THIS PROMISSORY NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933,
AS AMENDED (THE "ACT"), OR APPLICABLE STATE SECURITIES LAWS (THE "STATE ACTS"),
AND SHALL NOT BE SOLD, PLEDGED, HYPOTHECATED, DONATED OR OTHERWISE TRANSFERRED
(WHETHER OR NOT FOR CONSIDERATION) BY THE HOLDER EXCEPT UPON THE ISSUANCE TO
TIPPERARY CORPORATION OF A FAVORABLE OPINION OF THE HOLDER'S COUNSEL OR
SUBMISSION TO TIPPERARY CORPORATION OF SUCH OTHER EVIDENCE AS MAY BE
SATISFACTORY TO COUNSEL TO TIPPERARY CORPORATION, TO THE EFFECT THAT ANY SUCH
TRANSFER SHALL NOT BE IN VIOLATION OF THE ACT AND THE STATE ACTS.

                                   PROMISSORY NOTE

$5,500,000                                                      Denver, Colorado
                                                               December 22, 1998

     Tipperary Corporation, a Texas corporation ("Maker"), hereby promises to
pay to the order of Slough Estates USA Inc., a Delaware corporation ("Lender"),
at its office located at 33 West Monroe Street, Suite 2000, Chicago, Illinois
60603, or at any other place the holder hereafter designates, the principal sum
of $5,500,000, together with interest thereon in lawful money of the United
States as herein provided.

     1.   INTEREST.  The unpaid principal balance of this Note shall bear
interest commencing on the date all proceeds of the loan are received by Maker,
such interest to be at the three-month London Interbank Offered Rate ("LIBOR")
plus (i) 3.5% per year until such date as the unpaid principal balance of this
Note becomes due and payable and (ii) 6.0% per year after such date as the
unpaid principal balance of this Note becomes due and payable, whether at
maturity or pursuant to other default as provided hereunder; said interest rate
to be adjusted in accordance with changes to LIBOR at such times as LIBOR is
changed, payable in arrears in calendar quarterly installments.  Each such
quarterly interest payment shall be due and payable within five days of the end
of each calendar quarter.  Interest shall be calculated based on the actual
number of days the principal balance remains outstanding in a year of 365 days.

     2.   MATURITY.  The unpaid principal balance of this Note, together with
accrued and unpaid interest, shall be due and payable three years from the date
on which all proceeds of the loan have been received by Maker.

     3.   SECURITY.  This Note is secured by a security agreement of even date
herewith, in favor of Lender.

     4.   PREPAYMENT.  The unpaid principal balance of the Note, together with
accrued and unpaid interest, may be paid in whole or in part, at any time in the
sole discretion of Maker without penalty.  Any prepayment in part by Maker shall
be first allocated to any accrued and unpaid interest, with any remaining amount
being allocated to the unpaid principal.

     5.   DEFAULT.  If any of the following events occurs, all indebtedness
owing by Maker hereunder shall become forthwith due and payable to Lender, upon
delivery by Lender to Maker of a written notice of default and demand for
payment, and the expiration of the following periods from the delivery of such
notice, during which periods Maker shall have the ability to cure such default:
(i) in the case of (a) below, ten days, (ii) in the case of (b), (c) or (d)
below, 30 days and, (iii) in the case of (e) below, 15 days, or, if it is not
practicable for Maker to cure such default within said 15-day period and Maker
is diligently proceeding to cure such default, such time longer than 15 days as
is reasonable for Maker to cure such default.

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          (a)  Any default by Maker in the payment, when due, of any part of the
principal of or interest on this Note and the payment of any other sums payable
by Maker pursuant to the terms of this Note.

          (b)  The insolvency or bankruptcy of Maker or any of its direct or
indirect subsidiaries, the execution by Maker or any of its direct or indirect
subsidiaries of an assignment for the benefit of creditors of substantially all
of the assets of Maker or any such direct or indirect subsidiary, or Maker's or
any of its direct or indirect subsidiary's consent to the appointment of a
trustee or a receiver or other officer of a court or other tribunal.

          (c)  The appointment of a trustee or receiver or other officer of a
court for Maker or any of its direct or indirect subsidiaries, or for a
substantial part of their properties, without the consent of Maker or of such
direct or indirect subsidiary, where no discharge is effected within 30 days.

          (d)  The institution of bankruptcy, reorganization, insolvency, or
liquidation proceedings by or against Maker or any of its direct or indirect
subsidiaries, and if against Maker or such a direct or indirect subsidiary,
where such proceeding is consented to by Maker or such subsidiary or remains
undismissed for 30 days.

          (e)  Any breach or failure of Maker to perform any term or condition
of this Note.

     6.   COLLECTION.  Maker and all guarantors and endorsers of this Note shall
pay all costs and expenses of collection and enforcement of this Note, including
reasonable attorneys' fees.

     7.   WAIVER.  Demand, presentment for payment, notice of dishonor, protest
and notice of protest are hereby waived.

     8.   PROCEEDS.  The proceeds from this Note, to be given on and as of the
date of this Note, shall consist of (a) $1,700,000 in cash, (b) the cancellation
and surrender, by Lender to Maker of a Promissory Note made by Maker in favor of
Lender, dated December 20, 1996 in the principal amount of $2,300,000, and a
Promissory Note made by Maker in favor of Lender, dated August 31, 1998 in the
principal amount of $1,000,000, and (c) an acknowledgment, in the form attached
hereto as Exhibit A, that a loan of $500,000 advanced by Lender to Maker on
November 2, 1998 is repaid.  The $1,700,000 cash proceeds are to be used for the
repayment of bank debt and general corporate purposes of Maker.

     9.   ASSIGNMENT.  This Note may not be assigned by Lender or Maker without
the express written consent of the other party; provided, however, that Lender
may assign this Note to any of its affiliates without such consent.  Such an
affiliate, for purposes of this Section 9, is any person of which Lender owns
directly or indirectly more than 50% of the voting equity interests, or such
person as owns directly or indirectly more than 50% of the voting equity
interests of Lender.

     10.  GOVERNING LAW.  This Note is made and is being executed in the State
of Colorado, and the provisions hereof will be construed in accordance with the
laws of the State of Colorado.  Furthermore, Lender and Maker (and their lawful
assignees, successors and endorsers) further agree that in the event of default
this Note may be enforced in any court of competent jurisdiction in the States
of Colorado or Illinois, and they do hereby submit to such jurisdiction in the
States of Colorado or Illinois.

     11.  SEVERABILITY.  Invalidation of any of the provisions of this Note
shall not affect the remainder of this Note.

                                        -2-

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     12.  AMENDMENT.  This Note may not be amended or modified except by an
instrument in writing signed by both parties.

     13.  SUBORDINATION.  This Note is subject to the terms and provisions of a
Subordination Agreement, dated December 20, 1996, as amended, between Lender and
U.S. Bank, which terms and provisions are incorporated herein by reference.

                              TIPPERARY CORPORATION


                              By:  /s/ David L. Bradshaw
                                   ----------------------------------------
                                   David L. Bradshaw, President and   
                                   Chief Executive Officer  

                                        -3-

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                                                                       EXHIBIT A

                         ACKNOWLEDGMENT OF REPAYMENT OF DEBT

     This Acknowledgment, dated as of December 22, 1998, relates to a loan in
the principal amount of $500,000 (the "Loan") advanced on November 2, 1998 by
Slough Estates USA Inc. ("Slough") to Tipperary Corporation ("Tipperary").  Upon
execution of that certain Promissory Note in the amount of $5,500,000 of even
date herewith (the "Note"), by Tipperary, as Maker, and Slough, as Lender, and
the payment, by Tipperary to Slough of accrued but unpaid interest on the Loan
at the rate of 8.5% per year, the Loan is hereby acknowledged to be paid in full
by Tipperary.



                              SLOUGH ESTATES USA INC.



                              By:  /s/ Randall W. Rohner
                                   ----------------------------------------
                                   Randall W. Rohner, Vice President and
                                   Chief Financial Officer