Back then, "Jr.-Sr." relationships did not necessarily mean "Father-Son."  The terminology was nearer to the older usage of "Richard, the elder" and "Richard, the younger."  In this case, the Royal WILLIAMS above was Jr. to his uncle, Royal WILLIAMS, Sr., who did not have a son named Royal.  Both uncle and nephew lived contemporaneously in Middlebury, Mercer Co., MO, hence the need to distinquish between them.

1.  Family Group Sheet by Betty Ann (Matthiesen) Cogliati and her grandmother, Maude Irene (Thompson) Rose.

2.  1860 Census Images (online at Ancestry.com; Image #7 of 14):  Middlebury P.O., Washington Twp., Mercer Co., MO, p. 193, 678/678, enumerated 18 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Royal Williams Jr	34	M		Hotel Keeper	1600	600	Virginia
L.F.     "	22	F					Tennessee
W.R.     "	5	M					Missouri
D.L.     "	3	M					"
Lucy     "	1/12	F					"

Living next door to Royal's brother, James M. WILLIAMS; and, in the other direction, listed four doors from William Henry McCRAY, whose wife is Royal's first cousin, Macedonia Alice WILLIAMS. 

3.  1870 Census Images (online at Ancestry.com; Image #49 of 436):  Farmersville P.O., Chillicothe Twp., Livingston Co., MO, p. 438A, PN 9, 60/62, enumerated 13 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Williams Royal	47	M	W	Farmer			Va
________ Isabel	32	F	W	Keepinghouse			Ky
________ Richard	16	M	W				Mo

4.  1880 Census Images (online at Ancestry.com; Image #3 of 27):  Washington Twp., Mercer Co., MO, p. 139A, PN 3, SD 7, ED 231, enumerated 1 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	8	10	13	24	25	26
17	17	Williams Royl	W	M	55		/	Farmer	VA	VA	VA
		________ Isabel	W	F	42	Wife	/	Keeping House	KY	KY	KY

Living next door to Royal's widowed mother, Elizabeth WILLIAMS. 6.  Emails from Art Daly, Doreen McGowan, Lawrence May.