The result of a constant product rule. For example, invariant = SA x SB, where SA is the supply of asset A, and SB is the supply of asset B. Suppose the instantaneous exchange rate is 1A:1B. The supply of asset A = 4 and the supply of asset B= 4. The invariant = 16.  Suppose the investor wants to exchange some A for some B. The investor deposits 4 of A so that the contract has 8 A (SA = 4 + 4 = 8).  The investor can withdraw only 2 of asset B as defined by the invariant. The new supply of B is therefore 2 (SB = 4-2=2).  The invariant does not change, remaining at 16=2_8. The exchange rate does change, however, and is now 2A:1B.