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The wavy lines?

 

Are you referring to the wavy lines? It's quite typical of the Waltham railroad pocket watches. Hopefully this picture will post:



I recall, in my travels and conversations, that it was done on a machine similar to a pantograph with a small rotating sanding disk, somewhat similar to the ones used for cotes de Geneve except much, much smaller, or a grinding stone with a slight conical tip.

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