Not quite sure how all of these Moriarty folks connect, but there's little doubt that they are all connected. From the Kansas 1865 Census (August 31, 1865), Clear Creek Township, Nemaha County, Kansas.
John Moriarty 53 Farmer Real estate $500 Personal estate $475 born in Ireland ca. 1812
Catherine Moriarty 39 born in Ireland ca. 1826
Thomas Moriarty 19 Teacher of public s.[?] born in Ireland ca. 1846
Michael Moriarty 15 Teamster born in Ireland ca. 1850
Elisabeth Moriarty 10 born in Connecticut ca. 1855 (see elsewhere, in Wisconsin)
John Moriarty 5 born in Kansas ca. 1860
Thomas Moriarty 4 born in Kansas ca. 1861
Margaret Moriarty 2 born in Kansas ca. 1863/1864
Mary Ann Moriarty 4/12 born in Kansas in ca. April 1865
Patrick Hines 54 Farmer Real estate $600 Personal estate $800 born in Ireland
Margaret Hines 33 born in Virginia ca. 1832
Mary Moriarty 14 born in Virginia ca. 1851
Jane Moriarty 11 born in Virginia ca. 1854
John Moriarty 9 born in Virginia ca. 1856
James Moriarty 6 born in Kansas ca. 1859
Margaret Moriarty 3 born in Kansas ca. 1862
Julia Hines 4/12 born in Kansas ca. April 1865
Daniel Mitchell 57 born in Ireland ca. 1808
Mary Mitchell 39 born in Ireland ca. 1826
John Mitchell 19 born in Ireland ca. 1846*
William Mitchell 11 born in New York ca. 1856
etc. *Note: I read somewhere in a book that John Mitchell (born Ireland 1846-died 1890) and Mary (Moriarty) Mitchell of Clear Creek had a kid named Daniel S. Mitchell born June 23, 1875.
Also note: there are at least two Moriarty homesteaders in Clear Creek Township, Nemaha County, Kansas in 1859: J. and P. Moriarty.
Hoping to trace the Moriarty family/families back to Ireland.
Erik Donald France: firstname.lastname@example.org