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Diana, Goddess of the Hunt — for Ancestors!
 
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William LYON II
Alice ARMSTRONG
Ann FLEMING
Husband:  William LYON
Birth:  17 Mar 1728/9, Enniskillen, co. Fermanagh, NIRL
Death:  7 Feb 1809, Carlisle, Cumberland Co., PA
Y-DNA Haplogroup:  R1b-CTS6889, "North Irish"
Father:  John LYON
Mother:  Margaret ARMSTRONG
Marriage-1:
Wife-1:  Alice ARMSTRONG
Birth:  ca. 1739
Father:  John ARMSTRONG
Mother:  Rebecca LYON
Marriage-2:
Wife-2:  Ann FLEMING
Birth:  certainly by 1755, probably by 1750
Children with Alice ARMSTRONG — born in Carlisle, Cumberland Co., PA:
  1.  James LYON, b. Oct 1757
Children with Ann FLEMING — born in Carlisle, Cumberland Co., PA:
  2.  Margaret "Peggy" LYON, b. 9 May 1770
  3.  John LYON, b. 13 Oct 1771
  4.  William LYON, b. 17 Jun 1773
  5.  Samuel LYON, b. 20 Jan 1775
  6.  Mary LYON, b. 20 Aug 1776
  7.  Alexander-Parker LYON, b. 4 Aug 1778
  8.  Nancy LYON, b. 16 Aug 1780
  9.  Alice Armstrong LYON, b. 25 Sep 1781
10.  George Armstrong LYON, b. 11 Apr 1784
11.  (Son A) LYON, b. 1784-1790
12.  (Son B) LYON, b. 1790-1800
13.  (Daughter A) LYON, b. 1790-1800
Something's not right here.  The three boys born between 1774 and 1784 do not appear in the 1790 census, but do appear in 1800.  The discrepancy reads as though William married for a third time between 1790 and 1800, and that some of the children in the 1800 census are those of the third wife from her previous marriage.  Yet, the birth dates of the first 10 children read as though they came from a family bible, which surely would indicate who the parents were.  So, CAVEAT EMPTOR, there's something wrong here.
Keywords for search engines:  genealogy; NIRL, Northern Ireland; USA, US, United States, Pennsylvania

Sources:

1.  Marriage Record:

2.  1790 Census Index/Images (online at Ancestry.com, Image #39 of 42; extracted by Diana Gale Matthiesen):¤•
1790 PA Cumberland Co. Roll M637_8 p. 40 Ln. 64L William Lyon 3-0-4-6-1
These data indicate:
Gender and Type Age Class Therefore Born Individuals Inferred
3 free white males 16 or over in or bef. 1774 = William (b. 1728/9)
= John (b. 1771)
= William (b. 1773)
4 free white females all ages in or bef. 1790 = Ann
= Mary (b. 1776)
= Nancy (b. 1780)
= Alice (b. 1781)
6 other free people all ages in or bef. 1790 = ? ? ? ? ? ?
1 slave all ages in or bef. 1790 = ?
Where are the three youngest sons?  Listed next to William's late wife's father, John ARMSTRONG.

3.  1800 U.S. Census Index/Images (online at Ancestry.com, Image #13 of 13; official enumeration date 4 Aug 1800; extracted by Diana Gale Matthiesen):¤•
1800 PA Cumberland Co. Carlisle Roll M32_38 p. 192 Ln. 5 William Lyon 11311-10301-01
These data indicate:
No. & Sex  Age Class Therefore Born Individuals Inferred
1 male 9 or under 1790-1800 = Son B
1 male 10-15 1784-1790 = Son A
3 males 16-25 1774-1784 = George (b. 1784)
= Alexander (b. 1778)
= Samuel (b. 1775)
1 male 26-44 1755-1774 = William (b. 1773)
1 male 45 or over in or bef. 1755 = William (b. 1728/9)
1 female 9 or under 1790-1800 = Daughter A
3 females 16-25 1774-1784 = Alice (b. 1781)
= Nancy (b. 1780)
= Mary (b. 1776)
1 female 45 or over in or bef. 1755 = Ann
1 slaves all ages in or bef. 1800 = ?
Listed next to James ARMSTRONG.

4.  WorldConnect / WorldTree (online at RootsWeb.com/Ancestry.com). 

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