Last post I wrote that the Organ 16x257 needle is slightly hitting/rubbing the hook and that the scarf seems to catch on the hook. I then asked how to adjust the machine so that the needle is moved slightly to the left or the hook is moved slightly to the right to provide a bit of clearance.
Not receiving any answers, I decided to experiment a bit further. Since I have an old 31-15 machine from 1902, I thought I'd try a needle CDTthayer mentioned in his response.
I was able to obtain Schmetz 16x73 (16x1) needles [both numbers are listed on the box]. Although CDThayer mentioned that these are for foot-powered machines, I tend to sew slowly with my motor-powered machine. These needles are the same diameter as the 16x257, but do not have a scarf. However, they are about 1/32 of an inch longer than the 16x257 needles, so I adjusted the needle bar slightly to compensate.
For some reason, they do not rub the hook. These needles work great! No problems at all. So, I'm happy that the machine is running fine now. As long as I can obtain these needles, all is good. Again, thanks everyone for your help. Your comments set me on the track to find a needle that works.
However, I am still curious why the 16x257 needles (with a scarf) would rub the hook and if there are any adjustments that can be made to eliminate this. If anyone has an answer to this mystery, I'd love to know.