<PAGE>
                                                                   EXHIBIT 10(x)

                                     SECOND
                              AMENDED AND RESTATED
                                      NOTE

$5,000,000                                                        April 26, 2001



         FOR VALUE RECEIVED, UNITED STATES LIME & MINERALS, INC., a Texas
corporation (formerly known as Scottish Heritable, Inc.), TEXAS LIME COMPANY, a
Texas corporation, and ARKANSAS LIME COMPANY, an Arkansas corporation
(collectively referred to herein as "Borrowers"), jointly and severally promise
to pay to the order of FIRST UNION NATIONAL BANK (successor to CoreStates Bank,
N.A.), its successors and assigns ("Bank"), the lesser of (x) Five Million
Dollars ($5,000,000) or (y) the aggregate unpaid principal amount of all Cash
Advances made by Bank to Borrowers or any Borrower under the Amended and
Restated Loan and Security Agreement dated December 30, 1997, by and among
Borrowers and Bank (as the same has been amended and may hereafter be amended,
restated, supplemented or otherwise modified and in effect from time to time,
the "Loan Agreement"), which principal amount and all accrued and unpaid
interest thereon and Bank's Costs pertaining thereto shall be payable on the
Revolving Credit Termination Date.

         This Second Amended and Restated Note (this "Note") replaces Borrowers'
Amended and Restated Note dated December 30, 1997 in the original principal
amount of $4,000,000 (replacing Borrowers' Note dated October 20, 1993 in the
original principal amount of $6,000,000), but does not evidence repayment
thereof. This Note is issued pursuant to and entitled to the benefits of the
Loan Agreement to which reference is hereby made for a more complete statement
of the terms and conditions with respect hereto. All initially capitalized terms
used herein shall have the same meanings as ascribed to them in the Loan
Agreement unless the context clearly requires to the contrary.

         Borrowers promise to pay interest on the unpaid principal amount of all
Cash Advances from the date made to maturity (whether by acceleration or
otherwise) or earlier repayment, in accordance with Section 2.2.2 of the Loan
Agreement.

         Interest shall be payable on the outstanding principal balance hereof
as set forth in Section 2.4.5 of the Loan Agreement, at the Interest Rate Option
selected pursuant to Section 2.4.2 of the Loan Agreement. Interest shall be
calculated on the basis of a 360 day year, and charged for the number of days
actually elapsed during any year or part thereof.

         This Note may be prepaid at the times, in the amounts and with the
prepayment premiums set forth in Section 2.4.8 of the Loan Agreement.

         All payments hereunder shall be made by Borrowers jointly and severally
without defense, set off, or counterclaim and in same day funds and delivered to
Bank not later than 12:00 noon (Philadelphia time) on the date due at Bank's
office located at 1339 Chestnut Street, 11th Floor, Widener Building,
Philadelphia, PA 19107, or such other place as shall be designated in writing
for such purpose in accordance with the terms of the Loan Agreement.




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<PAGE>

         Each Borrower authorizes Bank to charge such Borrower's demand deposit
account with Bank in order to cause timely payment to be made to Bank of all
principal, interest and fees hereunder as provided in Section 1.5 of the Loan
Agreement.

         Whenever any payment on this Note shall be stated to be due on a day
which is not a Business Day, such payment shall be made on the next succeeding
Business Day and such extension of time shall be included in the computation of
interest on this Note.

         Any principal payment hereon not paid when due, and to the extent
permitted by applicable law, any interest payment hereon not paid when due, and
any other amount due to Bank hereunder, under the Loan Agreement or under any
other Loan Document not paid when due, in any case whether at stated maturity,
by notice of prepayment, by acceleration or otherwise, shall thereafter bear
interest payable upon demand at a rate which is, with respect to Adjusted LIBOR
Loans only, 5% per annum in excess of the Adjusted LIBOR until the expiration of
the then applicable Interest Period, and after the expiration of the then
applicable Interest Period, and in all cases with respect to Base Rate Loans, at
a rate which is 2.75% per annum in excess of the Base Rate.

         It shall be an event of default hereunder if an Event of Default shall
have occurred under the Loan Agreement (a "Default"). In addition to other
remedies of Bank as set forth in this Note, the Loan Agreement, or any other
Loan Document, upon the occurrence of a Default which shall be continuing, Bank
may, without demand, by written notice to Borrowers, cause this Note to become
immediately due and payable in the manner, upon the conditions and with the
effect provided in the Loan Agreement.

         THE FOLLOWING SETS FORTH A WARRANT OF ATTORNEY TO CONFESS JUDGMENT
AGAINST BORROWERS OR ANY BORROWER. IN GRANTING THIS WARRANT OF ATTORNEY TO
CONFESS JUDGMENT AGAINST BORROWERS OR ANY BORROWER, EACH BORROWER, FOLLOWING
CONSULTATION WITH (OR DECISION NOT TO CONSULT WITH) SEPARATE COUNSEL FOR SUCH
BORROWER, AND WITH KNOWLEDGE OF THE LEGAL EFFECT HEREOF, HEREBY WAIVES ANY AND
ALL RIGHTS SUCH BORROWER HAS, OR MAY HAVE TO PRIOR NOTICE AND AN OPPORTUNITY TO
BE HEARD UNDER THE CONSTITUTIONS AND LAWS OF THE UNITED STATES AND THE
COMMONWEALTH OF PENNSYLVANIA. EACH BORROWER SPECIFICALLY ACKNOWLEDGES THAT BANK
HAS RELIED ON THIS WARRANT OF ATTORNEY IN GRANTING THE FINANCIAL ACCOMMODATIONS
DESCRIBED HEREIN.

         EACH BORROWER IRREVOCABLY AUTHORIZES AND EMPOWERS ANY ATTORNEY OF ANY
COURT OF RECORD TO APPEAR FOR SUCH BORROWER IN ANY AND ALL ACTIONS, AND UPON THE
OCCURRENCE OF A DEFAULT TO: (I) ENTER JUDGMENT AGAINST SUCH BORROWER FOR THE
PRINCIPAL SUM HEREOF; OR (II) SIGN FOR SUCH BORROWER AN AGREEMENT FOR ENTERING
IN ANY COMPETENT COURT AN AMICABLE ACTION OR ACTIONS TO CONFESS JUDGMENT AGAINST
SUCH BORROWER FOR ALL OR ANY PART OF THE INDEBTEDNESS; AND IN EITHER CASE FOR
INTEREST AND COSTS TOGETHER WITH A REASONABLE COLLECTION FEE. EACH BORROWER
FURTHER IRREVOCABLY AUTHORIZES AND



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<PAGE>

EMPOWERS ANY ATTORNEY OF ANY COURT OF RECORD TO APPEAR FOR AND ENTER JUDGMENT
AGAINST SUCH BORROWER AND IN FAVOR OF BANK OR ANY HOLDER HEREOF WITH RESPECT TO
AN AMICABLE ACTION OF REPLEVIN OR ANY OTHER ACTION TO RECOVER POSSESSION OF ANY
COLLATERAL. EACH BORROWER WAIVES ALL RELIEF FROM ANY AND ALL APPRAISEMENT OR
EXEMPTION LAWS NOW IN FORCE OR HEREAFTER ENACTED. IF A COPY OF THIS NOTE,
VERIFIED BY AFFIDAVIT OF AN OFFICER OF BANK OR ANY OTHER HOLDER HEREOF, SHALL BE
FILED IN ANY PROCEEDING OR ACTION WHEREIN JUDGMENT IS TO BE CONFESSED, IT SHALL
NOT BE NECESSARY TO FILE THE ORIGINAL HEREOF AND SUCH VERIFIED COPY SHALL BE
SUFFICIENT WARRANT FOR ANY ATTORNEY OF ANY COURT OF RECORD TO APPEAR FOR AND
CONFESS JUDGMENT AGAINST EACH BORROWER AS PROVIDED HEREIN. JUDGMENT MAY BE
CONFESSED FROM TIME TO TIME UNDER THE AFORESAID POWERS WHICH SHALL NOT BE
EXHAUSTED BY ONE EXERCISE THEREOF.

         Borrowers hereby individually and collectively waive presentment,
demand for payment, notice of dishonor, protest or notice of protest and any and
all notices or demands and, to the full extent permitted by law, the right to
plead any statute of limitations as a defense to any demand hereunder in
connection with the delivery, acceptance or enforcement of this Note. The joint
and several liabilities and obligations of Borrowers hereunder shall be
unconditional without regard to the liability or obligations of any other party
and shall not be in any manner affected by any indulgence whatsoever granted or
consented to by Bank, including, but not limited to, any extension of time,
renewal, waiver or other modification. Any failure of Bank to exercise any right
hereunder shall not be construed as a waiver of the right to exercise the same
or any other right at any time and from time to time thereafter.

         This Note shall be governed as to its validity, interpretation and
effect by the internal laws of the Commonwealth of Pennsylvania. Any and all
actions at law or in equity relating to this Note and the Indebtedness shall be
brought, and jurisdiction may be had, in the courts of Philadelphia County,
Pennsylvania, or at the election of the holder hereof, the United States
District Court for the Eastern District of Pennsylvania. Borrowers consent in
advance to service of process by registered mail, return receipt requested, to
the address set forth in Section 9.3 of the Loan Agreement.

         EACH BORROWER AND BANK EXPRESSLY WAIVE ANY RIGHT TO TRIAL BY JURY IN
ANY ACTION BROUGHT BY ANY PARTY WITH RESPECT TO THE INDEBTEDNESS OR ANY LOAN
DOCUMENT.

         This Note may not be changed or amended orally but only by an agreement
in writing and signed by the party against whom enforcement of any waiver,
change, modification or discharge is sought.

         This Note is entitled to the benefits of certain other Loan Documents.

         If any provision of this Note shall for any reason be held to be
invalid or unenforceable, such invalidity or unenforceability shall not affect
any other provision hereof, but this Note shall be construed as if such invalid
or unenforceable provision had never been contained herein.



                                       3
<PAGE>

Borrowers promise to pay all Bank's Costs and expenses, including reasonable
attorneys' fees, as provided in Section 1.6 of the Loan Agreement, incurred in
the collection and enforcement of this Note. Each Borrower and endorsers of this
Note hereby consent to renewals and extensions of time at or after the maturity
hereof, without notice.

         IN WITNESS WHEREOF, and intending to be legally bound hereby, Borrowers
have executed this Note, as an instrument under seal, the day and year first
above written.

                                UNITED STATES LIME & MINERALS, INC.


                                BY:    /s/ Timothy W. Byrne
                                       -----------------------------------------
                                       TIMOTHY W. BYRNE, PRESIDENT


                                TEXAS LIME COMPANY


                                BY:    /s/ Timothy W. Byrne
                                       -----------------------------------------
                                       Timothy W. Byrne, President


                                ARKANSAS LIME COMPANY


                                By:    /s/ Timothy W. Byrne
                                       -----------------------------------------
                                       Timothy W. Byrne, President




                                       4
<PAGE>

                              TRANSACTIONS ON NOTE

<Table>
<Caption>
                                                             Outstanding
                                             Amount of        Principal
                        Amount of Loan     Principal Paid      Balance
        Date            Made This Date       This Date        This Date    Notation Made By
        ----            --------------     --------------    -----------   ----------------
<S>                     <C>               <C>                <C>           <C>

</Table>


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