There was plenty of time to dispose of the body unobserved--temporarily, at any rate.

Nobody had seen him come to the house, and nobody knew that he was there--if he _was_ there; and apparently no search was made either at the time or afterwards.

In fact, if it could be shown that the missing man ever left Hurst's house alive, or that he was wearing the scarab when he arrived there, things would look rather fishy for the Bellinghams--for, of course, the girl must have been in it if the father was.

But there's the crux: there is no proof that the man ever did leave Hurst's house alive.
And if he didn't--but there! as I said at first, whichever turning you take, you find that it ends in a blind alley." "A lame ending to a masterly exposition," was Thorndyke's comment.
"I know," said Jervis.

"But what would you have?
There are quite a number of possible solutions, and one of them must be the true one.