Thank you for the information. So far the particular branch of the Halton family that I ( and others within the family)have traced goes back to Ireland and Patrick Halton plus his wife Mary Anne.
Patrick was baptised in Dublin in Jan 1796 married circa 1818 and had one child John (born around 1819, married to Julia Ganley in 1838 died in 1888 in Mullingar). Recently we trraced the baptismal record of Patrick which recorded his parents as Michael(bc1770) & Elizabeth Halton of Dublin and a sponsor called Philip Halton (Philip with one "l" is still the traditional way of spelling the name in our family).
John and Julia had ten children Dr. Richard Joseph 1839-1880, Patrick William 1841-1909 (Manchester, UK), Dr.Matthew Corri 1843-1899 (Barnsley, UK), Mary Anne 1845-1846, John A 1847-1928 (New York, US from 1866), Ellen Mary 1849-1864, Dr. Frederick 1849-1928, Mary 1852-1927, James 1855-1856, and Dr. Michael Joseph 1858-1943. Richard Joseph's wife and six surviving children emmigrated to California,US after Richards death believed to have been between 1885 and 1890.
I have checked each family record for a Thomas, without success. However, there were many families with the Halton, Halton, Haltoun, Haltoon surname resident in the Westmeath/Dublin Area in the early to mid 1800's and it is quite possible there are links if we could go back far enough before 1770.
There is a family tradition that we moved to Ireland with the forces of Oliver Cromwell in the mid 1600's, which is unusual given the massacres he led in Ireland, and the temporary nature if the land grants he made there (repealed after 10 years). There was also a custom of forcing local families to use the surname of their local lords which may have led to the use of the name. There were Halton's in amongst Cromwells supporters especially from the Lancashire Region of the UK.
I hope this information is helpful, if only to eliminate some avenues of research.