Using your 1817 Large Cent as an example as to why there is such a difference in what you see in book prices and auction prices. First off, auction prices and e-bay can be anywhere, just the nature of the beast. But the a big reason why some coins in the same year, like your 1817 go for vastly different prices is not only because of condition, but because there is a demand for the rarer varieties of that year. Supply and Demand is in the coin industry just like anything else.
The 1817 Large Cent has 17 different varieties, most are relatively common, but there is one variety that is rare. Since there are a fair amount of Large Cent (variety) collectors in the world, the demand for that rare one would be there, and the bidding would go high, thus the exorbitant amount for a coin like that and any others that are very scarce or rare on the market.
Heritage will not give a appraisal (value) without charging you to do so. If you can get a clear photo of the coin, both front and back, and in a nice cropped big all coin photo, I can attribute the variety for you and most likely give very rough ballpark figure. Most ground found coppers do not demand what is even listed in Red book due to corrosion that is on the coin, whether you think so or not, but IF the coin is rare, they seem to be less strict on how they consider the coin for sale.
If you join or have joined Heritage's website, once a year they offer a free appraisal of a coin. I had one done this past year by them, but in my opinion, they low balled the coin, since I had it appraised by two other appraisers (professionals who are friends)before them.......... Thanks for the advice and ill get right back with some better pictures i hope
Don