MEMORANDUM

                   GUGGENHEIM DEFINED PORTFOLIOS, SERIES 1040
                              FILE NO. 333-188046

      The Prospectus and the Indenture filed with Amendment No. 2 to the
Registration Statement on Form S-6 have been revised to reflect information
regarding the deposit of securities on September 25, 2013 and to set forth
certain data based thereon. In addition, there are a number of other changes
from the Prospectus as originally filed.

      An effort has been made to set forth below certain of the changes and also
to reflect all changes by marking the Prospectus submitted with the Amendment.

                                 THE PROSPECTUS

      Part A. The date of the Prospectus has been updated.

      Part A. The "Essential Information" and "Fees and Expenses" sections,
      including applicable footnotes, have been updated.

      Part A. The period over which the deferred sales charge will be collected
      has been updated.

      Part A. The Trust Portfolio(s) and the related footnotes have been
      updated.

      Part A. The Statement(s) of Financial Condition and the related footnotes
      have been updated.

      Part A. The Report of Independent Registered Public Accounting Firm has
      been updated.

      Part B. The date of the Prospectus has been updated.

      Back Cover. The date of the Prospectus has been updated.

                             CHAPMAN AND CUTLER LLP

Chicago, Illinois
September 25, 2013