The April to June 1858 birth index Joseph Simpson, Penrith, Cumberland, volume 10b page 365.

In the 1861 census living at Parkhead, Kirkoswald, Cumberland. Registration District Penrith, sub registration district Kirkoswald.
Head, Richard Simpson,age 39, farmer of 72 acres employing 1 man, born at Longmartin [Long Marton], Westmorland.
Wife, Mary, age 32, farmer’s wife, Longmartin, Westmorland.
Son John Simpson, age 7, farmer’s son, born at Longmartin.
Son Thomas William Simpson age 4, born at Kirkoswald, Cumberland.
Son Joseph Simpson age 2, born at Kirkoswald, Cumberland.
Son George Simpson, age 6 months, born at Kirkoswald, Cumberland.
Brother Edward Simpson, age 48, Carter (Ag. Labourer), born at Longmartin.
Niece Mary Swage?, age 18, dairy maid, born at Longmartin.

In the 1871 census living at Glendowling, civil parish of Bridge and Yanwath, ecclesiatical parish Carlise, town of Yanwath, Westmorland, registration district West Ward, sub registration district Lowther.
Head Richard Simpson, age 49, farmer of 73 acres, born at Long Marton, westmorland.
Wife Mary Simpson age 42, born at Long Marton.
Son John Simpson, age 17, works on the farm.
Son Thomas William Simpson, age 14, born at Kirkoswald.
Son Joseph Simpson, age 12, born at Kirkoswald.
Son George Simpson age 10, born at Kirkoswald.
Son Richard B. Simpson age 4, born at Kirkoswald.
Mother in Law Mary Bellas, widow, age 74, Landowners?, born at Bongate?, Westmoreland.
and 1 servant.

In the 1891 census living at the same address.
Head Richard Simpson age 69, farmer, born at Longmartin.
Wife Mary Simpson, age 62, born at Longmartin.
Son Joseph Simpson, single, age 31, armers son, born at Kirkoswald.
2 servants, 1 agricultural, 1 domestic.

He must have died before 1911 as his mother lists only 1 living child in the 1911 census who would be her son Richard.