If I'm not mistaken, you have one of the jumping bean Security-Sixes. These were the initial models that had a wierd grip angle that made the gun want to jump out of your hands when you fire it. It got the SS off to a horrible start and ones designated 151+ corrected the problem. Still, the subsequent SSs had smallish grips that, while easier to shoot, still were on the skimpy side.
The Pachmayr rubber grips should make it a non-issue.
Incidentally, my first revolver was a stainless SS. I was poor back then and, on my way out to shoot, the local dealer set aside some grips and said they'd be there on my way back. Sure enough, after firing a couple of full throttle magnum rounds, I opted for the rubber grips and bought them on my way back. Shooting .38s was no problem.