Is this your James at home for the 1841 census?
James Mcarthur 46, coal miner
Agnes Mcarthur 46
Archibald Mcarthur 22
Rachel Mcarthur 15
James Mcarthur 13 b. Scotland
Agnes Mcarthur 11 b. Scotland
Mary Mcarthur 9
John Mcarthur 4
Address: Drumlunble, Campbeltown
Nancy and Ann are common variants of Agnes.
If the right family, your James and sister Agnes are showing as born outside the county of Argyll. Father's work as a coal miner might have meant that whilst they originated from Campeltown, his work may have taken his out of Argyll and some of the children born elsewhere.
Was James' mother Agnes McMillan? If so, these are some births showing for the children above to a James McArthur and Agnes McMillan. IGI only have a 'girls' batch' showing, SP may have more details including the male births/christenings:
1. CATHARINE MCARTHUR Birth: 11 JUL 1820/ Christening: 13 JUL 1820 Campbeltown, Argyll
2. MARGARET MCARTHUR Birth: 29 JUN 1822/ Christening: 30 JUN 1822 Campbeltown, Argyll
3. RACHEL MCARTHUR Birth: 06 JAN 1825/ Christening: 11 JAN 1825 Campbeltown, Argyll
4. AGNES MCARTHUR Christening: 27 MAY 1829 Old Monkland, Lanark
5. MARY MCARTHUR Birth: 28 SEP 1831/ Christening: 28 SEP 1831 Campbeltown, Argyll
Monica