Just a guess, but there was a company called “Monarch Metal Co.” in Chicago in the 1900s who made industrial equipment and components in brass, bronze and speciality metals using the trade name “Monarch Ball Metal”. Presumably this was some kind of alloy with a proprietary composition.
Your balls appear to have the letters “MET…” after the words “MONARCH BALL”, so I would think it might say “MONARCH BALL METAL”.
This company made heavy duty bearings among other things, but a bearing ball wouldn’t have a threaded hole in it. I wonder if what you have might be “governor balls” (also known as “fly-balls”) which were used as the centrifugal weights on governors for steam-powered equipment. This kind of thing:
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