The free "Quick Search" on the imuseum website has:
William Arthur Christian
Date/Epithet 24 July 1870
Category Baptisms
Parish Patrick
Abode Glen Rushen
Biography
Parents: Thomas Christian (miner) & Eleanor Christian
Nationality Manx

You could buy the marriage cert to see whether Thomas's occupation and residence matches the details given at the bapt. Assume you have checked censuses?

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