I can see Lumina as Jemima on the 1841 census for Sandwick, Orkney on Freecen.co.uk
Orkney, Sanwick, Freecen 1841:
Piece: SCT1841/27 Place: Sandwick -Orkney Enumeration District: 3
Civil Parish: Sandwick Ecclesiastical Parish, Village or Island: -
Folio: 3 Page: 11
Address: Lower Aith, Chamber Of Aith
James Irving M 40 Agricultural Labourer, born Orkney
Margaret Irving F 35, born Orkney
James Irving M 5, born Orkney
Matilda F 4, born Orkney
Jemima F 1, born Orkney
From the IGI
James Irvine
Scotland, Marriages, 1561-1910
marriage: 2 March 1830
Sandwick, Orkney, Scotland
spouse: Margaret Corgile
Their Children all born in Sandwick, Orkney:
Margaret Irivineborn 8th May 1831
Isobella Howie Currie Garson Irvine born 24th June1832
Meran Irvine born 21st March 1834
James Irvine born 25th May 1835
Matilda Clouston Irvine born 20th April 1837
Jemima Irvine born 16th April 1840
Ann Irvine born 1842 (? born in Sandwick? Not in IGI this one)
Matilda Irving/Irvine is not a common name in the 1851 census (paid version) for Scotland
http://www.scotlandspeople.gov.uk/people/matilda_irvine_1836_1852and
http://www.scotlandspeople.gov.uk/people/matilda_irving_1836_1852Old Parish Records Banns & Marriages 1829 - 1831 (paid version) show Margaret Corgile's marriage but not sure the original image would tell much more:
http://www.scotlandspeople.gov.uk/people/margaret_corgile_1829_1831