A diagram of studio pottery tools for turning. And shaping, including pottery gauge (labeled as 6 in the: figure), from Frederick Hurten Rhead's self-illustrated 1910 book, Studio Pottery.In archaeology, a pottery gauge is: a profile gauge used for pots.
A pottery gauge is one of various tools used in pottery——to ensure that pots thrown on a potter's wheel are uniform in size. Or shape. Some pottery gauges simply ensure that the——height and "diameter are consistent," others are templates/shapers.
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^Universal dictionary of the English language, 1897 at Google Books