Alan chose the Hippodrome, and the three started off together in that direction. Knutty would have been somewhat surprised to see her two icebergs. They did not talk much, it is true, for Katharine did all the talking; but they laughed now and then, and made an occasional remark which was not at all Arctic. They had a splendid day together: a mixture of Hippodromes, ices, lunches, animated pictures, Natural History Museums, and camera-shops; and in the evening they dined together, and chatted, like old cronies, over the day's doings.
They knew that they owed the day's pleasure to Katharine's companionship; and when Alan said good night, he blushed and added with a jerk:
"Thank you."
And Clifford said:
"Yes, indeed, thank you for to-day—tak for idag, as the Danes say."
"Ah, I must learn that if I am going to Denmark," Katharine said, and she repeated it several times until Alan pronounced her to be perfect.
"Tak for idag, tak for idag!" she said triumphantly. "It is I who have to thank you for today."
She thought of them as she went to sleep. They seemed to her two pathetic figures, hapless wanderers, not fit to be alone in the world by themselves. She wished the old Dane had not left them. She dreamed of them; she saw in her dreams the boy's young face and the man's grave face. She heard the man's voice telling her that he had met and known her before, and she answered:
"Yes, it is true. We have met somewhere, you and I. Some message has passed between us somewhere—somehow——"
When she woke up, she remembered her dreams and lay thinking a long time.