1.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Female: Vastine Birth: 24 Apr 1880, Birth Certificates, Manhattan, New York, New York Father: Wm. T. Vastine; Mother: Alice P. Carman Vastine Source: Manhattan Birth Certificates, 1866-1897. New York (New York). Department of Health

Apparently this child died before the census was enumerated on 1 Jun 1880.

2.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #14 of 33):  229 East 81st, Manhattan, New York City (Dist. No. 605), New York Co., NY, Roll T9_896, p. 277B, PN 14, SD 1, ED 605, enumerated 4/5 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	9	10	13	24	25	26
87	138	Vastine Wm	W	M	30	Husb		/	Mason	PA	PA	PA
		"    Alice	W	F	26	Wife		/	Keeps House	PA	PA	PA
		"    Sheffield	W	M	2	Son	/			PA	PA	PA

3a.  1890 Census:  the 1890 Census Population Schedules were destroyed.

3b.  New York City Cirectory, 1890 (online at Ancestry.com):

Vastine William T. mason, h 1069 Park av.

4.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #19 of 44):  534 Evergreen Ave., Borough of Brooklyn (Ward 28), City of New York, Kings Co., NY, Roll T623_1067, p. 103A, SN 10, SD 2, ED 516, enumerated 9 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):

1900:  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	7	8	9	10	11	12	13	14	15	19	20	21	22	23	24	25	26	27
*	534	113	222	Vastine William	Head	W	M	Nov 1850	49	M	22			PA	PA	PA	Rubber House Forman	0		Y	Y	Y	O	F	H
				_______ Alice	Wife	W	F	Sep 1853	46	M	22	2	2	PA	PA	PA				Y	Y	Y
				_______ Sheffield	Son	W	M	Feb 1878	22	S				PA	PA	PA	Stock Clerk Dry Goods	0		Y	Y	Y
				_______ Nellie M	Dau	W	F	Oct 1885	14	S				NY	PA	PA	At School		10	Y	Y	Y
*Evergreen Ave

5.  1910 Census Index/Images (online at Ancestry.com):  can't find anyone, except Sheffied, who is now married (q.v.).

6.  1920 Census Index/Images (online at Ancestry.com, Image #2 of 20):  868 St. Johns Place, Borough of Brooklyn, Kings Co., NY, Roll T625_1172, p. 81B, SN 1B, SD 3, ED 1081, enumerated 2 Jan 1920, official enumeration date 1 Jan 1920 (extracted by Diana Gale Matthiesen):

1920:  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	7	8	9	10	11	12	17	18	19	21	23	25	26	27	28
*	868	13	17	Vastine Nellie M	Head	O	M	F	W	30	S	Y	Y	NY	PA	PA	Y	Bookkeeper	Stain glass	W
				_______ Alice P	Mother			F	W	53	Wd	Y	Y	PA	PA	PA	Y	None
*St Johns Place

7.  1930 Census Index/Images (online at Ancestry.com, Image #11 of 36):  868 St. Johns Place, Brooklyn, New York City, Kings Co., NY, Roll 1528, p. 84A, SN 6A, ED 24-1655, SD 30, enumerated 5/7 Apr 1930, official enumeration date 1 Apr 1930 (extracted by Diana Gale Matthiesen):

1930:  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	7	8	9	10	11	12	13	14	15	16	17	18	19	20	24	25	26	27	28
*	868	66	96	Vastine Alice	Head	O	$9000	R	N	F	W	75	WD	23	N	Y	PA	PA	PA	Y	None
				Vastine Nellie	Dau					F	W	32	S		N	Y	NY	PA	PA	Y	Clerk	Int??? ???	W	Y
*St Johns Place