Here's a graph you may enjoy: 600 year graph. Note that this is a logarithmic graph, so the drop is actually way more significant.

Notably, silver seemed to be significantly more valuable in the 1400s 1500s than it is today. The 1770s' saw a slight decline, though I wouldn't necessarily attribute that to American independence, as it is part of a greater downward trend lasting more than 50 years. Likely due to new mines being discovered/opened and new mining techniques developed to more easily access the silver.

Also, it is interesting that ratio in value between gold and silver did not change much between the 1400's and 1800's, at about 15-20x value. I don't know why, but my speculation is that India's rise to wealth and their strong preference for gold jewelry has at least a little impact. I watched a documentary recently about this and i'll try and find the name.

The biggest shock to the silver market in recorded history was the failed Silver Market Corner by Nelson Bunker Hunt wiki, which is an important lesson taught in business school (one of my favorites). Basically in the late 70's, these rich guys decided that they'd "buy up all the silver" in order to increase the price. Once the price was high, they'd essentially own all the silver at this new high price and be hugely rich. This ultimately is unsustainable for several reasons: the amount of silver in the market is not fixed (more can be dug up, people will melt down their cutlery) which will reduce the price and the mere fact of trying to sell this new fortune will cause the price to fall back down, resulting in a net of 0 (or less than zero as other people have during this high time increased the supply). In the end these two brothers went bankrupt while new laws were enacted to prevent such market disruptions in the future.

Another cool graph: 100 year gold & silver - can you see where they tried to corner the market? :)