**EXHIBIT 31.2**

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**Certification of Chief Financial Officer UnderSection 302 of the Sarbanes-Oxley Act of 2002**

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**I, Joseph B. Feiten, Chief FinancialOfficer of Tipperary Corporation certify that:**

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**1.**                                       Ihave reviewed this Quarterly Report on Form 10-Q of Tipperary Corporation(“registrant”);

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**2.**                                       Basedon my knowledge, this report does not contain any untrue statement of amaterial fact or omit to state a material fact necessary to make the statementsmade, in light of the circumstances under which such statements were made, notmisleading with respect to the period covered by this report;

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**3.**                                       Basedon my knowledge, the financial statements, and other financial informationincluded in this report, fairly present in all material respects the financialcondition, results of operations and cash flows of the registrant as of, andfor, the periods presented in this report;

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**4.**                                       Theregistrant’s other certifying officer and I are responsible for establishingand maintaining disclosure controls and procedures (as defined in Exchange ActRule 13a-15(e) and 15d-15(e)) for the registrant and have:

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**(a)**                                  Designedsuch disclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under our supervision, to ensure that materialinformation relating to the registrant, including its consolidatedsubsidiaries, is made known to us by others within those entities, particularlyduring the period in which this report is being prepared;

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**(b)**                                 Reserved;

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**(c)**                                  Evaluatedthe effectiveness of the registrant’s disclosure controls and procedures andpresented in this report our conclusions about the effectiveness of thedisclosure controls and procedures, as of the end of the period covered by thisreport based on such evaluation; and

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**(d)**                                 Disclosedin this report any change in the registrant’s internal control over financialreporting that occurred during the registrant’s most recent fiscal quarter (theregistrant’s fourth fiscal quarter in the case of an annual report) that hasmaterially affected, or is reasonably likely to materially affect, theregistrant’s internal control over financial reporting; and

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**5.**                                       Theregistrant’s other certifying officer and I have disclosed, based on our mostrecent evaluation of internal control over financial reporting, to the registrant’sauditors and the audit committee of the registrant’s board of directors (orpersons performing the equivalent functions):

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**(a)**                                  Allsignificant deficiencies and material weaknesses in the design of operation ofinternal control over financial reporting which are reasonably likely toadversely effect the registrant’s ability to record, process, summarize andreport financial information; and

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**(b)**                                 Anyfraud, whether or not material, that involves management or other employees whohave a significant role in the registrant’s internal control over financialreporting.

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| **Date:**      | **August 16, 2004**    |
|----------------|-----------------------------|
|           |                        |
| **Signature:** | **/s/ Joseph B. Feiten**    |   |
|           |                        |
|           | **Joseph B. Feiten**        |
| **Title:**     | **Chief Financial Officer** |

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