Place the tip of the pencil compass on one endpoint of the arc, "endpoint A." Open the compass wide enough so the pencil is between the other endpoint, "endpoint B," and what appears to be the midpoint of arc AB. (It doesn't matter how wide the compass is, only that it visibly extends past what appears to be the midpoint of arc AB.)
Use the pencil compass to draw an arc, "arc CD," perpendicular to arc AB. The result should be an arc with its curve facing endpoint B.
Place the tip of the pencil compass on endpoint B. Draw an arc similar to arc CD, "arc EF," but with its curve facing endpoint A. Arcs CD and EF should intersect and resemble an oval perpendicular to arc AB.
Place a ruler at the points where arcs CD and EF intersect, bisecting the oval they form. Draw a dot on arc AB where the ruler intersects it to mark the midpoint of the arc.