I recently acquired my first Stevens, this one a #44 1/2 in .32-40.  It appears in good condition, unabused and unmolested.  It shows good preliminary accuracy but I've a question about the way its action functions.  According to de Hass the hammer should go to the safe position upon chambering a fresh round.  Mine does not always do this but sometimes allows the hammer to come to rest touching the firing pin as the action is closed.  I'd appreciate knowledgeable comments or ideas on the cause and correction of what appears to me to be an unsafe condition.  Thank you in advance for the benefit of your experience and expertise.  FCH

If it does not catch every time but does function some of the time it probably could use a good cleaning. Old dry oil will cause the trigger to drag enough so it does not engage the hammer notch.

Thanks for your advice and suggestions.  This afternoon I disassembled the rifle (short of removing the link) and gave it a good cleaning & inspection.  It was not very dirty and the parts all showed little wear; indeed were crisp.  Paid particular attention to the trigger where the both notches are in good shape.  I reassembled carefully looking at deHass' diagram and photos (of the hammer & fly) from a thread on the 44 1/2 double set trigger found on this forum.  Unfortunately nothing changed.
On inspection I noticed the hammer will rotate back just short of the half cock position when opening the action from the fired position and then move back forward as the action is fully opened.  Pressure on the back of the trigger has no effect but a very slight manual movement of the hammer back drops the trigger tip into the half cock notch. Does this suggest anything?
  Thanks again for your help. (Of course, now I know how to safely fire the rifle; just requires putting the hammer manually in safe/half cock before I open the action after I fire.  Once it's in half cock, it'll stay.)  But it ain't right!  FCH

Pull the breech block and check the link as mentioned.  For both position and wear.

This first picture shows the area of contact, between the link and the hammer, that pushes the hammer back

The second picture show the way it should be assembled.  The arrow is just showing the off-set of the hump in the plunger for proper installation.  If you need to remove the link be careful, this plunger has some pressure on it.

I am assuming yours is a single trigger and not a double set.   
So, when you drop the breach block watch the plunger in the frame as shown in this picture by the arrow.  It puts pressure to the front of the breech block.  This plunger and spring is pressure loaded from the front of the frame and beside the barrel.  As the bb drops down the plunger will come out.  Forearm needs to come off to access the pressure screw.  If the plunger is hammer shaped it is directional for reassembly.

Bob

As a result of expert alerts, suggestions , guidance, images, instructions, etc., from this august group I have discovered the cause of the function abnormality in my Stevens 44 1/2.  The cause is most probably due to a "refinement" of the link profile/shape by a previous custodian of the rifle.  As mentioned above, it's safe to fire the rifle as is but I'll likely find an unmolested link to complete the adventure.  My sincere thanks to the several experts on this forum who generously offered their knowledge to help me resolve the problem.  FCH

Ordered.  Lots'a good stuff!  Thanks,FCH