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It is well known that drills and other tools of the same class which are guided by their cutting edges tend to, or at any rate can produce holes which are not circular in section, and further, that if the tool haven equidistant edges, the hole which it produces, if not circular in section, will haven +1 sides or similar arcs,* but the exact shape of these holes and the limits to their possible departure from circularity have not as far as I am aware been hitherto examined.

V. On curves circumscribing rotating polygons with reference to the shape of drilled holes