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                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
     We, the undersigned directors and officers of Cabot Corporation, hereby
severally constitute and appoint Robert Rothberg and Sarah W. Saunders, and each
of them, our true and lawful attorneys with full power to (i) sign for us and in
our names in the capacities indicated below Annual Reports on Form 10-K pursuant
to Section 13 or 15(d) of the Securities Exchange Act of 1934 of Cabot
Corporation for the fiscal year ended September 30, 1998, and any and all
amendments thereto, hereby ratifying and confirming our signatures as they may
be signed by our said attorneys, or any of them, to said Reports and to any and
all amendments to said Reports; and (ii) to file such Reports and amendments
with the Securities and Exchange Commission and with applicable stock exchanges
on behalf of Cabot Corporation.
 
     WITNESS our hands and common seal on the date set forth below.
 


                   SIGNATURE                                    TITLE                      DATE
                   ---------                                    -----                      ----
                                                                               
 
              /s/ SAMUEL W. BODMAN                Director, Chairman and Chief       November 13, 1998
- ------------------------------------------------    Executive Officer
                Samuel W. Bodman
 
             /s/ KENNETT F. BURNES                Director and President             November 13, 1998
- ------------------------------------------------
               Kennett F. Burnes
 
              /s/ ROBERT L. CULVER                Executive Vice President and       November 13, 1998
- ------------------------------------------------    Chief Financial Officer
                Robert L. Culver
 
            /s/ WILLIAM T. ANDERSON               Controller                         November 13, 1998
- ------------------------------------------------
              William T. Anderson
 
              /s/ JANE C. BRADLEY                 Director                           November 13, 1998
- ------------------------------------------------
                Jane C. Bradley
 
              /s/ JOHN G.L. CABOT                 Director                           November 13, 1998
- ------------------------------------------------
                John G.L. Cabot
 
             /s/ JOHN S. CLARKESON                Director                           November 13, 1998
- ------------------------------------------------
               John S. Clarkeson
 
            /s/ ARTHUR L. GOLDSTEIN               Director                           November 13, 1998
- ------------------------------------------------
              Arthur L. Goldstein
 
            /s/ ROBERT P. HENDERSON               Director                           November 13, 1998
- ------------------------------------------------
              Robert P. Henderson
 
              /s/ ARNOLD S. HIATT                 Director                           November 13, 1998
- ------------------------------------------------
                Arnold S. Hiatt
 
               /s/ GAUTAM S. KAJI                 Director                           November 13, 1998
- ------------------------------------------------
                 Gautam S. Kaji

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                   SIGNATURE                                    TITLE                      DATE
                   ---------                                    -----                      ----
                                                                               
              /s/ JOHN H. MCARTHUR                Director                           November 13, 1998
- ------------------------------------------------
                John H. McArthur
 
           /s/ RODERICK C.G. MACLEOD              Director                           November 13, 1998
- ------------------------------------------------
             Roderick C.G. MacLeod
 
              /s/ JOHN F. O'BRIEN                 Director                           November 13, 1998
- ------------------------------------------------
                John F. O'Brien
 
              /s/ DAVID V. RAGONE                 Director                           November 13, 1998
- ------------------------------------------------
                David V. Ragone
 
           /s/ CHARLES P. SIESS, JR.              Director                           November 13, 1998
- ------------------------------------------------
             Charles P. Siess, Jr.
 
              /s/ MORRIS TANENBAUM                Director                           November 13, 1998
- ------------------------------------------------
                Morris Tanenbaum
 
              /s/ LYDIA W. THOMAS                 Director                           November 13, 1998
- ------------------------------------------------
                Lydia W. Thomas
 
              /s/ MARK S. WRIGHTON                Director                           November 13, 1998
- ------------------------------------------------
                Mark S. Wrighton