[EXHIBIT 4h TO COLONIAL GAS COMPANY
                    10-K FOR YEAR ENDED DECEMBER 31, 1998]


                        AMENDMENT TO RIGHTS AGREEMENT

            This  AMENDMENT,  dated as of October 17, 1998, is between  Colonial
Gas Company, a Massachusetts corporation (the "Company"), and BankBoston,  N.A.,
as rights agent (the "Rights Agent").

                                   Recitals

            A.  The  Company  and the  Rights  Agent  are  parties  to a  Rights
Agreement dated as of December 1, 1993 (the "Rights Agreement").

            B. Eastern Enterprises ("Eastern") and the Company have entered into
an Agreement and Plan of  Reorganization  (the "Merger  Agreement")  pursuant to
which the  Company  will  merge  (the  "Merger")  with and into a  Massachusetts
corporation to be formed as a wholly-owned subsidiary of Eastern ("Merger Sub").
The Board of Directors of the Company has approved the Merger  Agreement and the
Merger.

            C.  Pursuant  to Section 27 of the  Rights  Agreement,  the Board of
Directors  of the  Company  has  determined  that  an  amendment  to the  Rights
Agreement as set forth herein is necessary and desirable in connection  with the
foregoing and the Company and the Rights Agent desire to evidence such amendment
in writing.

            Accordingly, the parties agree as follows:

            1. Amendment of Section 1(a).  Section 1(a) of the Rights  Agreement
is amended to add the following sentence at the end thereof:

            "Notwithstanding  anything in this Rights Agreement to the contrary,
            neither  Eastern  nor any of its  existing or future  Affiliates  or
            Associates  shall be  deemed  to be an  Acquiring  Person  solely by
            virtue  of (i) the  execution  of the  Merger  Agreement,  (ii)  the
            acquisition of Common Stock pursuant to the Merger  Agreement or the
            consummation of the Merger,  or (iii) the  consummation of the other
            transactions contemplated by the Merger Agreement."

            2. Amendment of Section 1(ah). Section 1(ah) of the Rights Agreement
is amended to add the following proviso at the end thereof:

            "; provided,  however,  that no Triggering Event shall result solely
            by virtue of (i) the  execution  of the Merger  Agreement,  (ii) the
            acquisition of Common Stock pursuant to the Merger  Agreement or the
            consummation of the Merger,  or (iii) the  consummation of the other
            transactions contemplated by the Merger Agreement."

            3.  Amendment  of Section 1.  Section 1 of the Rights  Agreement  is
further amended to add the following subparagraphs at the end thereof:

                  (ai)  "Eastern" shall mean Eastern Enterprises, a
            Massachusetts business trust.
<PAGE>


                  (aj)  "Merger" shall have the meaning set forth in the
            Merger Agreement.

                  (ak) "Merger  Agreement"  shall mean the Agreement and Plan of
            Reorganization  dated as of October 17, 1998, by and between Eastern
            and the Company, as amended from time to time."

            4. Amendment of Section 3(a).  Section 3(a) of the Rights  Agreement
is amended to add the following sentence at the end thereof:

            "Notwithstanding  anything in this Rights Agreement to the contrary,
            a Distribution  Date shall not be deemed to have occurred  solely by
            virtue  of (i) the  execution  of the  Merger  Agreement,  (ii)  the
            acquisition of Common Stock pursuant to the Merger  Agreement or the
            consummation of the Merger,  or (iii) the  consummation of the other
            transactions contemplated by the Merger Agreement."

            5. Amendment of Section 7(a).  Section 7(a) of the Rights  Agreement
is amended to add the following sentence at the end thereof:

            "Notwithstanding  anything in this Rights Agreement to the contrary,
            neither  (i)  the  execution  of  the  Merger  Agreement;  (ii)  the
            acquisition of Common Stock pursuant to the Merger  Agreement or the
            consummation of the Merger;  nor (iii) the consummation of the other
            transactions  contemplated in the Merger Agreement,  shall be deemed
            to be events that cause the Rights to become exercisable pursuant to
            the provisions of this Section 7 or otherwise."

            6.  Amendment of Section 11.  Section 11 of the Rights  Agreement is
amended to add the following sentence after the first sentence of said Section:

            "Notwithstanding  anything in this Rights Agreement to the contrary,
            neither  (i)  the  execution  of  the  Merger  Agreement;  (ii)  the
            acquisition of Common Stock pursuant to the Merger  Agreement or the
            consummation of the Merger;  nor (iii) the consummation of the other
            transactions  contemplated in the Merger Agreement,  shall be deemed
            to cause the  Rights to be  adjusted  or to  become  exercisable  in
            accordance with this Section 11."

            7.  Amendment of Section 13.  Section 13 of the Rights  Agreement is
amended to add the following sentence at the end thereof:

            "Notwithstanding  anything in this Rights Agreement to the contrary,
            neither  (i)  the  execution  of  the  Merger  Agreement;  (ii)  the
            acquisition of Common Stock pursuant to the Merger  Agreement or the
            consummation of the Merger;  nor (iii) the consummation of the other
            transactions  contemplated in the Merger Agreement,  shall be deemed
            to be events of the type  described  in this  Section 13 or to cause
            the Rights to be adjusted  or to become  exercisable  in  accordance
            with Section 13."
<PAGE>

            8. Effectiveness. This Amendment shall be deemed effective as of the
date first written above, as if executed on such date. Except as amended hereby,
the  Rights  Agreement  shall  remain  in full  force  and  effect  and shall be
otherwise unaffected hereby.

            9.  Miscellaneous.  This Amendment  shall be deemed to be a contract
made under the laws of the  Commonwealth of  Massachusetts  and for all purposes
shall be governed by and  construed  in  accordance  with the laws of such state
applicable  to contracts to be made and  performed  entirely  within such state.
This  Amendment  may be  executed  in any number of  counterparts,  each of such
counterparts  shall for all purposes be deemed to be an  original,  and all such
counterparts shall together  constitute but one and the same instrument.  If any
provision,  covenant  or  restriction  of this  Amendment  is held by a court of
competent   jurisdiction   or  other   authority  to  be  invalid,   illegal  or
unenforceable,   the   remainder  of  the  terms,   provisions,   covenants  and
restrictions  of this Amendment  shall remain in full force and effect and shall
in no way be effected, impaired or invalidated.

            EXECUTED under seal as of the date set forth above.


                                        COLONIAL GAS COMPANY


                                        By:s/Nickolas Stavropoulos
                                           Nickolas Stavropoulos
                                           Executive Vice President-Finance,
                                           Marketing and CFO




                                        RIGHTS AGENT:
                                        BANKBOSTON, N.A.

                                        By:    s/Joshua P. McGinn
                                        Name:  Joshua P. McGinn
                                        Title: Sr. Account Manager


                  [END OF EXHIBIT 4h TO COLONIAL GAS COMPANY
                    10-K FOR YEAR ENDED DECEMBER 31, 1998]