<PAGE>   1
                                                                      EXHIBIT 10


                               FIRST AMENDMENT TO
                AMENDED AND RESTATED LOAN AND SECURITY AGREEMENT

         This First Amendment to Amended and Restated Loan and Security
Agreement (this "First Amendment") dated August ___, 1998 by and among United
States Lime & Minerals, Inc., a Texas corporation (formerly known as Scottish
Heritable, Inc.) ("U.S. Lime"), Texas Lime Company, a Texas corporation ("TLC"),
and Arkansas Lime Company, an Arkansas corporation ("ALC," and together with
U.S. Lime and TLC, collectively referred to as the "Borrowers" and individually
as a "Borrower"), and First Union National Bank, a national banking association,
as successor to CoreStates Bank, N.A. ("Bank").

                                   BACKGROUND

         A. Borrowers and Bank are parties to an Amended and Restated Loan and
Security Agreement dated December 30, 1997 (the "Loan Agreement"), pursuant to
which Bank continued and restated certain credit facilities for the benefit of
Borrowers under the terms and conditions set forth therein. All initially
capitalized terms used in this First Amendment, unless otherwise specifically
defined herein, shall have the meanings ascribed to them in the Loan Agreement.

         B. Borrowers have requested that Bank agree to amend the Loan Agreement
to: (i) increase from $15,000,000 to $18,500,000 the principal amount of the
Term Loan which aggregate amount would be subject to an 84 month amortization
schedule but payable over a 60 month period; (ii) establish a supplemental
committed revolving credit in the maximum principal amount outstanding at any
one time of $5,000,000 (the "Second Revolving Credit") to fund Borrowers'
initial costs and expenses related to ALC's plant expansion in Arkansas; and
(iii) modify the interest rates applicable to the Term Loan, the Revolving
Credit, the Second Revolving Credit, and the Line of Credit to a formula based
on the Borrowers' ratio of consolidated Funded Debt to EBITDA. Additionally,
Bank desires to: (x) re-secure the prompt payment and performance of the
Revolving Credit by cross-collateralizing the Revolving Credit with the security
interests in Borrowers' personal property granted to Bank to secure the Term
Loan; (y) expand Bank's security interest in Borrowers' personal property to
include all accounts receivable and inventory as additional security for the
Term Loan, the Revolving Credit and the Second Revolving Credit; and (z) reduce
the maximum principal amount which may be outstanding at any one time under the
Line of Credit from $25,000,000 to $20,000,000. Bank and Borrowers have agreed
to such modifications subject to the terms and conditions hereof.

         NOW, THEREFORE, in consideration of the foregoing and of the mutual
covenants set forth herein, the parties hereto, intending to be legally bound
hereby, agree as follows:

         1. Ratification. This First Amendment is a modification of the Loan
Agreement pursuant to Section 9.2 thereof. Except as expressly set forth herein,
or in any amendment to any of the documents referred to herein, Borrowers and
Bank acknowledge and agree that each and every term, condition and provision of
the Loan Agreement is hereby ratified and confirmed in full.

         2. Indebtedness. Borrowers hereby unconditionally acknowledge that, as
of the date hereof, the outstanding principal amount of the Term Loan is
$14,142,862, and there are no amounts outstanding under the Revolving Credit
(excluding the face amount of outstanding and undrawn letters of credit) or the
Line of Credit, and that the foregoing balance of the Term Loan, together


<PAGE>   2


with interest which shall accrue from the date hereof at the rates set forth in
the Notes, are owing to Bank without claim, counterclaim, recoupment, defense or
setoff of any kind.

         3.  Definitions.

                  3.1 New Definitions. Each of the following terms is hereby
added to Section 1.1 of the Loan Agreement and shall have the meaning herein
ascribed to it for the purposes hereof and for each of the Loan Documents:

                  "Cash Flow Ratio" means, for a specified period, the ratio of
Borrowers' consolidated Funded Debt to EBITDA for such period.

                  "EBIT" means Borrowers' consolidated Net Income for a period,
plus the sum of the following for such period (without duplication and only to
the extent each is deducted from Borrowers' revenues to determine Net Income):
(i) Interest Expense, and (ii) taxes.

                  "EBITDA" means Borrowers' consolidated Net Income for a
period, plus the sum of the following for such period (without duplication and
only to the extent each is deducted from Borrowers' revenues to determine Net
Income): (i) Interest Expense, (ii) taxes, (iii) depreciation, and (iv)
amortization.

                  "Funded Debt" means the Loans and all other obligations of
Borrowers or any Borrower for borrowed money, Capital Lease Expense, the
deferred purchase price for property of a Borrower or Borrowers, all obligations
under conditional sales or other title retention agreements of a Borrower or
Borrowers, all indebtedness for borrowed money of a third party secured by any
lien upon property of a Borrower or Borrowers (limited to the lesser of the
indebtedness or the fair market value of the property), and all indebtedness of
others of a type described above which is guarantied or endorsed by a Borrower
or Borrowers (limited to the extent of the liability of the Borrower or
Borrowers).

                  "Second Mortgages" means, collectively, (i) the Second
Mortgage, Assignment of Leases, Rents and Profits, Security Agreement, Financing
Statement and Fixture Filing of even date herewith, executed by ALC in favor of
Bank, and (ii) the Second Deed of Trust, Assignment of Rents, Security
Agreement, Financing Statement and Fixture Filing, of even date herewith,
executed by TLC in favor of Bank.

                  "Second Revolving Credit" means the aggregate secured
revolving credit facility under which Bank has undertaken to make Cash Advances
to one or more of the Borrowers, in the maximum principal amount outstanding at
any one time of $5,000,000, as more fully described in and subject to the terms
of Section 2.5 hereof.

                  "Second Revolving Credit Note" means the promissory note made
by Borrowers payable to the order of Bank in the original principal amount of
$5,000,000 to evidence Borrowers' joint and several repayment obligations under
this Agreement with respect to the Second Revolving Credit.

                  "Second Revolving Credit Termination Date" means July 31, 2000
or such later date as may be agreed to in writing by Bank and Borrowers.


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<PAGE>   3


                  3.2 Amended and Restated Definitions. Each of the following
definitions in Section 1.1 of the Loan Agreement is hereby amended and restated
in its entirety as follows:

                  "Adjusted LIBOR Loans" means applicable portions of the
Revolving Credit, the Second Revolving Credit, the Term Loan, and the Line of
Credit bearing interest at a rate determined with reference to the Adjusted
LIBOR.

                  "Base Rate Loans" mean applicable portions of the Revolving
Credit, the Second Revolving Credit, the Term Loan, and the Line of Credit
bearing interest at a rate determined with reference to the Base Rate.

                  "Cash Advance" means any advance of cash to any Borrower under
the Revolving Credit (including draws under Letters of Credit), the Second
Revolving Credit, or the Line of Credit, subject to and in accordance with the
provisions of Article 2 hereof.

                  "Line of Credit" means the aggregate secured line of credit
facility under which Bank may, in its discretion, make Cash Advances to one or
more of the Borrowers, in the maximum principal amount outstanding at any one
time of $20,000,000, as more fully described in and subject to the terms of
Section 2.3 hereof.

                  "Line of Credit Termination Date" means January 15, 2000 or
such other date agreed to in writing by Bank pursuant to Section 2.3.1 hereof.

                  "Loans" mean collectively the Term Loan, the Revolving Credit,
the Second Revolving Credit, and the Line of Credit, and a "Loan" means any of
the Term Loan or any Cash Advance under the Revolving Credit, the Second
Revolving Credit or the Line of Credit, as applicable.

                  "Loan Documents" mean this Agreement, as amended and as may be
hereafter amended, the Notes, as amended and as hereafter may be amended, the
Mortgages, as amended and confirmed by the Mortgage Confirmations, the Second
Mortgages, all financing statements and fixture filings filed or recorded in
connection with this Agreement, and all certificates of Borrowers, or any
Borrower, delivered pursuant to this Agreement.

                  "Mortgages" mean collectively the mortgage granted by ALC and
TLC individually to Bank, each dated as of October 20, 1993 and executed in
connection with the Prior Documents, as confirmed and amended by the Mortgage
Confirmations, and the Second Mortgages.

                  "Notes" means each of the Revolving Credit Note, the Second
Revolving Credit Note, the Term Note and any Line of Credit Note, together with
any substitution therefor and any extension, supplement, amendment, allonge or
addendum thereto.

                  "Revolving Credit Termination Date" means January 15, 2000, or
such later date as may be agreed to in writing by Bank.

                  "Term Loan" means the secured term loan in the maximum
principal amount of



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<PAGE>   4


$18,500,000 as more fully described in and subject to the terms of section 2.1
hereof.

         4. Term Loan Increased. The maximum principal amount of the Term Loan
shall be increased from $15,000,000 to $18,500,000, and Bank shall, subject to
the conditions precedent set forth in Section 17 hereof, fund the additional
$3,500,000 upon request of the Borrowers in one or more installments on or
before October 1, 1998.

         5. Term Loan Interest Rate. Section 2.1.1 of the Loan Agreement is
hereby amended and restated in its entirety as follows:

            2.1.1 Term Loan Interest Rate. The outstanding principal balance of
            the Term Loan shall bear interest at the Interest Rate Option
            selected by Borrowers pursuant to a Notice of Borrowing delivered to
            Bank within the applicable time periods for such Interest Rate
            Option (or at the Base Rate if notice is not given within the
            applicable time periods for other Interest Rate Options). The
            Interest Rate Options for the outstanding principal balance of the
            Term Loan shall be (i) the sum of (A) the Base Rate or the Adjusted
            LIBOR on the relevant Interest Rate Determination Date as selected
            by Borrowers at the time a Notice of Borrowing or Notice of Rate
            Election is given pursuant to sections 2.4.1 and 2.4.2 hereof, plus
            (B) an additional percentage per annum determined in reference to
            Borrowers' Cash Flow Ratio set forth in the table below, or (ii) a
            Fixed Rate:

                             Term Loan Interest Rate

<TABLE>
<CAPTION>
Cash Flow Ratio                                              LIBOR plus                    Base Rate

Greater than or equal to:      But less than:                --------------                ----------------
<S>                            <C>                           <C>                           <C>  
4.0:1                          -----                         2.75%                         plus 0.25%
3.5:1                          4.0:1                         2.50%                         plus 0.25%
3.0:1                          3.5:1                         2.25%                         plus 0
2.5:1                          3.0:1                         1.75%                         plus 0
-------                        2.5:1                         1.50%                         minus 0.25%
</TABLE>



            The Cash Flow Ratio shall be determined and calculated in accordance
            with Section 6.1.13.3 hereof as of the last day of each Calendar
            Quarter on a rolling four Calendar Quarter historical basis. The
            applicable interest rate for the outstanding principal balance of
            the Term Loan shall change when and as the Cash Flow Ratio changes
            as reported to Bank on a properly completed and executed certificate
            substantially in the form attached hereto as Schedule 2.1.1 (each a
            "Ratio Certificate") within thirty days after the expiration of each
            Calendar Quarter. Any change in the Cash Flow Ratio shall change the
            interest rate applicable to all outstanding portions of the Term
            Loan and shall become effective five days after Bank's timely
            receipt of a properly completed and executed Ratio Certificate
            without retroactive effect.



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<PAGE>   5


         6. Term Loan Amortization. Section 2.1.2 of the Loan Agreement is
hereby amended and restated in its entirety as follows:

                           2.1.2 Payment of Principal and Interest. Principal
                  with respect to the Term Loan shall be paid in equal monthly
                  installments of $178,571 each, commencing on the first
                  Business Day of the month next following the Term Loan
                  Amortization Date (Borrowers and Bank acknowledge that no
                  payments of principal have been made or were required to be
                  made prior to October 1, 1998). Commencing on October 1, 1998,
                  the outstanding principal balance of the Term Loan shall be
                  repaid in 59 equal monthly installments of $220,238 each, with
                  a final balloon payment equal to the remaining outstanding
                  principal balance ($5,505,958 if all monthly payments of
                  principal have been made), together with all accrued and
                  unpaid interest and Bank's Costs pertaining thereto, due on
                  September 1, 2003.

         7. Term Loan Fee. Borrowers agree to pay to Bank a fee equal to $17,500
(calculated as 0.5% of $3,500,000) upon the execution of this First Amendment
for structuring the increase to the Term Loan.

         8. Revolving Credit Interest Rate. Section 2.2.2 of the Loan Agreement
is hereby amended and restated as follows:

                  2.2.2 Revolving Credit Interest Rate. Cash Advances under the
         Revolving Credit shall bear interest on the unpaid principal balance
         thereof from the Funding Date until paid in full (whether by
         acceleration or otherwise) at the sum of (i) the Base Rate or the
         Adjusted LIBOR on the relevant Interest Rate Determination Date as
         selected by Borrowers at the time a Notice of Borrowing or Notice of
         Rate Election is given pursuant to Sections 2.4.1 and 2.4.2 hereof,
         plus (ii) an additional percentage per annum determined in reference to
         Borrowers' Cash Flow Ratio set forth in the table below:

                         Revolving Credit Interest Rate

<TABLE>
<CAPTION>
Cash Flow Ratio                                              LIBOR plus                    Base Rate

Greater than or equal to:      But less than:                --------------                ----------------
<S>                            <C>                           <C>                           <C>  
4.0:1                          -----                         2.55%                         plus 0.25%
3.5:1                          4.0:1                         2.30%                         plus 0
3.0:1                          3.5:1                         2.10%                         plus 0
2.5:1                          3.0:1                         1.65%                         plus 0
-------                        2.5:1                         1.40%                         minus 0.25%
</TABLE>



                  The Cash Flow Ratio shall be determined and calculated in
                  accordance with Section 6.1.13.3. hereof as of the last day of
                  each Calendar Quarter on a rolling four Calendar Quarter
                  historical basis. The applicable interest rate for Cash
                  Advances under the Revolving Credit shall change when and as
                  the Cash Flow Ratio changes as reported



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<PAGE>   6


                  to Bank on a properly completed and executed Ratio Certificate
                  within 30 days after the expiration of each Calendar Quarter.
                  Any change in the Cash Flow Ratio shall change the interest
                  rate applicable to all outstanding Cash Advances under the
                  Revolving Credit and shall become effective five days after
                  Bank's timely receipt of a properly completed and executed
                  Ratio Certificate without retroactive effect.

         9.       Line of Credit Reduced. The references to "$25,000,000" in
line six of Section 2.3.1 and in line two of Section 2.3.5 (as the maximum
amount of Cash Advances under the Line of Credit which may be outstanding at any
one time) are hereby replaced with "$20,000,000."

         10.      Line of Credit Interest Rate. Section 2.3.2 of the Loan
Agreement is hereby amended and restated as follows:

                  2.3.2 Line of Credit Interest Rate. Cash Advances under the
         Line of Credit shall bear interest on the unpaid principal balance
         thereof from the Funding Date until paid in full (whether by
         acceleration or otherwise) at the sum of (i) the Base Rate or the
         Adjusted LIBOR on the relevant Interest Rate Determination Date as
         selected by Borrowers at the time a Notice of Borrowing or Notice of
         Rate Election is given pursuant to Sections 2.4.1 and 2.4.2 hereof.,
         plus (ii) an additional percentage per annum determined in reference to
         Borrowers' Cash Flow Ratio set forth in the table below:

                          Line of Credit Interest Rate

<TABLE>
<CAPTION>
Cash Flow Ratio                                              LIBOR plus                    Base Rate

Greater than or equal to:      But less than:                --------------                ----------------
<S>                            <C>                           <C>                           <C>  
4.0:1                          -------------                 2.75%                         plus 0.25%
3.5:1                          4.0:1                         2.50%                         plus 0.25%
3.0:1                          3.5:1                         2.25%                         plus 0
2.5:1                          3.0:1                         1.75%                         plus 0
-------                        2.5:1                         1.50%                         minus 0.25%
</TABLE>



                  The Cash Flow Ratio shall be determined and calculated in
                  accordance with Section 6.1.13.3 hereof as of the last day of
                  each Calendar Quarter on a rolling four Calendar Quarter
                  historical basis. The applicable interest rate for Cash
                  Advances under the Line of Credit shall change when and as the
                  Cash Flow Earnings Ratio changes as reported to Bank on a
                  properly completed and executed Ratio Certificate within 30
                  days after the expiration of each Calendar Quarter. Any change
                  in the Cash Flow Ratio shall change the interest rate
                  applicable to all outstanding Cash Advances under the Line of
                  Credit and shall become effective five days after Bank's
                  timely receipt of a properly completed and executed Ratio
                  Certificate without retroactive effect.

         11.      Notice of Borrowing and Notice of Rate Election Replaced. 
Schedule 2.4.1, the form of Notice of Borrowing, and Schedule 2.4.2, the form of
Notice of Rate Election, are each hereby


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<PAGE>   7


amended and restated in the forms attached to this First Amendment as Schedule
2.4.1 and Schedule 2.4.2, respectively. The interest rates applicable to
Interest Rate Options selected by Borrowers in a Notice of Borrowing or Notice
of Rate Election shall be determined with reference to the most recent Ratio
Certificate prepared by Borrowers for the preceding Calendar Quarter.

         12.      Maximum Available Credit. The references to "$44,000,000" in
the fourth and fifth lines of Section 2.4.13 (as the aggregate maximum available
credit under all Loans) are hereby replaced with "$47,500,000."

         13.      Mandatory Payments. Section 2.4.14 of the Loan Agreement is
hereby amended and restated as follows:

                  2.4.14 Mandatory Payments. In the event that the principal
                  amount outstanding under (i) the Revolving Credit shall at any
                  time exceed $4,000,000, (ii) the Term Loan shall at any time
                  exceed $18,500,000, (iii) the Line of Credit shall at any time
                  exceed $20,000,000, or (iv) the Second Revolving Credit shall
                  at any time exceed $5,000,000, then in any such case,
                  Borrowers shall immediately repay the excess to Bank.


         14.      Second Revolving Credit. The following paragraphs are hereby
added to the Loan Agreement as Section 2.5 and related subsections:

                  2.5 Second Revolving Credit.

                           2.5.1 Amount; Duration; Minimum Advance. Subject to
                  the terms and conditions set forth herein, and provided that
                  no Event of Default or Unmatured Event of Default has occurred
                  and is continuing, commencing on August 19, 1998 and
                  terminating on the Second Revolving Credit Termination Date,
                  Bank shall, upon Borrowers' written request, extend to
                  Borrowers the Second Revolving Credit pursuant to which Bank
                  shall make Cash Advances to Borrowers in an aggregate amount
                  outstanding at any one time not to exceed $5,000,000, which
                  amounts shall be at least $250,000 or integral multiples
                  thereof, and which Borrowers may, from time to time, borrow,
                  repay and re-borrow. On the Second Revolving Credit
                  Termination Date all Cash Advances under the Second Revolving
                  Credit shall become due and payable in accordance with Section
                  2.5.3 hereof and the Second Revolving Credit shall terminate.

                           2.5.2 Interest Rate. Cash Advances under the Second
                  Revolving Credit shall bear interest on the unpaid principal
                  balance thereof from the Funding Date until paid in full
                  (whether by acceleration or otherwise) at the sum of (i) the
                  Base Rate or the Adjusted LIBOR on the relevant Interest Rate
                  Determination Date as selected by Borrowers at the time a
                  Notice of Borrowing or Notice of Rate Election is given
                  pursuant to Sections 2.4.1 and 2.4.2 hereof., plus (ii) an
                  additional percentage per annum determined in reference to
                  Borrowers' Debt to Earnings Ratio set forth in the table
                  below:



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<PAGE>   8



                      Second Revolving Credit Interest Rate
<TABLE>
<CAPTION>
Cash Flow Ratio                                              LIBOR plus                    Base Rate

Greater than or equal to:      But less than:                --------------                ----------------
<S>                            <C>                           <C>                           <C>  
4.0:1                          ------                        2.75%                         plus 0.25%
3.5:1                          4.0:1                         2.50%                         plus 0.25%
3.0:1                          3.5:1                         2.25%                         plus 0
2.5:1                          3.0:1                         1.75%                         plus 0
-------                        2.5:1                         1.50%                         minus 0.25%
</TABLE>


                  The Cash Flow Ratio shall be determined and calculated in
                  accordance with Section 6.1.13.3 hereof as of the last day of
                  each Calendar Quarter on a rolling four Calendar Quarter
                  historical basis. The applicable interest rate for Cash
                  Advances under the Second Revolving Credit shall change when
                  and as the Cash Flow Ratio changes as reported to Bank on a
                  properly completed and executed Ratio Certificate within 30
                  days after the expiration of each Calendar Quarter. Any change
                  in the Cash Flow Ratio shall change the interest rate
                  applicable to all outstanding Cash Advances under the Second
                  Revolving Credit and shall become effective five days after
                  Bank's timely receipt of a properly completed and executed
                  Ratio Certificate without retroactive effect.

                  Notwithstanding the provisions of Section 2.4.4 to the
                  contrary, all Cash Advances under the Second Revolving Credit
                  which are Adjusted LIBOR Loans shall have Interest Periods of
                  30 days.

                           2.5.3 Payment of Principal and Interest. The
                  outstanding principal balance of, and any accrued and unpaid
                  interest on, each Cash Advance under the Second Revolving
                  Credit, and all Bank's Costs pertaining thereto, shall be
                  payable on the earlier of the Second Revolving Credit
                  Termination Date or the date on which the same is payable as
                  provided in Section 8.2 hereof. Interest on the Second
                  Revolving Credit shall be payable as provided in Section 2.4.5
                  hereof.

                           2.5.4 Second Revolving Credit Note. To evidence
                  Borrowers' joint and several obligations under the Second
                  Revolving Credit, Borrowers shall execute and deliver the
                  Second Revolving Credit Note to Bank.

                           2.5.5 Maximum Second Revolving Credit. If the
                  outstanding principal balance of all Cash Advances under the
                  Second Revolving Credit exceeds $5,000,000, Borrowers shall
                  immediately repay such excess to Bank without demand or
                  notice.

                           2.5.6 Conditions Precedent. In addition to the terms
                  and conditions set forth in this Section 2.5, as conditions
                  precedent to the extension by Bank of each Cash Advance under
                  the Second Revolving Credit, Borrowers agree to provide to
                  Bank, in



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<PAGE>   9


                  form and substance satisfactory to Bank and Bank's counsel,
                  the following:

                             (i)     a copy of the invoice or definitive or
                  proposed agreement for the Capital Expenditure to which such
                  Cash Advance relates, together with copies of all other
                  relevant documentation relating thereto; and

                             (ii)    such additional documents or instruments
                  as Bank may reasonably require.


                       2.5.7 Second Revolving Credit Fee. Borrowers shall pay to
                  Bank a fee equal to $25,000 (calculated as 0.5% of $5,000,000)
                  for establishing the Second Revolving Credit.

                       2.5.8 Use of Proceeds. The proceeds of the Second
                  Revolving Credit shall be used by Borrowers for capital
                  improvements related to the ALC plant.

         15.      Additional Collateral.

                  15.1 Revolving Credit and Second Revolving Credit
Collateralized. Borrowers hereby ratify and confirm the grant of security
interests in and to the personal property of Borrowers described in Section
3.1.1 of the Loan Agreement to secure the prompt and full payment of the Term
Loan Indebtedness and performance of the Loan Documents, and Borrowers hereby
re-grant, re-assign and deliver to Bank a security interest in the personal
property described in Section 3.1.1 to secure the prompt and full payment of all
Cash Advances, Bank's Costs and other costs, fees and expenses arising under or
in connection with the Revolving Credit and the Second Revolving Credit.

                  15.2 Accounts; Inventory As additional collateral security for
the prompt and full payment of all of the Indebtedness, all Bank's Costs in
connection therewith and performance of the Loan Documents, in consideration of
the increase to the Term Loan and the establishment of the Second Revolving
Credit, each Borrower hereby grants to Bank a security interest in and lien on
all of such entity's right, title and interest in, to, and under the following
assets, whether now owned or hereafter acquired, created, or reacquired:

                       (i)     all Accounts (as defined in the Uniform
Commercial Code as enacted in Pennsylvania), including without limitation,
accounts receivable, contract rights, book debts, notes, drafts and other
obligations or indebtedness owing to any Borrower that evidence or arise from
the sale, lease, or exchange of goods or other property and/or the performance
of services, rights to any goods, services or other property represented by the
foregoing (including returned or repossessed goods and unpaid Sellers' rights of
rescission, replevin, reclamation and rights to stoppage in transit), moneys due
or to become due to any Borrower under all contracts for the sale, lease or
exchange of goods or other property and/or performance of services (whether
earned by performance), and all proceeds of the foregoing and all collateral
security and guaranties of any kind given by any person with respect to the
foregoing;

                       (ii)    all Inventory (as defined in the Uniform
Commercial Code as enacted in Pennsylvania) wherever located, including without
limitation, finished goods, raw materials,



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<PAGE>   10


work in process, parts, materials, supplies (including packaging and shipping
materials) used or consumed in the quarrying, pyroprocessing, crushing of
limestone or otherwise in the production or manufacture of goods or services for
sale, including all returned and repossessed goods; and

                       (iii)    all proceeds of the foregoing, including 
proceeds of proceeds.

                  15.3 Covenants Regarding Accounts. Except as otherwise
provided herein, each Borrower shall continue to collect, at its own expense,
all amounts due or to become due such Borrower under the Accounts. In connection
with such collections, each Borrower may take such action as such Borrower may
deem necessary or advisable to enforce collection of the Accounts; provided,
that Bank shall have the right at any time after the occurrence of an Event of
Default to: (a) notify the customers or obligors on any Accounts of the
assignment of such Accounts to Bank and to direct such customers or obligors to
make payment of all amounts due or to become due directly to Bank; (b) enforce
collection of any such Accounts; and (c) adjust, settle or compromise the amount
or payment of such Accounts. After the occurrence of an Event of Default: (i)
all amounts and proceeds (including instruments) received by any Borrower with
respect to the Accounts shall be received in trust for the benefit of Bank,
shall be segregated from other funds of Borrowers and shall be forthwith paid
over to Bank in the same form as so received (with any necessary endorsement);
and (ii) no Borrower shall adjust, settle or compromise the amount of payment of
any Account, or release wholly or partly any customer or obligor thereof, or
allow any credit or discount thereon without the prior consent of Bank.

                  15.4 Bank Appointed Attorney-in-Fact.

                       (a) Each Borrower hereby irrevocably appoints Bank as
such Borrower's attorney-in-fact, with full authority in the place and stead of
such Borrower and in the name of such Borrower, Bank or otherwise, from time to
time, upon the occurrence and during the continuance of an Event of Default, in
Bank's reasonable discretion to take any action and to execute any instrument
that Bank may deem necessary or advisable to accomplish the purposes of this
Agreement, including, without limitation:

                           (i)     to obtain and adjust insurance required to be
                  paid to Bank;

                           (ii)    to ask, demand, collect, sue for, recover,
                  compound, receive and give acquittance and receipts for moneys
                  due and to become due under or in respect of any of the
                  Collateral;

                           (iii)   to receive, endorse, and collect any drafts 
                  or other instruments, documents and chattel paper, in 
                  connection with clauses (i) and (ii) above;

                           (iv)    to file any claims or take any action or
                  institute any proceedings that Bank may deem necessary or
                  desirable for the collection of any of the Collateral or
                  otherwise to enforce the rights of Bank with respect to any of
                  the Collateral;

                           (v)     to pay or discharge taxes or liens levied or
                  placed upon or threatened against the Collateral, the legality
                  or validity thereof, and the amounts necessary to discharge
                  the same to be determined by Bank in its sole discretion, and



                                       10
<PAGE>   11



                  such payments made by Bank to become obligations of such
                  Borrower to Bank, due and payable immediately without demand;

                           (vi)    to sign and endorse any invoices, freight or
                  express bills, bills of lading, storage or warehouse receipts,
                  assignments, verifications and notices in connection with
                  Accounts; and

                           (vii)   generally to sell, transfer, pledge, make any
                  agreement with respect to or otherwise deal with any of the
                  Collateral as fully and completely as though Bank were the
                  absolute owner thereof for all purposes, and to do, at Bank's
                  option and Borrowers' expense, at any time or from time to
                  time, all acts and things that Bank reasonably deems necessary
                  to protect, preserve or realize upon the Collateral.

                       (b) Notwithstanding any limitation on the exercise of the
Bank's power contained in (a) above, each Borrower hereby irrevocably appoints
Bank as such Borrower's attorney-in-fact, with full authority in the place and
stead of such Borrower and in the name of such Borrower, Bank or otherwise, at
all times and from time to time, in Bank's discretion, to sign and endorse any
financing statements, continuation statements and other documents necessary or
advisable to perfect the security interests relating to the Collateral.

Each Borrower hereby ratifies, confirms and approves all acts of Bank made or
taken pursuant to this Section. Neither Bank nor any person designated by Bank
shall be liable for any acts or omissions or for any error of judgment or
mistake of fact or law unless the same shall constitute gross negligence or
willful misconduct. This power, being coupled with an interest, is irrevocable
so long as this Agreement shall remain in force.

         16. Financial Covenants. Section 6.1.13.3 of the Loan Agreement is
hereby deleted and replaced with the following:

             6.1.13.3 Cash Flow Ratio. Maintain at all times the Borrowers' Cash
             Flow Ratio at no greater than 4.5:1. Borrowers' Cash Flow Ratio
             shall be tested quarterly by Borrowers' delivery to Bank within 30
             days after each Calendar Quarter of a completed and executed Ratio
             Certificate as of the last day of such Calendar Quarter on a
             rolling four Calendar Quarter historical basis, commencing with the
             Calendar Quarter ending December 31, 1998;

             6.1.13.4 Interest Coverage Ratio. Maintain at all times the ratio
             of Borrowers' EBIT to Interest Expense at no less than 1.5:1 which
             shall be tested annually upon Borrowers' submission of their
             audited consolidated Financial Statements, commencing with the
             Fiscal Year ending December 31, 1998.

         17. Representations and Warranties. To induce Bank to enter into this
First Amendment, Borrowers jointly and severally represent and warrant to Bank
as follows:


                                       11
<PAGE>   12


                  17.1 After giving effect to the modifications contained
herein, all representations, warranties and covenants made by Borrowers to Bank
in the Loan Agreement (except those relating to a specific date) are true and
correct in all material respects as of the date hereof, with the same force and
effect as though made as of the date hereof;

                  17.2 No Event of Default or Unmatured Event of Default has
occurred and is continuing under the Loan Agreement as of the date hereof;

                  17.3 Each Borrower is a corporation validly subsisting under
the laws of the state of its incorporation; the execution, delivery and
performance of this First Amendment and any other documents and instruments
executed and delivered to Bank in connection herewith (i) are within each
Borrower's corporate powers, (ii) have been duly authorized by each Borrower's
Board of Directors, (iii) do not contravene any provision of law or any
indenture, agreement or undertaking to which any Borrower is a party or is
otherwise bound, any Borrower's Certificate of Incorporation, bylaws, or any
resolution of the Board of Directors of any Borrower, and (iv) require no
consent or approval of any governmental authority or any third party; and

                  17.4 This First Amendment and any other documents and
instruments executed and delivered to Bank in connection herewith have been
validly executed and are enforceable against the Borrower or Borrowers party
thereto in accordance with their respective terms.

Any breach by Borrowers of any of the representations and warranties contained
in this First Amendment shall constitute an Event of Default under the Loan
Agreement.

         18. Conditions Precedent. The effectiveness of this First Amendment,
and the performance by Bank of its obligations described herein, are subject to
the conditions precedent that Bank shall have received, in form and substance
satisfactory to Bank:

                  18.1 an Allonge to the Amended and Restated Term Note in the
form attached hereto as Exhibit "A" duly executed by Borrowers;

                  18.2 an Allonge to the Amended and Restated Note in the form
attached hereto as Exhibit "B" duly executed by Borrowers;

                  18.3 the Second Revolving Credit Note in the form attached
hereto as Exhibit "C" duly executed by Borrowers;

                  18.4 the Second Mortgages in the forms attached hereto as
Exhibits "D" and "E" duly executed by Borrowers;

                  18.5 title searches of the Real Estate dated within 15 days
prior to the date hereof in all respects satisfactory to Bank;

                  18.6 a completed and executed Ratio Certificate for the
Calendar Quarter ended June 30, 1998;

                  18.7 a certificate signed by the Secretary of each Borrower
certifying that there have been no amendments or other alterations to such
Borrower's Certificate of Incorporation or



                                       12
<PAGE>   13


Bylaws since December 30, 1997, or if there has been any such modifications,
attaching a true, correct and complete copy thereof;

                  18.8 resolutions of the Boards of Directors of each Borrower
authorizing the execution, delivery and performance of this First Amendment, and
the other documents and instruments executed and delivered to Bank in connection
herewith, certified by such Borrower's Secretary that the same are true and
complete copies of the originals thereof and remain in full force and effect,
not having been modified or rescinded, as of the date hereof; and

                  18.9 UCC-1 Financing Statements listing each Borrower as
debtor and Bank as secured party with respect to the Accounts and Inventory.

                  In addition to the conditions precedent set forth above,
Borrowers agree to obtain within 120 days after the date hereof Phase I
environmental site assessments (the "Site Assessments") of each of the Arkansas
Real Estate and the Texas Real Estate performed by an environmental engineering
firm or firms satisfactory to Bank and promptly and fully to communicate to Bank
the results of such Site Assessments. Borrowers shall comply with all applicable
laws, ordinances, rules, and regulations regarding the cleanup and disposal of
any hazardous substances, pollutants, contaminants, hazardous waste, residual
waste, or solid waste (as such terms are defined in Section 5.1.14 of the Loan
Agreement) on, in and under the Real Estate. It shall be an additional Event of
Default under the Loan Agreement if the anticipated costs of environmental
remediation required by such laws, ordinances, rules and regulations would
result in a Materially Adverse Effect on any Borrower or materially reduce the
value of the Real Estate as a whole or the mineral reserves therein.

         19.  Miscellaneous.

                  19.1 Entire Agreement. The Loan Agreement, as amended by this
First Amendment, and the other Loan Documents, embody the entire agreement and
understanding between Bank and Borrowers. The Loan Agreement, together with this
First Amendment, and all documents executed and delivered herewith, supersede
all prior agreements and understandings relating to subject matter hereof. This
First Amendment together with the Loan Agreement, and the documents executed and
delivered in connection herewith and therewith shall be construed as one
agreement, and in the event of any inconsistency, the provisions of any
promissory note evidencing a portion of the Indebtedness shall control over the
provisions of this First Amendment.

                  19.2 Counterparts. This First Amendment may be executed in any
number of counterparts and by different parties on separate counterparts, each
of which counterparts, when so executed and delivered, shall be deemed to be an
original and all of which counterparts, taken together shall constitute but one
and the same agreement. This First Amendment shall be effective upon the
execution and delivery of a counterpart hereof by each of the parties hereto.

                  19.3 Captions. The captions or headings in this First
Amendment are for convenience of reference only and in no way define, limit, or
describe the scope or intent of any provision of this First Amendment.

                  19.4 Successors and Assigns; Governing Law. This First
Amendment shall be binding upon and inure to the benefit of the respective
successors and assigns of the parties hereto



                                       13
<PAGE>   14


and shall be governed by, and construed and enforced in accordance with, the
internal laws of the Commonwealth of Pennsylvania without regard to its
principles of conflicts of laws.

         IN WITNESS WHEREOF, the undersigned have executed this First Amendment
as of the day and year first written above.



                                      BANK:


                                         FIRST UNION NATIONAL BANK
                                         (successor to CoreStates Bank, N.A.)


                                         By:
                                            --------------------------
                                                CLIFFORD W. KEWLEY,
                                                Vice President

                                   BORROWERS:

                                         UNITED STATES LIME & MINERALS, INC.
Attest:

By: /s/ LARRY T. OHMS                    By: /s/ TIMOTHY W. BYRNE
   --------------------                     ----------------------------
      Larry T. Ohms, Controller             Timothy W. Byrne, President
      and Assistant Treasurer

                                         TEXAS LIME COMPANY


By: /s/ LARRY T. OHMS                    By: /s/ TIMOTHY W. BYRNE
   --------------------                     ----------------------------
      Larry T. Ohms, Controller             Timothy W. Byrne, President
      and Assistant Treasurer

                                         ARKANSAS LIME COMPANY


By: /s/ LARRY T. OHMS                    By: /s/ TIMOTHY W. BYRNE       
   --------------------                     ----------------------------
      Larry T. Ohms, Controller             Timothy W. Byrne, President
      and Assistant Treasurer



                                       14
<PAGE>   15



                                 Schedule 2.1.1

     Cash Flow Ratio Certificate for the Calendar Quarter ended ___________


Clifford W. Kewley, Vice President
1339 Chestnut Street
Transportation, Leasing and Construction Industry Services
11th Floor, Widener Building
FC #1-8-11-24
Philadelphia, PA 19101


         I, ___________________, the undersigned officer of each of United
States Lime & Minerals, Inc. ("U.S. Lime"), Arkansas Lime Company ("ALC") and
Texas Lime Company ("TLC") (U.S. Lime, ALC and TLC shall be referred to herein
collectively as the "Borrowers"), hereby certify to First Union National Bank,
as successor to CoreStates Bank, N.A. ("Bank") that the following information,
with respect to the determination of Borrowers' Cash Flow Ratio for compliance
with the financial covenant in Section 6.1.13.3 of the Amended and Restated Loan
and Security Agreement dated December 30, 1997, as amended, by and among
Borrowers and Bank (the "Loan Agreement") and determining the applicable
additional spread over the Interest Rate Options, is true and correct as of the
date hereof::


<TABLE>
<CAPTION>
Funded Debt
<S>                                   <C>                             <C>
         Term Loan                    $________________
         Revolving Credit             $________________
         Second Revolving Credit      $________________
         Line of Credit               $________________
         Other Funded Debt            $________________

                                          Total Funded Debt          (A) $__________________

EBITDA

         Net Income                   $________________
         plus Interest Expense        $________________
         plus Federal and State taxes $________________
         plus Depreciation            $________________
         plus Amortization            $________________

                                           EBITDA                    (B) $___________________

Ratio (A): (B)             ___________________
Maximum Ratio              4.5:1
</TABLE>

         All initially capitalized terms herein that are not defined herein
shall have the meanings



                                       15
<PAGE>   16



ascribed to them in the Loan Agreement, unless the context requires to the
contrary.

                    The undersigned hereby certifies that no Event of Default or
Unmatured Event of Default under the Loan Agreement has occurred and is
continuing.

                                         UNITED STATES LIME & MINERALS, INC.
                                         ARKANSAS LIME COMPANY
                                         TEXAS LIME COMPANY

                                         By:
                                            ----------------------------


                                       16
<PAGE>   17




                                 Schedule 2.4.1

                               NOTICE OF BORROWING
                       United States Lime & Minerals, Inc.
                              Arkansas Lime Company
                               Texas Lime Company


Clifford W. Kewley
Vice President
First Union National Bank
1339 Chestnut Street
Transportation, Leasing and Construction Industry Services
11th Floor, Widener Building
FC #1-8-11-24
Philadelphia, PA 19101
                                                           _________, 19__


                    This Notice of Borrowing ("Notice") is provided to First
Union National Bank ("Bank") to evidence the request of United States Lime &
Minerals, Inc., Arkansas Lime Company and Texas Lime Company ("Borrowers") to
borrow funds pursuant to Section 2.4.1 of the Amended and Restated Loan and
Security Agreement, dated December 30, 1997, as amended, by and among Borrowers
and Bank (the "Loan Agreement"). All capitalized terms not defined herein shall
have the same meanings as provided in the Loan Agreement unless the context
clearly requires to the contrary.

                    Borrowers desire to borrow _____________________________
__________ to be funded on ____________, 19__ (the "Funding Date"). This Notice
is provided to Bank by 11:00 am. (Philadelphia time) on the same Business Day as
the Funding Date.

                    The Cash Advance requested hereby is to be under the:

                    [ ] Revolving Credit;

                    [ ] Line of Credit, and is accompanied (or preceded) by
                        the documents listed in Section 2.3.6 of the Loan
                        Agreement;

                    [ ] Second Revolving Credit, and is accompanied by the
                        documents listed in Section 2.5.6 of the Loan Agreement.

                    The representations and warranties set forth in the Loan
Agreement and the other Loan Documents (except those which relate to a specific
date) are true and correct as if made on the date hereof. [Include if applicable
-- Borrowers hereby request Bank to open Letters of Credit in the face amount of
$__________ in form of ___________________ with an expiration date of
_____________ to be paid in accordance with the notation attached hereto.]



                                       17
<PAGE>   18



The undersigned hereby certifies that no Event of Default or Unmatured Event of
Default under the Loan Agreement has occurred and is continuing.

                                       UNITED STATES LIME & MINERALS, INC.
                                       ARKANSAS LIME COMPANY
                                       TEXAS LIME COMPANY

                                       By:
                                          ----------------------------

                    This Notice is provided to Bank to confirm a telephone
Notice of Borrowing by Borrowers on __________________, 19__, at approximately
_________________ _.m. (Philadelphia time), as provided in subsection 2.4.1 of
the Loan Agreement.

                                       UNITED STATES LIME & MINERALS, INC.
                                       ARKANSAS LIME COMPANY
                                       TEXAS LIME COMPANY

                                       By:
                                          ----------------------------


                                       18
<PAGE>   19



                                 Schedule 2.4.2

                             NOTICE OF RATE ELECTION
                       United States Lime & Minerals, Inc.
                              Arkansas Lime Company
                               Texas Lime Company


Clifford W. Kewley
First Union National Bank
Vice President
1339 Chestnut Street
Transportation, Leasing and Construction Industry Services
11th Floor, Widener Building
FC #1-8-11-24
Philadelphia, PA 19101
                                                           _________, 19__

         This Notice of Rate Election ("Notice") is provided to First Union
National Bank ("Bank") to evidence the desire of United States Lime & Minerals,
Inc., Arkansas Lime Company and Texas Lime Company ("Borrowers") to continue or
change the basis for determining the interest rate on Loans pursuant to the
Amended and Restated Loan and Security Agreement, dated December 30, 1997, as
amended, by and among Borrowers and Bank (the "Loan Agreement"). All capitalized
terms not defined herein shall have the same meaning as provided in the Loan
Agreement.

         Borrowers desire to (change) (continue) $____________ of (Revolving
Credit Loans) (Term Loans) (Line of Credit Loans) (Second Revolving Credit
Loans) for which (there is no present Interest Period) (the Interest Period
expires on _________) (to) (as) (Adjusted LIBOR Loans) (a Fixed Rate Loan) as
follows:

$___________     Adjusted LIBOR Loans with an Interest Period of _____________
                 months, pursuant to Section 2.4.2 (or with an interest period
                 of one month pursuant to Section 2.5.2) of the Loan Agreement;
                 the first day of such Interest Period is hereby requested to be
                 ______.


$___________     Base Rate Loan commencing _______________.

$___________     Fixed Rate Loan to bear interest at __% per annum for the
                 period from ___________ to _____________, pursuant to Section
                 2.1.4 of the Loan Agreement.

         This Notice, if requesting an Adjusted LIBOR Loan, shall be irrevocable
on and after the Interest Rate Determination Date requested herein. The
undersigned hereby certifies that no Event of Default or Unmatured Event of
Default under the Loan Agreement has occurred and is continuing.

                                       UNITED STATES LIME & MINERALS, INC.
                                       ARKANSAS LIME COMPANY
                                       TEXAS LIME COMPANY

                                       By:
                                          ----------------------------
<PAGE>   20


                                                                     Exhibit "A"

                                     ALLONGE
                                       TO
                         AMENDED AND RESTATED TERM NOTE


                    ALLONGE, dated August ___, 1998 attached to and forming a
part of the Amended and Restated Term Note, dated December 30, 1997 (the "Term
Note"), made by 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,
the "Borrowers"), payable to the order of First Union National Bank, as
successor to CoreStates Bank, N.A. (the "Bank") in the original principal amount
of $15,000,000.

                    The first paragraph of the Term Note is amended and restated
to read in full as follows:

                  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, a national
                  banking association, as successor to CoreStates Bank, N.A.,
                  its successors and assigns ("Bank"), the principal sum of
                  Eighteen Million Five Hundred Thousand Dollars ($18,500,000)
                  together with interest thereon at (i) a fluctuating rate per
                  annum equal to the Base Rate or the Adjusted LIBOR plus an
                  additional percentage per annum determined with reference to
                  Borrowers' Cash Flow Ratio pursuant to the table set forth in
                  Section 2.1.1 of the Amended and Restated Loan and Security
                  Agreement of even date herewith, as amended (the "Loan
                  Agreement") by and among Bank and Borrowers, which fluctuating
                  rate shall change at the times and under the conditions set
                  forth in the Loan Agreement, or (ii) at a Fixed Rate per
                  annum, payable in accordance with Section 2.1 of the Loan
                  Agreement.


                    The third paragraph of the Term Note is amended and restated
to read in full as follows:

                  Principal shall be paid in equal monthly installments of
                  $178,571 each commencing on the first business day of the
                  month next following the Term Loan Amortization Date
                  (Borrowers and Bank acknowledge that no payments of principal
                  have been made or were required to be made prior to October 1,
                  1998). Commencing on October 1, 1998, the outstanding
                  principal balance of the Term Loan shall be repaid in 59 equal
                  monthly installments of $ 220,238 each followed by a final
                  balloon payment of the remaining outstanding principal balance
                  of the Term Loan, together with all accrued and unpaid
                  interest and Bank's Costs pertaining thereto, due on September
                  1, 2003. Each installment of principal hereunder, including
                  the final balloon payment, shall be due on the first Business
                  Day of each month.


<PAGE>   21

                    In all other respects, the Term Note is confirmed, ratified
and approved and, as amended by this Allonge, shall continue in full force and
effect.

                    IN WITNESS WHEREOF, the Borrowers and the Bank have caused
this Allonge to be executed and delivered by their respective duly authorized
officers as of the date and year first above written.

Attest:                                  UNITED STATES LIME & MINERALS, INC.


By: /s/ LARRY T. OHMS                    By: /s/ TIMOTHY W. BYRNE
   -----------------------------            ------------------------------
    Larry T. Ohms, Controller               Timothy W. Byrne,
    and Assistant Treasurer                 President


Attest:                                  TEXAS LIME COMPANY


By: /s/ LARRY T. OHMS                    By: /s/ TIMOTHY W. BYRNE         
   -----------------------------            ------------------------------
    Larry T. Ohms, Controller               Timothy W. Byrne,
    and Assistant Treasurer                 President


Attest:                                  ARKANSAS LIME COMPANY


By: /s/ LARRY T. OHMS                    By: /s/ TIMOTHY W. BYRNE
   -----------------------------            ------------------------------
    Larry T. Ohms, Controller               Timothy W. Byrne,
    and Assistant Treasurer                 President



                                         Accepted and agreed to:

                                         FIRST UNION NATIONAL BANK,
                                         (successor to CoreStates Bank, N.A.)

                                         By:
                                            ------------------------------
                                                  Clifford W. Kewley
                                                  Vice President


                                     ( 2 )
<PAGE>   22

                                                                     Exhibit "B"

                                     ALLONGE
                                       TO
                            AMENDED AND RESTATED NOTE


                    ALLONGE, dated August 31, 1998 attached to and forming a
part of the Amended and Restated Note, dated December 30, 1997 (the "Note"),
made by 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, the "Borrowers"),
payable to the order of First Union National Bank, as successor to CoreStates
Bank, N.A. (the "Bank") in the original principal amount of $4,000,000.

                    The third paragraph of the Note is amended and restated to
read in full as follows:

                          "Borrowers also 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 at a fluctuating rate
                          per annum equal to the Base Rate or the Adjusted LIBOR
                          plus an additional percentage per annum determined
                          with reference to Borrowers' Cash Flow Ratio pursuant
                          to the table set forth in Section 2.2.2 of the Loan
                          Agreement, which fluctuating rate shall change at the
                          times and under the conditions set forth in the Loan
                          Agreement."

                    In all other respects, the Note is confirmed, ratified and
approved and, as amended by this Allonge, shall continue in full force and
effect.

                    IN WITNESS WHEREOF, the Borrowers and the Bank have caused
this Allonge to be executed and delivered by their respective duly authorized
officers as of the date and year first above written.

Attest:                             UNITED STATES LIME & MINERALS, INC.


By: /s/ LARRY T. OHMS               By: /s/ TIMOTHY W. BYRNE
   ------------------------------      --------------------------------
        Larry T. Ohms, Controller      Timothy W. Byrne,
        and Assistant Treasurer        President



                       [Signatures continued on next page]


<PAGE>   23




Attest:                             TEXAS LIME COMPANY


By: /s/ LARRY T. OHMS               By: /s/ TIMOTHY W. BYRNE
   ------------------------------      --------------------------------
        Larry T. Ohms, Controller      Timothy W. Byrne,
        and Assistant Treasurer        President


Attest:                             ARKANSAS LIME COMPANY


By: /s/ LARRY T. OHMS               By: /s/ TIMOTHY W. BYRNE
   ------------------------------      --------------------------------
        Larry T. Ohms, Controller      Timothy W. Byrne,
        and Assistant Treasurer        President



                                    Accepted and agreed to:

                                    FIRST UNION NATIONAL BANK,
                                    (successor to CoreStates Bank, N.A.)

                                    By:
                                       --------------------------------
                                             Clifford W. Kewley
                                             Vice President


                                     ( 2 )
<PAGE>   24

                                                                     Exhibit "C"
                             SECOND REVOLVING CREDIT
                                      NOTE

$5,000,000                                             August 31, 1998

         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, a national banking
association, as successor to CoreStates Bank, N.A., and 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 Second Revolving Credit pursuant to the Amended and
Restated Loan and Security Agreement dated December 30, 1997, by and among
Borrowers and Bank, as amended by the First Amendment to Amended and Restated
Loan and Security Agreement of even date herewith (collectively, the "Loan
Agreement"), which principal amount and all accrued and unpaid interest thereon
and Bank's Costs pertaining thereto shall be payable on July 31, 2000, or such
later date as may be agreed to in writing by Bank.

         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, at a fluctuating rate per annum equal to the
sum of the Base Rate or the Adjusted LIBOR plus an additional percentage per
annum determined with reference to Borrrowers' Cash Flow Ratio pursuant to the
table set forth in Section 2.5.2 of the Loan Agreement, which fluctuating rate
shall change at the times and under the conditions set forth in 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, Transportation, Leasing and Construction
Industry Services, 11th Floor, Widener Building, FC #1-8-11-24, Philadelphia, PA
19101, or such other place as shall be designated in writing for such purpose in
accordance with the terms of the Loan Agreement.

         Each Borrower authorizes Bank to charge such Borrower's demand deposit
account with



<PAGE>   25


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 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



                                     ( 2 )
<PAGE>   26



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 performance 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>   27



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.


Attest:                             UNITED STATES LIME & MINERALS, INC.


By: /s/ LARRY T. OHMS               By: /s/ TIMOTHY W. BYRNE
   ------------------------------      --------------------------------
        Larry T. Ohms, Controller      Timothy W. Byrne,
        and Assistant Treasurer        President


                                    TEXAS LIME COMPANY


By: /s/ LARRY T. OHMS               By: /s/ TIMOTHY W. BYRNE
   ------------------------------      --------------------------------
        Larry T. Ohms, Controller      Timothy W. Byrne,
        and Assistant Treasurer        President


Attest:                             ARKANSAS LIME COMPANY


By: /s/ LARRY T. OHMS               By: /s/ TIMOTHY W. BYRNE
   ------------------------------      --------------------------------
        Larry T. Ohms, Controller      Timothy W. Byrne,
        and Assistant Treasurer        President



                                     ( 4 )
<PAGE>   28


                              TRANSACTIONS ON NOTE

<TABLE>
<CAPTION>
                                         Amount of       Outstanding 
                      Amount of Loan     Principal Paid  Principal Balance  Notation Made
Date                  Made This Date     This Date       This Date          By
----                  --------------     --------------  -----------------  -------------
<S>                   <C>                <C>             <C>                <C>    
</TABLE>


                                     ( 5 )