By ordinance of May 10, 1836 the Second Municipality Council authorized the issuance of $200,000 in bonds and the creation of a Sinking Fund for the "extinguishment" of those bonds. The Sinking Fund was to be financed by an annual payment of $12,000 out of the revenues of the St. Mary Market. The fund was to be "invested in such securities as the Council may from time to time direct."

On January 5, 1837 the Council created the Commissioners of the Sinking Fund, made up of the Recorder and the members of the Council's Finance Committee. This body supervised the management of the fund, but any investments still had to be approved by the full Council. This ordinance also provided for the Comptroller to keep the accounts of the fund and to report to the Council each January on the condition of the fund.

Additional bonds were issued in later years and additional monies provided for the operation of the Sinking Fund. By ordinance of April 2, 1839, the Council provided that "the revenue arising from the whargage tax is hereby specially pledged to insure annuual payment by the Treasurer of $4800 into a sinking fund in the Union Bank." This may have been the beginning of what came to be referred to as Sinking Fund #2, while the original fund was known as Sinking Fund #1.

On April 22, 1845 another ordinance (#1099) authorized the sale by the Commissioners of the Sinking Fund certain specified lots belonging to the municipality with proceeds to remain in Sinking Fund #1 "to be applied to the payment of the bonds of the municipality." In 1848 (January 4) all ordinances and resolutions relating to Sinking Fund #1 were repealed, the bonds of the Municipality having been paid. The ordinance does, however, refer to the continuation of Sinking Fund #2, still funded by monies from the Wharfage tax and market revenues.

The Commissioners of the Sinking Fund apparently no longer met after 1848, nor do the separate record books for the fund continue beyond that year. There is no ready evidence that either the Commissioners or the fund itself were formally dissolved.