1.  Marriage Record:

2.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #51 of 66):  Jay, Essex Co., NY, Roll M432_504, p. 213A, 3025/3099, enumerated 13 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Joseph Bruce	54	M		Farmer	4000
Rebecca	33	F
Franklin	33	M		"
Lorrain	32	F
Louisa	8	F
Robert	3	M
Daniel Hopper	15	M
Hannah Felt	33	F

Rebecca should be 53, not 33, not if she's really Franklin's mother.

3.  1860 Census Every-Name-Index/Images (online at Ancestry.com):  can't find, and I even did a page-by-page search of Jay.  Also didn't find J.F.'s father, who should also be in Jay.  Were they missed by the enumerator?  Or did they slip off to Canada for a few years?

4.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #24-5 of 63):  Whallonsburgh [Whallonsburg] P.O., Jay, Essex Co., NY, Roll M593_936, pp. 122B-123A, PN 24-25, 182/194, enumerated 22 Jun 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Bruce J F	54	M	W	Retired from business	1800	12000	NY
_____ Loraine	52	F	W	Keeping house			NY
_____ Lydia	18	F	W	Teaching School			NY
[next page]
Bruce Mattie	15	F	W	at home			NY
_____ Cora	12	F	W	Attending School			NY

Listed next to Joshua's first cousin, Henry S. BRUCE (son of Joshua's uncle, Jonah BRUCE).

5.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #5 of 8):  Village of Lower Jay, Essex Co., NY, Roll T9_0832, p. 122A, PN 23, SD 7, ED 45, enumerated 20 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

11

13

24

25

26

254

234

Bruce J F

W

M

64

/

Farmer

NY

VT

VT

_____ Lorain

W

F

63

Wife

/

Keeping house

NY

VT

MA

_____ Cora E

W

F

23

Dau

/

At home

NY

VT

VT

Southm?? Mary ?

W

F

37

Dau

/

At home

NY

NY

NY

Obviously, Cora's parents were born in NY, not VT.  Listed three households from Arby BRUCE (æ 45, b. NY).

6.  1890 Census:  the 1890 Census Population Schedules were destroyed.

7.  1900 Census Every-Name-Index/Images (online at Ancestry.com):  not found.

8.  H.P. Smith.  1885.  History of Essex County [New York].  D. Mason & Co., Publ., Syracuse, NY (online at Ancestry.com).  On p. 717:

Bruce.  The Bruce family is among the first families of Jay.  Their ancestor, Benjamin Bruce, first settled in Jay in 1804.  He was a shoemaker by trade and a soldier of the Revolution.  He died September 11th, 1839, leaving six children:  Joseph, Jonah, Anna, Polie, Phila, and Hannah.  Joseph was married to Rebecca Houghton, a native of Vermont, and the venerable Joshua F. Bruce, of Jay, is her only son.  He married Loraine, daughter of James Kimball; they have four children living: Mary, who is widow of Wesley Southmaid; Robert, a farmer of Essex; Martha, now Mrs. Henry Beckwith, of Schuyler Falls, N.Y.; and Cora, now Mrs. C.W. Smith, of Wells, N.Y.