Because there are so many varieties of Sharps bullets, I'll give you your specimen's specific ID.
At almost "an inch long" (as you say) ...if it is .95-to-.98" long, it is a Long-model "Commercial" Sharps bullet, made for the .52-caliber Sharps Rifle/Carbine. It is called the "commercial" Sharps bullet because it was put on the market for civilian use, rather than for the army. (That is why we civil war relic-hunters dig significantly fewer of this type than the types sold to the US Army in vast quatities. The "commercial" version is distinguished by not having a raised ring around its base.
There is also a Short-model (.89-to-.90") Sharps Commercial .52 bullet ...as shown in the photo posted by Timekiller. To determine for certain which one you found, check its length with some digital calipers. (Every bullet-digger & collector should own such calipers -- which now sell for less than $20. If you don't, please check Ebay or your local Harbor Freight Tools store or Home Depot. Heck, WalMart might even have them nowadays.