What is "with all one's might and main"

Main \Main\, n. [AS. m[ae]gen strength, power, force; akin to OHG. magan, Icel. megin, and to E. may, v. [root]103. See May, v.]

1. Strength; force; might; violent effort. [Obs., except in certain phrases.]

   There were in this battle of most might and main.
   --R. of Gl.

   He 'gan advance, With huge force, and with importable main.
   --Spenser.

2. The chief or principal part; the main or most important thing. [Obs., except in special uses.]

   Resolved to rest upon the title of Lancaster as the main, and to use the other two . . . but as supporters.
   --Bacon.

3. Specifically:

   1. The great sea, as distinguished from an arm, bay, etc.; the high sea; the ocean. ``Struggling in the main.''
      --Dryden.

   2. The continent, as distinguished from an island; the mainland. ``Invaded the main of Spain.''
      --Bacon.

   3. principal duct or pipe, as distinguished from lesser ones; esp. (Engin.), a principal pipe leading to or from a reservoir; as, a fire main.

      Forcing main, the delivery pipe of a pump.

      For the main, or In the main, for the most part; in the greatest part.

      With might and main, or With all one's might and main, with all one's strength; with violent effort.

      With might and main they chased the murderous fox.
      --Dryden.