Alan Bellingham Cairnes (b 1880) was the thirteenth child of William Bellingham Cairnes and Elizabeth Matthews.
I found his photo on Trove, and the Australian War Memorial provided these details:
"First World War Embarkation Roll - Alan Bellingham Cairnes. Service number: 2622. Rank: Private. Roll title: 58 Infantry Battalion - 6 to 9 Reinforcements (October 1916 - August 1917) Date of embarkation: 2 October 1916. Place of embarkation: Melbourne."
There is also information that at that time he was single and a bookkeeper living at 83 The Avenue, in the suburb of Coburg, and that his father, William Bellingham Cairnes, lived at 7 Bancroft St, Bendigo. He served in 58 Battalion and was wounded in action in France on 26/9/1917. He survived the war, and in 1923 he was at Vergemont Station near Longreach, Queensland.
This is one of a series of photographs taken by the Darge Photographic Company which had the concession to take photographs at the Broadmeadows and Seymour army camps during the First World War. In the 1930's, the Australian War Memorial purchased the original glass negatives from Algernon Darge, along with the photographers' notebooks. The notebooks contain brief details, usually a surname or unit name, for each negative. The names are transcribed as they appear in the note books. Place made: Australia: Victoria, Melbourne, Broadmeadows. Date made: ca. 14 August 1916. Darge Photographic Company Studio portrait of 2622 Private Alan Bellingham Cairnes, 58th Battalion from Coburg, Victoria. A 35 year old bookkeeper prior to enlisting on 3 July 1916, he embarked for overseas with the 6th.