I have an old break-top H&R handgun that appears to be .32 cal. The cylinder is approximately 1.00" long which is much longer than an average .32 case. Does this indicate a .32 S&W Long cartirdge and if so, can I shoot regular .32's out of it?

If it is indeed chambered for .32 S&W long, it is safe to shoot the shorter standard .32 S&W cartridges through it...

It's not a .32 s&w long unless it says so on the barrel. Cylinder length has nothing to do with it, what matters is the depth of the chamber.

The gun is a nickle plated gun. It has Harington & Richardson and the patent on the barrel, no serial numbers no caliber info. I know it's a .32 by the diameter between the barrel lands but I don't know "which" .32. The cylinder chambers are smooth straight through so there's no depth there to check.

The gun is a nickle plated gun with Harrington and Richardson and the Patent date on the barrel. There is no serial number of caliber number anywhere on the gun. I know it's a .32 by the diameter of the barrel lands. The cylinder is smooth straight through so there's no depth to check there.

be careful that its not a 32 rim

How old is the gun?