How do the other characters know that the Time Traveler has been detained?

he leaves a note, just in case;

"‘You’ve just come? It’s rather odd. He’s unavoidably detained. He asks me in this note to lead off with dinner at seven if he’s not back. Says he’ll explain when he comes.’

‘It seems a pity to let the dinner spoil,’ said the Editor of a well-known daily paper; and thereupon the Doctor rang the bell."