Watson was able to infer from looking at Stapleton that he was the naturalist that had been spoken of. Watson did this by noticing the things Stapleton had with him: "A tin box for botanical specimens hung over his shoulder and he carried a green butterfly-net in one of his hands."
Watson also noticed that Stapleton had an unusual energy and manner about him. Here is the description Watson gives of watching Stapleton run across the moor:
"...in an instant Stapleton was rushing with extraordinary energy and speed in pursuit of it. To my dismay the creature flew straight for the great mire, and my acquaintance never paused for an instant, bounding from tuft to tuft behind it, his green net waving in the air. His gray clothes and jerky, zigzag, irregular progress made him not unlike some huge moth himself."
While Watson will leave the Stapletons with nothing but a sense of concern for how isolated they are, this description, combined with Stapleton's questions, will begin to plant seeds of suspicion later on.