The Tree of Heaven by May Sinclair

It was as Nicholas had said. Anthony and John were rejected; Anthony on account of his age, John because of the mitral murmur that he didn't know about.

The guv'nor had lied, John said, like a good 'un; swore he was under thirty-five and stuck to it. He might have had a chance if he'd left it at that, because he looked a jolly sight better than most of 'em when he was stripped. But they'd given him so good an innings that the poor old thing got above himself, and spun them a yarn about his hair having gone grey from a recent shock. That dished him. They said they knew that sort of hair; they'd been seeing a lot of it lately.