Eric,

The William Edward White you are researching was baptised at St Mary's R.C. Church, Douglas, I.O.M.

William White & Bridget Murphy were married there on 27 July 1878. So far I can't find a baptism for Patrick.

Their children's baptisms from baptismal register at St. Mary's:

Mary Frances b. 21 April 1879 Bp. 25 April godparents Joseph Murphy & Mary Canton ?

William Edward b. 29 May1883 Bp. 03 June g.parents Lawrence White & Mary Ann Murphy
The entry is annotated with a record of his marriage at St. Patrick's Church, Adelaide, Australia, to Isabella Jane Brown 21 June 1919

Joseph Lawrence b. 20 Feb 1886 Bp. 28 Feb g.p's Patrick & Mary Murphy

John James b, 06 Feb 1889 Bp. 17 Feb g.parents Thomas Abbott & Elizabeth White
married at St Mary's Douglas to Florence Callister 26 Nov 1910

Beatrice Lizzie ( The christian name is missing in baptismal register) b. 10 May 1890 Bp. 18 May g.p's Thomas Carpenter & Elizabeth Murphy

Edmund George, b. 26 April 1892 Bp. 05 May
g.p's Patrick & Mary White

Ellen May, b. 27 August 1893, Bp. 10 Sept. g.p's William White & Catherine Finn

Hope this is of some use to you.
Marie Radcliffe