There aren't many Archibalds on the Orkney census. According to the census transcripts on the Orkney family history society website, there are only four households with anyone named Archibald in 1861.
In Stromness
1. William Archibald, (M), 40, Head, Mar, Labourer, Fifeshire, Fife
2. Margaret Archibald, (F), 36, Wife, Mar, , Sandwick
3. John Archibald, (M), 8, Son, , Scholar, Stromness
4. Isabella Archibald, (F), 4, Dau, , Scholar, Stromness
5. Margaret Archibald, (F), 2, Dau, , , Stromness
In Firth and Stennes with a Cusiter family
6. William Archibald, (M), 10, Servant, , , Stromness (probably the 1851 birth to William and Margaret found by Annie)
Also in Stromness are
1. Hannah Archibald, (F), 80, Head, Wid, Soldiers Wife, Fifeshire, Fife
2. Margaret Archibald, (F), 36, Dau, S, Stocking Knitter, Stromness
And in Harray
1. William Archibald, (M), 45, Lodger, Mar, Road Lab, Fifeshire
By the 1871 census, the only William Archibald in Orkney is the one married to Margaret, aged 55 and still a labourer. There's another daughter, Jean aged 7. It looks like John and Isabella are both servants in other households.