Using a piercing saw on silver was one of the first things I learned to do as an apprentice (after perfecting the art of tea making!) A piercing saw has fine blades, so that sometimes it was easier to feel which way the teeth run than to see the teeth. The blade was inserted into the saw and then tightened into place at top and bottom. The blade had to not just be secure but also have just the right amount of tension. Too tight and it would break, sometimes before you had started cutting. Too loose and it would drag then catch on whatever you were sawing. We had to tighten the frame then pluck the blade like a guitar or violin to test the tension. if it made a musical noise it was ok, a metallic twang, it was too loose and a very high note meant it was too tight. in that case it probably broke anyway!
After this painstaking preparation you were ready to cut into the metal. the textbooks all suggest using beeswax to stop the blade getting hot and breaking but spit works as well and is usually readily available. Piercing saw blades break if too hot or pushed or sometimes if you look at them. The trick is to let the blade cut on the downstrokeand just follow the cut rather than pushing the saw. Turning corners or changing direction is another danger point. The trick is to do the sawing equivalent of treading water, sawing on the spot but moving the blade a tiny way in the new direction. It was possible to buy coarser blades but they weren't as accurate and wasted material unnecessarily. They still broke easily too.
Breaking blades was bad news for a number of reasons. Blades were very expensive for a start but it was best to be philosophical about that. In the same way that you can't make an omelette without breaking eggs, there is no shame in breaking one or two saw blades while making a piece of jewellery. Sometimes a break in the blade meant a break in your concentration and maybe an excuse for another cup of tea. Every now and then, but only if you were pushing the blade, it would break and pierce your finger which was horrible. if the teeth were pointing away from the entry point, you effectively sawed your finger as you pulled it out! How we suffered for our art.
Broken sawblades are extremely sharp and nowadays would probably have to be put into a sharps box but we often just left them on the bench until we could find a use for them like propping up a link while you soldered it to the edge of a pendant. If a blade just broke near the end we could adjust the piercing saw frame down to fit the blade length.