Good luck. The cylinders and split springs on these guns are the two parts that inevitably fail (or in the case of the cylinder, just get lost), and S&W stopped making replacements for them eons ago. Your best bet will be eBay or GunBroker, but I see cylinders very infrequently and when I do they usually go for a tidy sum.
If you find a cylinder, it'll almost certainly need to be fitted to the gun by a gunsmith to get the timing correct.
As an aside ... the Model 1's had assembly marks (usually two or three letters/numbers) stamped on the face of the barrel, the face of the cylinder, and the inside of the frame where the grip panel would cover. Those assembly marks are generally how one can identify that a Model 1 has its factory-correct components and not a hodgepodge of parts taken from different guns. I say that only to warn you that a replacement cylinder likely isn't going to have a matching assembly mark ... so be careful how much you invest in the gun.
Mike
