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                                                                    EXHIBIT 23.1
 
                            [FURMAN SELZ LETTERHEAD]
 
                           CONSENT OF FURMAN SELZ LLC
 
     We hereby consent to the use in the Registration Statement of Eastern
Enterprises on Form S-4, and in the related Proxy Statement of Essex County Gas
Company, of our opinion dated December 19, 1997 appearing as Annex B to such
Proxy Statement/Prospectus, and to the description therein of such opinion and
to the references therein to us under the headings "SUMMARY" and "THE MERGER".
In giving the foregoing consent, we do not admit that we come within the
category of persons whose consent is required under Section 7 of the Securities
Act of 1933, as amended (the "Securities Act"), or the rules and regulations
promulgated thereunder, nor do we admit that we are experts with respect to any
part of such Registration Statement within the meaning of the term "experts" as
used in the Securities Act or the rules and regulations promulgated thereunder.
 
FURMAN SELZ LLC
 
By: /s/ WILLIAM K. PERRIN
 
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    William K. Perrin
    Managing Director
 
New York, New York
May 7, 1998