ARCH FUNDS INC
497J, 1998-04-01
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<PAGE>   1
                             THE ARCH FUND(R), INC.
                               3435 Stelzer Road
                              Columbus, Ohio 43219
                                        
                                        
                                 April 1, 1998


VIA EDGAR TRANSMISSION
- ----------------------

Securities and Exchange Commission
Judiciary Plaza
450 Fifth Street, N.W.
Washington, D.C. 20549


     Re:  THE ARCH FUND, INC.
          (1933 ACT REGISTRATION NO. 2-79285)
          (1940 ACT REGISTRATION NO. 811-3567)
          ------------------------------------

Ladies and Gentlemen:

          On behalf of The ARCH Fund, Inc. (the "Fund") and pursuant to Rule
497(j) of the Securities Act of 1933 (the "1933 Act"), I hereby certify that:

     (i)  the Prospectuses for the Fund's

          (a)  Trust Shares, dated March 31, 1998;

          (b)  Trust Shares of the Treasury Money Market, Money Market and
               Tax-Exempt Money Market Portfolios, dated March 31, 1998;

          (c)  Institutional Shares, dated March 31, 1998; and

          (d)  Investor A Shares and Investor B Shares, dated March 31, 1998;

     and the Statement of Additional Information for the Fund, dated March 31,
     1998 that would have been filed under paragraph (c) of Rule 497 of the
     1933 Act would not have differed from the Prospectuses and Statement of
     Additional Information referenced above contained in Post-Effective
     Amendment No. 44 to the Fund's Registration Statement on Form N-1A under
     the Securities Act of 1933 and the Investment Company Act of 1940, which
     was filed on March 31, 1998, and

     (ii) the text of Post-Effective Amendment No. 44 has been filed
     electronically.

          If you have any questions or comments regarding this filing, do not
hesitate to contact Allan J. Oster, Esq. at (215) 988-2935.

                                             Very truly yours,

                                             The ARCH Fund, Inc.

                                             By: /s/ David Bunstine
                                                 ---------------------------
                                                  Assistant Secretary


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