There could be an element of joy in this headstone inscription, joy that after four years with no news of her son's fate, Mrs Adela Marion Adam eventually discovered that he had died on the day that he went missing and that the Germans had buried him. In 1920 she published a memoir of her son, 'Arthur Innes Adam', in which she was forced to conclude, "Exhaustive enquiries in Germany, and through several neutral countries and America, have failed to discover the least vestige" of his fate, "there is no glimmer to lighten the impenetrable darkness".
In their history of the Cambridgeshire Regiment, ≈'The Cambridgeshires 1914-1919', Riddell and Clayton record how on 16 September Lieutenant Shaw led an attack on a German strong point, which failed. Shaw withdrew his men successfully but went back when he discovered one man was missing. Captain Adam went with him. He was not meant to have been there but, as the History relates [pp55/6]:

"Under the scheme for the attack Shaw was to be the only officer with the party; but they were all mere lads, and who could blame one so young and fearless for desiring to be with those he commanded in their hour of danger? He had worked for his men day in and day out, and loved them all. As a soldier he was wrong, but as a man he felt he could not leave them."

Both Shaw and Adam were shot and wounded. Another officer went out to find them. He too was shot. During the night another party was sent out but had to be withdrawn as it grew light. The following night a patrol went out and discovered, "All traces of the wounded officers and stretcher-bearers had disappeared".
In September 1920 the Graves Registration Unit located Adam's body in Achiet-le-Petit Communal Cemetery German Extension. And in 1924 it was exhumed and reinterred in Achiet-le-Grand.
Arthur Innes Adam was a prize-winning scholar at Winchester and Balliol College, Oxford. He never returned for his final year but took a commission in the Cambridgeshire Regiment, relieved that his extreme shortsightedness hadn't in the end prevented him from foreign service. He was full of ability and potential but his mother concluded her memoir by saying, "It is idle to enquire what he might have become; let us sing Laus Deo for what he was".
But we might allow ourselves to speculate. On 2 November 1915 he wrote to his sister, Barbara, saying that for the last two years he had had 'a kind of hope in him' that some day they might be able to work together towards lessening the misery caused by wrong-doing. And that "at least, if I am killed, I will now have mentioned the idea to you ..." . Barbara Adam married Jack Wootton in September 1917. He died of wounds six weeks later. In 1958 Barbara Adam, "an acknowledged expert in criminology, penology, and social work" [Oxford DNB], was created Baroness Wootton of Abinger. What might her brother have done too?