Brian, apart from the James/John issue, the entries that Butterlily has found would look to correspond with the children of John and Margaret. From IGI:
1. SARAH DICK HAMILTON Birth: 14 APR 1857 Calton, Glasgow
2. WILLIAM HAMILTON Birth: 06 MAR 1859 Calton, Glasgow
3. JOHN HAMILTON Birth: 28 MAY 1864 High Church, Glasgow
4. ROBERT SHAW HAMILTONBirth: 01 MAR 1868 Calton, Glasgow
5. ELIZABETH HAMILTON Birth: 04 APR 1871 High Church, Glasgow
The family's 1861 census entry in Calton shows father as John from Co. Antrim (rather than Glasgow born as per later censuses).
John Hamilton 26, tailor b. Co. Antrim
Margret Hamilton 25 b. Galston Ayrshire
Sarah Hamilton 4
William Hamilton 2
Monica
