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                                                                    EXHIBIT 4(e)

                               February 25, 2004

Applied Industrial Technologies, Inc.
One Applied Plaza
Cleveland, Ohio 44115

      Re: AMENDMENT TO PRIVATE SHELF AGREEMENT

Ladies and Gentlemen:

      Reference is made to that certain Private Shelf Agreement dated as of
November 27, 1996 (as amended prior to the date hereof, the "AGREEMENT") between
Applied Industrial Technologies, Inc., an Ohio corporation formerly known as
Bearings, Inc. (the "COMPANY"), and The Prudential Insurance Company of America
("PRUDENTIAL"), pursuant to which the Company issued and sold and Prudential
purchased the Company's 6.60% Series B Notes in the original aggregate principal
amount of $50,000,000, due December 8, 2007. Capitalized terms used herein and
not otherwise defined herein shall have the meanings assigned to such terms in
the Agreement.

      Pursuant to the request of the Company and in accordance with the
provisions of paragraph 11C of the Agreement, the parties hereto agree as
follows:

      SECTION 1. Amendment. From and after the date this letter becomes
effective in accordance with its terms, the Agreement is amended as follows:

      1.1   The first sentence of Paragraph 1 of the Agreement is amended by
deleting the phrase "no less than seven (7) years and no more than twenty (20)
years after the issuance thereof," and replacing it with the following:

            "no more than twelve (12) years after the issuance thereof, to have
      an average life, in the case of each Note so issued, of no more than ten
      (10) years after the date of original issuance thereof,".

      1.2   Paragraph 2B of the Agreement is amended to delete in its entirety
clause (i) thereof and to substitute therefor the following: "(i) February 25,
2007, and".

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Applied Industrial Technologies, Inc.
February 25,2004
Page 2

      1.3   The Company and Prudential (as such term is defined in the Agreement
after giving effect to this letter) expressly agree and acknowledge that as of
the date hereof the Available Facility Amount is $100,000,000. NOTWITHSTANDING
THE FOREGOING, THIS AMENDMENT AND THE AGREEMENT HAVE BEEN ENTERED INTO ON THE
EXPRESS UNDERSTANDING THAT NEITHER PRUDENTIAL NOR ANY PRUDENTIAL AFFILIATE (AS
SUCH TERM IS DEFINED IN THE AGREEMENT AFTER GIVING EFFECT TO THIS LETTER) SHALL
BE OBLIGATED TO MAKE OR ACCEPT OFFERS TO PURCHASE PRIVATE SHELF NOTES, OR TO
QUOTE RATES, SPREADS OR OTHER TERMS WITH RESPECT TO SPECIFIC PURCHASES OF
PRIVATE SHELF NOTES, AND THE FACILITY SHALL IN NO WAY BE CONSTRUED AS A
COMMITMENT BY PRUDENTIAL OR ANY PRUDENTIAL AFFILIATE.

      1.4   Paragraph 3A(5) of the Agreement is amended by replacing the
reference to "Regulation G" with a reference to "Regulation T, U or X".

      1.5   Paragraph 8I of the Agreement is amended by: (a) replacing the
reference to "REGULATION G, Etc." in the title of such paragraph with a
reference to "USE OF PROCEEDS."; (b) replacing the reference to "Regulation G
(12 CFR Part 207)" in the second sentence of such paragraph with a reference to
"Regulation U (12 CFR Part 221)"; (c) replacing the other two references to
"Regulation G" in the second sentence of such paragraph with a reference to
"Regulation U"; (d) replacing the reference to "Regulation G" in the third
sentence of such paragraph with a reference to "Regulation T, Regulation U or
any other regulation"; and (e) inserting the following new sentence at the end
of such paragraph:

            "The Company is not a Person described in Section 1 of the
      Anti-Terrorism Order and none of the proceeds from the issuance of the
      Notes will, to the Company's knowledge, directly or indirectly, be
      transferred to or used for the benefit of any such Person."

      1.6   Paragraph 9B of the Agreement is amended and restated to read in its
entirety as follows:

            "9B. SOURCE OF FUNDS. At least one of the following statements is an
      accurate representation as to each source of funds (a "SOURCE") to be used
      by such Purchaser to pay the purchase price of the Notes to be purchased
      by such Purchaser hereunder:

                  (i)   the Source is an "insurance company general account" (as
      the term is defined in the United States Department of Labor's Prohibited
      Transaction Exemption ("PTE") 95-60) in respect of which the reserves and
      liabilities (as defined by the annual statement for life insurance
      companies

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Applied Industrial Technologies, Inc.
February 25,2004
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      approved by the National Association of Insurance Commissioners (the "NAIC
      ANNUAL STATEMENT")) for the general account contract(s) held by or on
      behalf of any employee benefit plan together with the amount of the
      reserves and liabilities for the general account contract(s) held by or on
      behalf of any other employee benefit plans maintained by the same employer
      (or affiliate thereof as defined in PTE 95-60) or by the same employee
      organization in the general account do not exceed 10% of the total
      reserves and liabilities of the general account (exclusive of separate
      account liabilities) plus surplus as set forth in the NAIC Annual
      Statement filed with such Purchaser's state of domicile; or

                  (ii)  the Source is a separate account that is maintained
      solely in connection with such Purchaser's fixed contractual obligations
      under which the amounts payable, or credited, to any employee benefit plan
      (or its related trust) that has any interest in such separate account (or
      to any participant or beneficiary of such plan (including any annuitant))
      are not affected in any manner by the investment performance of the
      separate account; or

                  (iii) the Source is either (a) an insurance company pooled
      separate account, within the meaning of PTE 90-1 or (b) a bank collective
      investment fund, within the meaning of the PTE 91-38 and, except as
      disclosed by such Purchaser to the Company in writing pursuant to this
      clause (iii), no employee benefit plan or group of plans maintained by the
      same employer or employee organization beneficially owns more than 10% of
      all assets allocated to such pooled separate account or collective
      investment fund; or

                  (iv)  the Source constitutes assets of an "investment fund"
      (within the meaning of Part V of PTE 84-14 (the "QPAM EXEMPTION")) managed
      by a "qualified professional asset manager" or "QPAM" (within the meaning
      of Part V of the QPAM Exemption), no employee benefit plan's assets that
      are included in such investment fund, when combined with the assets of all
      other employee benefit plans established or maintained by the same
      employer or by an affiliate (within the meaning of Section V(c)(1) of the
      QPAM Exemption) of such employer or by the same employee organization and
      managed by such QPAM, exceed 20% of the total client assets managed by
      such QPAM, the conditions of Part I(c) and (g) of the QPAM Exemption are
      satisfied, neither the QPAM nor a person controlling or controlled by the
      QPAM (applying the definition of "control" in Section V(e) of the QPAM
      Exemption) owns a 5% or more interest in the Company and (a) the identity
      of such QPAM and (b) the names of all employee benefit plans whose assets
      are included in such investment fund have been disclosed to the Company in
      writing pursuant to this clause (iv); or

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Applied Industrial Technologies, Inc.
February 25,2004
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                  (v)   the Source constitutes assets of a "plan(s)" (within the
      meaning of Section IV of PTE 96-23 (the "INHAM EXEMPTION")) managed by an
      "in-house asset manager" or "INHAM" (within the meaning of Part IV of the
      INHAM exemption), the conditions of Part I(a), (g) and (h) of the INHAM
      Exemption are satisfied, neither the INHAM nor a person controlling or
      controlled by the INHAM (applying the definition of "control" in Section
      IV(h) of the INHAM Exemption) owns a 5% or more interest in the Company
      and (a) the identity of such INHAM and (b) the name(s) of the employee
      benefit plan(s) whose assets constitute the Source have been disclosed to
      the Company in writing pursuant to this clause (v); or

                  (vi)  the Source is a governmental plan; or

                  (vii) the Source is one or more employee benefit plans, or a
      separate account or trust fund comprised of one or more employee benefit
      plans, each of which has been identified to the Company in writing
      pursuant to this clause (vii); or

                  (viii) the Source does not include assets of any employee
      benefit plan, other than a plan exempt from the coverage of ERISA.

            As used in this paragraph 9B, the terms "EMPLOYEE BENEFIT PLAN",
      "GOVERNMENTAL PLAN", and "SEPARATE ACCOUNT" shall have the respective
      meanings assigned to such terms in Section 3 of ERISA."

      1.7   The Agreement (and each of its Schedules and Exhibits) is amended by
replacing each reference to "The Prudential Insurance Company of America" with a
reference to "Prudential Investment Management, Inc."

      1.8   The definition of "Affiliate" in paragraph 10B of the Agreement is
amended and restated to read in its entirety as follows:

            "`Affiliate' of any Person shall mean (i) any other Person directly
or indirectly controlling, controlled by, or under direct or indirect common
control with such Person (except, with respect to the Company, a Subsidiary) and
(ii) with respect to Prudential, shall include any managed account, investment
fund or other vehicle for which Prudential or any Prudential Affiliate acts as
investment advisor or portfolio manager. A Person shall be deemed to control a
corporation if such Person possesses, directly or indirectly, the power to
direct or cause the direction of the management and policies of such
corporation, whether through the ownership of voting securities, by contract or
otherwise."

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Applied Industrial Technologies, Inc.
February 25,2004
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      1.9   Paragraph 10B of the Agreement is amended by inserting the following
new definition of "Anti-Terrorism Order" in proper alphabetical order:

            "`ANTI-TERRORISM ORDER' means Executive Order No. 13,224, 66 Fed.
      Reg. 49,079 (2001) issued by the President of the U.S. (Executive Order
      Blocking Property and Prohibiting Transactions with Persons Who Commit,
      Threaten to Commit, or Support Terrorism)."

      1.10  Clause (ii) of the definition of "Authorized Officer" in paragraph
10B of the Agreement is amended and restated to read in its entirety as follows:

      "(ii) in the case of Prudential, any officer of Prudential designated as
      its `Authorized Officer' in the Information Schedule or any officer of
      Prudential designated as its `Authorized Officer' for the purpose of this
      Agreement in a certificate executed by one of its Authorized Officers."

      1.11  The definition of "Prudential" in paragraph 10B of the Agreement is
amended and restated to read in its entirety as follows:

            "'Prudential' shall mean Prudential Investment Management, Inc."

      1.12  The definition of "Prudential Affiliate" in paragraph 10B of the
Agreement is amended and restated to read in its entirety as follows:

            "'Prudential Affiliate' shall mean any Affiliate of Prudential."

      1.13  Paragraph 10C of the Agreement is amended by adding the following
sentence at the end thereof:

            "Any reference herein to any specific citation, section or form of
      law, statute, rule or regulation shall refer to such new, replacement or
      analogous citation, section or form should such citation, section or form
      be modified, amended or replaced."

      1.14  The Agreement is hereby amended by adding the Information Schedule
attached hereto as Exhibit A.

      1.15  Each of Exhibit A (Form of Note) to the Agreement and each Note
currently outstanding is amended by replacing each reference to "Morgan Guaranty
Trust Company of New York" in such exhibit with a reference to "The Bank of New
York".

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Applied Industrial Technologies, Inc.
February 25,2004
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      1.16  Exhibit D-2 (Form of Opinion of Company's Counsel) is amended by
replacing the reference to "Regulation G" in paragraph 4 thereof with a
reference to "Regulation T, U or X".

      SECTION 2. Representation and Warranty. The Company hereby represents and
warrants that no Default or Event of Default exists under the Agreement as of
the date hereof.

      SECTION 3. Assumption. From and after the date this letter becomes
effective in accordance with its terms, Prudential Investment Management, Inc.
("PIM") hereby assumes from The Prudential Insurance Company of America each of
the rights and obligations of "Prudential" under the Agreement. It being
understood and agreed that (a) neither The Prudential Insurance Company of
America nor any other holder of Notes is hereby assigning any portion of their
interests in their respective Notes to PIM and (b) The Prudential Insurance
Company of America and each other holder of Notes hereby retain all of their
rights, powers, remedies and privileges conferred upon a holder of Notes under
the Agreement.

      SECTION 4. Conditions Precedent. This letter shall be deemed effective as
of the date hereof upon (i) the return on or before March 5, 2004 by the Company
to PIM of a counterpart hereof duly executed by the Company, PIM and each holder
of Notes, and (ii) the payment of a $45,000 non-refundable structuring fee to
PIM at its account as follows: The Bank of New York, New York, New York, ABA #
021 000 018, Acct # 890 0496 916 (reference Applied Industrial). Upon execution
hereof by the Company, this letter should be returned to: Prudential Capital
Group, Two Prudential Plaza, Suite 5600, Chicago, Illinois 60601, Attention:
Armando M. Gamboa.

      SECTION 5. Reference to and Effect on Agreement. Upon the effectiveness of
this letter, each reference to the Agreement and the Notes in any other
document, instrument or agreement shall mean and be a reference to the Agreement
and the Notes as modified by this letter. Except as specifically set forth in
Section 1 hereof, each of the Agreement and the Notes shall remain in full force
and effect and each is hereby ratified and confirmed in all respects.

      SECTION 6. Confirmation of Guarantees. By its signature below, each
Subsidiary party to a Guaranty of Payment of Debt agrees and consents to the
terms and provisions of this Amendment and agrees that its Guaranty of Payment
of Debt shall remain in full force and effect and is hereby ratified and
confirmed in all respects after giving effect to this Amendment.

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Applied Industrial Technologies, Inc.
February 25,2004
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      SECTION 7. Governing Law. THIS LETTER SHALL BE CONSTRUED AND ENFORCED IN
ACCORDANCE WITH, AND THE RIGHTS OF THE PARTIES SHALL BE GOVERNED BY, THE LAW OF
THE STATE OF ILLINOIS (EXCLUDING ANY CONFLICTS OF LAW RULES WHICH WOULD
OTHERWISE CAUSE THIS LETTER TO BE CONSTRUED OR ENFORCED IN ACCORDANCE WITH, OR
THE RIGHTS OF THE PARTIES TO BE GOVERNED BY, THE LAWS OF ANY OTHER
JURISDICTION).

            [THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK.]

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Applied Industrial Technologies, Inc.
February 25,2004
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      SECTION 8. Counterparts; Section Titles. This letter may be executed in
any number of counterparts and by different parties hereto in separate
counterparts, each of which when so executed and delivered shall be deemed to be
an original and all of which taken together shall constitute but one and the
same instrument. The section titles contained in this letter are and shall be
without substance, meaning or content of any kind whatsoever and are not a part
of the agreement between the parties hereto.

                                       Very truly yours,

                                       PRUDENTIAL INVESTMENT
                                       MANAGEMENT, INC.

                                       By:   /s/ Mathew Douglass
                                          -------------------------------------
                                                     Vice President

                                       THE PRUDENTIAL INSURANCE COMPANY
                                          OF AMERICA

                                       By:   /s/ Mathew Douglass
                                          -------------------------------------
                                                     Vice President

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Applied Industrial Technologies, Inc.
February 25,2004
Page 9

Agreed and Accepted:

APPLIED INDUSTRIAL TECHNOLOGIES, INC.

By:    /s/ Mark O. Eisele
   --------------------------------------------
Name:      Mark O. Eisele
Title:     Vice President-CFO & Treasurer

Consented to:

APPLIED INDUSTRIAL TECHNOLOGIES-CA LLC
APPLIED INDUSTRIAL TECHNOLOGIES-DBB, INC.
APPLIED INDUSTRIAL TECHNOLOGIES-DIXIE, INC.
APPLIED INDUSTRIAL TECHNOLOGIES-INDIANA LLC
APPLIED INDUSTRIAL TECHNOLOGIES-MAINLINE, INC.
APPLIED INDUSTRIAL TECHNOLOGIES-TX LP
APPLIED INDUSTRIAL TECHNOLOGIES-PA LLC
AIR AND HYDRAULICS ENGINEERING, INCORPORATED
ESI ACQUISITION CORPORATION
THE OHIO BALL BEARING COMPANY
BEARINGS PAN AMERICAN, INC.
BEARINGS SALES AND SERVICES, INC.
AIR DRAULICS ENGINEERING CO.
APPLIED LINK, INC.
APPLIED-MICHIGAN, LTD
APPLIED INDUSTRIAL TECHNOLOGIES-CAPITAL LLC

By:   /s/ Mark O. Eisele
   --------------------------------------------
Name:     Mark O. Eisele
Title:    Vice President-CFO & Treasurer