SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G
                                 (Rule 13d-102)

             INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT
          TO RULES 13d-1 (b) (c), AND (d) AND AMENDMENTS THERETO FILED
                           PURSUANT TO RULE 13d-2 (b)

                              Newmarket Corporation
--------------------------------------------------------------------------------
                                (Name of Issuer)

                           Common Stock, no par value
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    651587107
--------------------------------------------------------------------------------
                                 (CUSIP Number)

                                October 19, 2006
--------------------------------------------------------------------------------
             (Date of Event which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:
         |X|  Rule 13d-1(b)
         |_|  Rule 13d-1(c)
         |_|  Rule 13d-1(d)

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).



CUSIP No. 651587107                   13G                      Page 2 of 8 Pages
--------------------------------------------------------------------------------
1.    NAMES OR REPORTING PERSONS
      S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS

      Renaissance Technologies Corp.              13-3127734
--------------------------------------------------------------------------------
2.    CHECK APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS):
      (a) |_|
      (b) |_|
--------------------------------------------------------------------------------
3.    SEC USE ONLY


--------------------------------------------------------------------------------
4.    CITIZENSHIP OR PLACE OF ORGANIZATION

      Delaware
--------------------------------------------------------------------------------
               5.    SOLE VOTING POWER

                     1,008,100
               -----------------------------------------------------------------
  NUMBER OF    6.    SHARED VOTING POWER
   SHARES
 BENEFICIALLY        0
  OWNED BY     -----------------------------------------------------------------
    EACH       7.    SOLE DISPOSITIVE POWER
  REPORTING
   PERSON            1,008,100
    WITH       -----------------------------------------------------------------
               8.    SHARED DISPOSITIVE POWER

                     0
--------------------------------------------------------------------------------
9.    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      1,008,100
--------------------------------------------------------------------------------
10.   CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
      (SEE INSTRUCTIONS)                                                     |_|

--------------------------------------------------------------------------------
11.   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

      5.84%
--------------------------------------------------------------------------------
12.   TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

      IA
--------------------------------------------------------------------------------


                               Page 2 of 8 Pages


CUSIP No. 651587107                   13G                      Page 3 of 8 Pages
--------------------------------------------------------------------------------
1.    NAMES OR REPORTING PERSONS
      S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS

      James H. Simons
--------------------------------------------------------------------------------
2.    CHECK APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS):
      (a) |_|
      (b) |_|
--------------------------------------------------------------------------------
3.    SEC USE ONLY


--------------------------------------------------------------------------------
4.    CITIZENSHIP OR PLACE OF ORGANIZATION

      United States
--------------------------------------------------------------------------------
               5.    SOLE VOTING POWER

                     1,008,100
               -----------------------------------------------------------------
  NUMBER OF    6.    SHARED VOTING POWER
   SHARES
 BENEFICIALLY        0
  OWNED BY     -----------------------------------------------------------------
    EACH       7.    SOLE DISPOSITIVE POWER
  REPORTING
   PERSON            1,008,100
    WITH       -----------------------------------------------------------------
               8.    SHARED DISPOSITIVE POWER

                     0
--------------------------------------------------------------------------------
9.    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      1,008,100
--------------------------------------------------------------------------------
10.   CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
      (SEE INSTRUCTIONS)                                                     |_|

--------------------------------------------------------------------------------
11.   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

      5.84%
--------------------------------------------------------------------------------
12.   TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

      IN
--------------------------------------------------------------------------------


                               Page 3 of 8 Pages


CUSIP No. 651587107                   13G                      Page 4 of 8 Pages

Item 1.

      (a)   Name of Issuer.

            Newmarket Corporation

      (b)   Address of Issuer's Principal Executive Offices.

            330 South Fourth Street
            Richmond, Virginia 23218-2189

Item 2.

      (a)   Name of Person Filing.

            This Schedule 13G is being filed by Renaissance Technologies Corp.
            ("RTC") and James H. Simons ("Simons").

      (b)   Address of Principal Business Office or, if none, Residence.

            The principal business address of the reporting persons is:

            800 Third Avenue
            New York, New York 10022

      (c)   Citizenship.

            Dr. Simons is a United States citizen and RTC is a Delaware
            corporation

      (d)   Title of Class of Securities.

            Common Stock, no par value

      (e)   CUSIP Number.

            651587107


                               Page 4 of 8 Pages


Item 3. If this statement is filed pursuant to Rule 13d-1(b) or 13d-2(b) or (c),
        check whether the person filing is a:

      (a) |_| Broker or dealer registered under Section 15 of the Act.
      (b) |_| Bank as defined in Section 3(a)(6) of the Act.
      (c) |_| Insurance Company as defined in Section 3(a)(19) of the Act.
      (d) |_| Investment Company registered under Section 8 of the Investment
              Company Act.
      (e) |X| Investment Adviser in accordance with Sec. 240.13d-1(b)(1)(ii)(E).
      (f) |_| Employee Benefit Plan or Endowment Fund in accordance with Sec.
              240.13d1(b)(1)(ii)(F).
      (g) |_| Parent holding company, in accordance with Sec.
              240.13d-1(b)(ii)(G).
      (h) |_| A savings association as defined in Section 3(b) of the Federal
              Deposit Insurance Act.
      (i) |_| A church plan that is excluded from the definition of an
              investment company under Section 3(c)(14) of the Investment
              Company Act of 1940.
      (j) |_| Group, in accordance with Sec. 240.13d-1(b)(1)(ii)(J).

      If this statement is filed pursuant to Sec. 240.13d-1(c), check this box
|_|.

Item 4. Ownership

      (a)   Amount Beneficially Owned.

            RTC:    1,008,100 shares

            Simons: 1,008,100 shares, comprising the shares beneficially owned
                    by RTC, because of Dr. Simons' position as control person of
                    RTC.

      (b)   Percent of Class.   RTC:      5.84%
                                Simons:   5.84%

      (c)   Number of shares as to which each such person has

            (i)   sole power to vote or to direct the vote:   RTC:     1,008,100
                                                              Simons:  1,008,100

            (ii)  shared power to vote or to direct the vote:          0

            (iii) sole power to dispose or to direct the
                  disposition of:                             RTC:     1,008,100
                                                              Simons:  1,008,100

            (iv)  shared power to dispose or to direct
                  the disposition of:                                  0


                               Page 5 of 8 Pages


Item 5. Ownership of Five Percent or Less of a Class.

            If this statement is being filed to report the fact that as of the
            date hereof the reporting person has ceased to be the beneficial
            owner of more than five percent of the class of securities, check
            the following |_|

Item 6. Ownership of More than Five Percent on Behalf of Another Person.

            Certain funds and accounts managed by RTC have the right to receive
            dividends and proceeds from the sale of the securities which are the
            subject of this report. RIEF Trading LLC holds of record more than
            5% of such securities.

Item 7. Identification and Classification of the Subsidiary Which Acquired the
        Security Being Reported on by the Parent Holding Company or Control
        Person.

            Not applicable.

Item 8. Identification and Classification of Members of the Group.

            Not applicable.

Item 9. Notice of Dissolution of Group.

            Not applicable.


                               Page 6 of 8 Pages


Item 10. Certification.

      By signing below I certify that, to the best of my knowledge and belief,
the securities referred to above were not acquired and are not held for the
purpose of or with the effect of changing or influencing the control of the
issuer of the securities and were not acquired and are not held in connection
with or as a participant in any transaction having that purpose or effect.

                                    SIGNATURE

      After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Date: February 12, 2007

                                                  /s/ James H. Simons
                                                  ------------------------------
                                                          James H. Simons


                                                  Renaissance Technologies Corp.

                                                  By: /s/ Mark Silber
                                                      --------------------------
                                                      Mark Silber
                                                      Vice President

      Attention: Intentional misstatements or omissions of fact constitute
Federal criminal violations (see 18 U.S.C. 1001).


                               Page 7 of 8 Pages