This is the first character that we are introduced to. He goes unnamed throughout the story, so we'll just call him "the married man" from now on. His "married-ness" is an important attribute: he appears with his wife and children lagging slightly behind him on the path, and he is completely obsessed with memories of his proposal to another woman (Lily), fifteen-years ago in this very garden:
<em>We sat somewhere over there by a lake and I begged her to marry me all through the hot afternoon</em> (3).
You might think—dude, fifteen years ago, time to move on. We'd have to agree, but still, this bit is significant because Woolf uses the man's memories to show how the natural world acts upon characters thoughts. In the case of the married man, the experience of being in the garden is kind of like a walk down memory lane. He's also not the only character who's obsessed with memories in this story—so we'll want to keep thinking about this relationship between nature and memory.
The man's preoccupations with the past also isolate him from the other characters—he is keeping his distance from his family in order "to go on with his thoughts." In this way, Woolf also highlights the alienation and isolation that many characters experience in the garden: it's a social setting, but the married man (like certain others) is locked up in his own interior world.