First off... that Model 19 you have is a GREAT gun...excellent choice, it is a classic.
The Model 19, as others have said was a joint project by Bill Jordan and S&W. It was intended to be a Peace Officers Dream Gun. Easier to carry, and powerful enough to get the job done with authority, in a package that is easy to shoot well...K Frame.
The original intent was for officers to practice with a steady diet of 38 Specials and load 125 grain 357 Magnum defensive loads for serious social purposes.
Problems developed with the forcing cone, when doctrines changed. There was a school of thought that stated that an officer should practice with the load they will actually use in combat...the 125 gr 357 Magnum. With a steady diet of these high pressure loads, problems developed with the forcing cone cracking. S&W corrected this by developing the 686/586 series of firearms built on the L Frame.
So, your Model 19 should be fine with 125 gr 357 Magnums, but not with a steady diet of them.
Hope this helps...