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                                                                    EXHIBIT 99.4

                            [CORE INDUSTRIES INC LOGO]
 
                                  July 2, 1997
 
To Our Stockholders:
 
     I am pleased to inform you that on June 25, 1997, Core Industries Inc
("Core") entered into an Agreement and Plan of Merger ("Merger Agreement") with
United Dominion Industries Limited ("UDI") and UD Nevada Corp. ("Acquisition"),
a wholly owned subsidiary of UDI, pursuant to which Acquisition has commenced
today a tender offer for all outstanding shares of Core Common Stock for $25.00
per share in cash. Following the completion of the tender offer, upon the terms
and subject to conditions of the Merger Agreement, Acquisition will be merged
into Core (the "Merger"), and each share of Core Common Stock, other than shares
of Common Stock owned by Core, UDI, Acquisition or any direct or indirect wholly
owned subsidiary of Core or of UDI immediately prior to the effective time of
the Merger, will be cancelled and converted into the right to receive $25.00 in
cash, the same price per share paid pursuant to the tender offer.
 
     Your Board of Directors has unanimously approved the tender offer and the
Merger, has determined that the tender offer and the Merger are fair to, and in
the best interests of, the stockholders of Core, and recommends that
stockholders accept the tender offer and tender all their shares pursuant to the
offer.
 
     In arriving at its decision, your Board of Directors gave careful
consideration to a number of factors described in the enclosed Schedule 14D-9
that is being filed today with the Securities and Exchange Commission,
including, among other things, the opinion of Goldman, Sachs & Co., Core's
financial advisor, to the effect that, as of the date of such opinion, the
tender offer and the Merger were fair to the stockholders of Core. The enclosed
Schedule 14D-9 describes the Board's decision and contains other important
information relating to that decision. We urge you to read it carefully.
 
     Accompanying this letter, in addition to the Schedule 14D-9, is the Offer
to Purchase, together with related materials including a Letter of Transmittal
for use in tendering shares. These documents set forth the terms and conditions
of the tender offer and provide instructions as to how you can tender your
shares. We urge you to read the enclosed materials carefully and consider all
the factors set forth therein before making your decision with respect to the
tender offer.
 
                                          Sincerely,
 
                                          /s/ DAVID R. ZIMMER
 
                                          David R. Zimmer
                                          President and Chief Executive Officer