What is "on the strength of"

Strength \Strength\, n. [OE. strengthe, AS. streng[eth]u, fr. strang strong. See Strong.]

1. The quality or state of being strong; ability to do or to bear; capacity for exertion or endurance, whether physical, intellectual, or moral; force; vigor; power; as, strength of body or of the arm; strength of mind, of memory, or of judgment.

   All his [Samson's] strength in his hairs were.
   --Chaucer.

   Thou must outlive Thy youth, thy strength, thy beauty.
   --Milton.

2. Power to resist force; solidity or toughness; the quality of bodies by which they endure the application of force without breaking or yielding; -- in this sense opposed to frangibility; as, the strength of a bone, of a beam, of a wall, a rope, and the like. ``The brittle strength of bones.''
   --Milton.

3. Power of resisting attacks; impregnability. ``Our castle's strength will laugh a siege to scorn.''
   --Shak.

4. That quality which tends to secure results; effective power in an institution or enactment; security; validity; legal or moral force; logical conclusiveness; as, the strength of social or legal obligations; the strength of law; the strength of public opinion; strength of evidence; strength of argument.

5. One who, or that which, is regarded as embodying or affording force, strength, or firmness; that on which confidence or reliance is based; support; security.

   God is our refuge and strength.
   --Ps. xlvi. 1.

   What they boded would be a mischief to us, you are providing shall be one of our principal strengths.
   --Sprat.

   Certainly there is not a greater strength against temptation.
   --Jer. Taylor.

6. Force as measured; amount, numbers, or power of any body, as of an army, a navy, and the like; as, what is the strength of the enemy by land, or by sea?

7. Vigor or style; force of expression; nervous diction; -- said of literary work.

   And praise the easy vigor of a life Where Denham's strength and Waller's sweetness join.
   --Pope.

8. Intensity; -- said of light or color.

   Bright Ph[oe]bus in his strength.
   --Shak.

9. Intensity or degree of the distinguishing and essential element; spirit; virtue; excellence; -- said of liquors, solutions, etc.; as, the strength of wine or of acids.

10. A strong place; a stronghold. [Obs.]
    --Shak.

    On the strength of, or Upon the strength of, in reliance upon. ``The allies, after a successful summer, are too apt, upon the strength of it, to neglect their preparations for the ensuing campaign.''
    --Addison.

    Syn: Force; robustness; toughness; hardness; stoutness; brawniness; lustiness; firmness; puissance; support; spirit; validity; authority. See Force.