What is "to swing round the circle"

Swing \Swing\, v. i. [imp. & p. p. Swung; Archaic imp. Swang; p. pr. & vb. n. Swinging.] [OE. swingen, AS. swingan to scourge, to fly, to flutter; akin to G. schwingen to winnow, to swingle, oscillate, sich schwingen to leap, to soar, OHG. swingan to throw, to scourge, to soar, Sw. svinga to swing, to whirl, Dan. svinge. Cf. Swagger, Sway, Swinge, Swink.]

1. To move to and fro, as a body suspended in the air; to wave; to vibrate; to oscillate.

   I tried if a pendulum would swing faster, or continue swinging longer, in case of exsuction of the air.
   --Boyle.

2. To sway or move from one side or direction to another; as, the door swung open.

3. To use a swing; as, a boy swings for exercise or pleasure. See Swing, n., 3.

4. (Naut.) To turn round by action of wind or tide when at anchor; as, a ship swings with the tide.

5. To be hanged. [Colloq.]
   --D. Webster.

   To swing round the circle, to make a complete circuit.

   He had swung round the circle of theories and systems in which his age abounded, without finding relief.
   --A. V. G. Allen.