Living with Jacob & Mary is Mary's sister Martha Armitage:
1851
HO107 Piece 2294 Folio 7 Page 6
RD: Huddersfield
Address: 943, Newsome Cross
BARRACLOUGH, Jacob Head Married M 42 1809 Blacking Manufacturer Kirkburton, Yorkshire
BARRACLOUGH, M Wife Married F 39 1812 Kirkburton, Yorkshire
BARACLOUGH, John Son Unmarried M 18 1833 Stone Mason Almondbury, Yorkshire
BARACLOUGH, J Son M 16 1835 Joiner Apprentice Almondbury, Yorkshire
BARACLOUGH, B Son M 14 1837 Errand Boy Blacking Almondbury, Yorkshire
BARACLOUGH, S Daughter F 10 1841 Scholar Almondbury, Yorkshire
BARACLOUGH, C A Daughter F 9 1842 Scholar Almondbury, Yorkshire
ARMITAGE, Martha Sister Married [?] F 27 1824 Cotton Warper Almondbury, Yorkshire
1861
RG9 3255 Folio: 89 Page: 26 Schedule: 134
Place: Almondbury -West Riding of Yorkshire Enumeration District: 5
Civil Parish: Almondbury Ecclesiastical Parish: Lockwood
Address: 943 Newsome Cross
Surname First name(s) Rel Status *** Age Occupation Where Born Remarks
BARRACLOUGH Jacob Head W M 51 Blacking Maker Yorkshire - Kirkburton
BARRACLOUGH Sarah Dau U F 22 Dress Maker Yorkshire - Almondbury
ARMITAGE Martha Lodger U F 37 Dress Maker Yorkshire - Almondbury
Baptism of Martha:
Baptised 14.3.1824 Martha Armitage d/o James, a mason & Betty (nee Oxley) abode: Newsome
Martha ARMITAGE c. 14 Mar 1824 Almondbury, Yorkshire, England
JAS. & Betty
Date and place fit but the names are not Francis & Betty.
Unless Francis/Frances is a mistranscription of James.