For Catherine FERGUSON to have been Catherine ADAMS's mother, the former had to be at the youngest age in her age ranges in the censuses.

1.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):

Adams, Matthew	Barnett, Ester	Apr 1, 1788	Lincoln Co.
Adams, Matthew	Ferguson, Catherine	Nov 6, 1802	Christian Co.
Adams, Robert	Cates, Sintha	Jan 3, 1814	Hopkins Co.

Kentucky did not become a state until 1792, so when Matthew married Ester, it was Lincoln Co., VA, not KY.

2.  1790 Census Index/Images (online at Ancestry.com):  the VA census was lost.

3.  1800 Census Index/Images (online at Ancestry.com):  the KY census was lost.

4.  1810 Census Index/Images (online at Ancestry.com, Image #2 of 11 — indexed "Mattie Adamy"; extracted by Diana Gale Matthiesen):

1810

KY

Hopkins Co.

Madisonville

Roll 6

p. 372/487

Ln. 3

Mattw Adams

00210-51110-01

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	16-25	1784-1794	=? Matthew (b. 1799) = Robert (b. 1794) = James (b. 1790)
1 male	26-44	1765-1784	= Matthew (b. 1767)
5 females	9 or under	1800-1810	= Daughter B = Juliet = Agnes (b. 1807) = Ann (b. 1805) = Polly (b. 1803)
1 female	10-15	1794-1800	= Elizabeth (b. 1796)
1 female	16-25	1784-1794	= Daughter A (b. ca. 1792)
1 female	26-44	1765-1784	= Catherine
1 slaves	all ages	by 1810	= ?

Which of the three sons is not living at home?  Or did the enumerator err?  Or is Matthew ADAMS, Jr., not his son?  Also in Madisonville, James ADAMS (æ 45+), Robert ADAMS (æ 25-45), and Thomas ADAMS (æ 24-45).

5.  1820 Census Index/Images (online at Ancestry.com):  not found, but our subject is said to have moved to what was Missouri Territory in 1817.  Even though Arkansas Territory was formed in 1819, there was no Arkansas (or Missouri) territorial census in 1820.

6.  1830 Census Index/Images (online at Ancestry.com, Image #1-2 of 16; extracted by Diana Gale Matthiesen):

1830

Arkansas Territory

Izard Co.

Roll 5

pp. 105B-106A

Ln. 1

Matthew Adams Sr

001 000 001 - 110 020 001

010000-010000

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	10-14	1815-1820	= Son A
1 white male	60-69	1760-1770	= Matthew (b. 1767)
1 white female	4 or under	1825-1830	= granddaughter?
1 white female	5-9	1820-1825	= Catherine (b. 1821)
2 white females	20-29	1800-1810	= Daughter B? = Juliet?
1 white female	60-69	1760-1770	= Catherine
1 male slave	10-23	1806-1820	= ?
1 female slave	10-23	1806-1820	= ?

Catherine's age has to be wrong here and correct in 1840 because, otherwise, she is too old to be Catherine's mother.  Listed nine lines from Matthew ADAMS, Jr. (æ 30-40; b. 1790-1800), who is eight lines from their son-in-law, Edmund TYLER.  Also in Izard County:  Jesse ADAMS, Sr., John ADAMS, Peter F. ADAMS, and Robert ADAMS, Sr.

7.  1840 Census Index/Images (online at Ancestry.com, Image #3 of 4; extracted by Diana Gale Matthiesen):

1840

AR

Pope Co.

Liberty Twp.

Roll 19

p. 139A

Ln. 6

Edmund Tyler

111 001 - 001 001 001

[second page missing]

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= son TYLER
1 male	5-9	1830-1835	= son TYLER
1 male	10-14	1825-1830	= son TYLER
1 male	30-39	1800-1810	= Edmund TYLER (b. 1802)
1 female	10-14	1825-1830	= daughter TYLER
1 female	30-39	1800-1810	= Ann (ADAMS) TYLER (b. 1805)
1 female	60-69	1770-1780	= Catherine (FERGUSON) ADAMS

8.  Anon.  1990.  Logan County, Kentucky, Taxpayers, 1792-1799.  T.L.C. Genealogy, Miami Beach, FL:

Year	Name
1792-94	[not found]
1795	Adams, Matthew
1796	Adams, Matthew
1797	Adams, Matthew
1798	[list non-existant]
1799	[not found]

Matthew is not found in Logan County in 1798 because Christian County was formed in 1797.  The only other ADAMS found in any year is Alexander ADAMS in 1799.

9.  Anon.  1991.  The 1795 Census of Kentucky [as constructed from tax lists].  T.L.C. Genealogy, Miami Beach, FL (said to include every extant tax list from every county existing in the state of Kentucky in 1795):

Pg	Name	County
2	Adams, Matthew	Logan
	Adams, Matthew	Madison

These are the only Matthew ADAMS'es on the list.

10.  A.B. Willhite.  [n.d.]  Christian Co., Kentucky, Tax List, 1804-1809.  (self-published; available from author at 4396 Coopertown Rd., Russellville, KY 42276, or from the Christian County Genealogical Society, Hopkinsville, KY):

Pg. in Willhite	Year	Dist.*	Last Name	First Name	A	B	C	D	E	Acres	Watercourse
15	1804	North	Adams	Matthew	1	-	2	2	4	200	West Fork of Red River
-	1805	[records missing]
69	1806	South	Adams	Matthew	1	-	-	-	6	300	West Fork of Red River
114	1807	East	Adams	Matthew	1	1	-	-	4	400	West Fork of Red River
155	1808	East	Adams	Matthew	1	1	-	-	7	830?	West Fork and Elk Fork of Red River
-	1809	[not found, which is consistent with their move to Hopkins County]
Legend for numerical data: A = White Males 21 or over; B = White Males 16-20 (this column not used in 1809); C = Blacks over 16; D = Total Blacks; E = Horses
Abbreviations:  W = WF = W F R R = WF Red R = West Fork of the Red River
*The county was divided into just two districts:  from 1804 to 1806, into North and South Districts; and from 1807 to 1809, into East and West Districts.  The change tells us that Matthew was in the southeast quadrant of early Christian County, which later became the southwest quadrant of Todd Co., when it was formed in 1820.  This location is confirmed by the location of the West Fork of the Red River in today's southwestern Todd Co.

In 1804:  also on WFRR:  James ADAMS; also in Christian County:  Jesse ADAMS, Alexander ADAMS, and Robert ADAMS.
In 1806:  also on WFRR:  James ADAMS and Robert ADAMS; also in Christian County:  Jesse ADAMS, et al.
In 1807:  also on WFRR:  Matthew ADAMS, James ADAMS, James ADAMS, Jr., Robert ADAMS; also in Christian County:  Jesse ADAMS, et al.
In 1808:  also on WFRR:  James ADAMS, Jr., Robert ADAMS.  Also in Christian County:  Jesse ADAMS, et al.
Also in 1808, Matthew ADAMS and Jacob W. WALKER, are administrators of the estate of Alexander ADAMS, which consists of 200 acres on the Elk Fork and 300 acres on the West Fork of Red River.

11.  Karr Shannon.  1947.  A History of Izard County, Arkansas.  Democrat Printing and Lithographing Co., Little Rock, AR (online at Ancestry.com):

p. 13	The first county officials of the county were J.P. Houston,
p. 14	clerk; John Adams, sheriff.  These two men were elected in 1825 to serve terms of two years.  Both were re-elected in 1827.  No other offices appeared until 1829 when Matthew Adams was chosen judge and H.C. Roberts coroner.  J.P. Houston and John Adams were elected to a third term to their respective offices.  Jesse Adams became clerk in 1830 and served two terms...

12.  Messages posted to the Adams Family Genealogy Forum (online at GenForum.com).

13.  OneWorldTree (online at Ancestry.com).

14.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).