SCHEDULE 14A

                   PROXY STATEMENT PURSUANT TO SECTION 14(a)
                    OF THE SECURITIES EXCHANGE ACT OF 1934
                                (AMENDMENT NO. )

Filed by the Registrant [X] 
Filed by a Party other than the Registrant [ ] 
Check the appropriate box:
      [ ]  Preliminary Proxy Statement
      [ ]  Confidential, for Use of the Commission Only (as
            permitted by Rule 14a- 6(e)(2))
      [ ]  Definitive Proxy Statement
      [X]  Definitive Additional Materials
      [ ]  Soliciting Material Pursuant to ss. 240.14a-11(c) or
            ss. 240.14a-12

                        THE MERIDIAN RESOURCE CORPORATION
              (Name of Registrants as Specified In Their Charters)

                                       N/A
                   (Name of Person(s) Filing Proxy Statement,
                          if other than the Registrant)

Payment of Filing Fee (Check the appropriate box):

      [ ]   No fee required.
      [ ]   Fee computed on table below per Exchange Act Rules 14a-6(i)(4)
            and 0-11.
            (1)   Title of each class of securities to which transaction
                  applies:
            (2)   Aggregate number of securities to which transaction
                  applies:  __________.
            (3)   Per unit price or other underlying value of transaction
                  computed pursuant to Exchange Act Rule 0-11 (Set forth the
                  amount on which the filing fee is calculated and state how it
                  was determined):
            (4)   Proposed maximum aggregate value of the transaction:
                  $__________.
            (5)   Total fee paid: $______. 
      [X]   Fee previously paid with preliminary materials. 
      [ ]   Check box if any part of the fee is offset as provided by
            Exchange Act Rule 0-11(a)(2) and identify the filing for which
            the offsetting fee was paid previously.  Identify the previous
            filing by registration statement number, or the Form or Schedule
            and the date of its filing.
            (1)   Amount Previously Paid:  N/A.
            (2)   Form, Schedule or Registration Statement No.:  N/A.
            (3)   Filing Party:  N/A.
            (4)   Date Filed:  N/A.

                        THE MERIDIAN RESOURCE CORPORATION
                            15995 N. BARKERS LANDING
                              HOUSTON, TEXAS 77079

July 8, 1998

Dear Shareholders:

      At the Special Meeting of Shareholders of the Company (the "Meeting") held
on Tuesday, June 30, 1998, the shareholders of the Company approved the
Agreement and Plan of Merger dated March 27, 1998, by and among the Company,
LOPI Acquisition Corp., a wholly-owned subsidiary of the Company, Shell
Louisiana Onshore Properties Inc. and Louisiana Onshore Properties Inc., and the
related Required Future Share Issuances, as more fully described in the
Company's Proxy Statement dated June 10, 1998 (the "Proxy Statement"). The
Company, however, had not received prior to the Meeting the requisite two-thirds
vote of the shares of common stock outstanding as of the record date for the
Meeting needed to pass Proposal Two - the amendment to the Company's Second
Amended and Restated Articles of Incorporation, as amended, to increase the
number of authorized shares of the Company's common stock, $.01 par value, from
100,000,000 shares to 200,000,000 shares. Due to a technical requirement of the
New York Stock Exchange, brokers who did not receive from their clients specific
voting instructions on Proposal Two were unable to vote a significant portion of
the shares registered in their names by June 30, 1988, and accordingly, a motion
to adjourn the Meeting to 9:00 a.m., July 20, 1998, at the Company's principal
offices at 15995 N. Barker's Landing, Houston, Texas 77079, was approved to give
all of the Company's shareholders additional time to vote on this important
matter.

      We would like to renew our request that you return a proxy indicating how
you desire your shares to be voted on Proposal Two. In the event we have not
received your proxy for the Meeting, either directly or through your broker or
bank, we urge you to please return your proxy before July 20, 1998, to ensure
representation of your shares. In the event you already have given a proxy to be
voted at the Meeting, you do not have to submit a new proxy; your proxy will be
voted on Proposal Two at the reconvened Meeting on July 20, 1998, as you
indicated on your proxy card. Any proxy may be revoked at any time prior to the
voting on July 20, 1998, by giving written notice to the Secretary of the
Company or by submitting a new proxy or by voting in person at the reconvened
Meeting.

      For the reasons previously set forth in the Proxy Statement, THE BOARD OF
DIRECTORS RECOMMENDS A VOTE IN FAVOR OF PROPOSAL TWO. This letter supplements
the Proxy Statement, which was previously provided to you.

      We hope that you will act promptly in returning your proxy and we greatly
appreciate your continued support.

                                    Sincerely,

                                    Joseph A. Reeves, Jr.
                                    Chairman of the Board