Though, when she went over close to him again, she saw that even this pause had allowed him time to think, and that his face was once more overcome by melancholy, although he greeted her with a smile.
Something further must be done.
"Henry," she said, cooingly, kneeling down beside him and taking his hand, "will you promise me something, please.

I am not clever like you, but I do know one splendid recipe for taking away pain; every time the thought of Sabine comes up to you and the old pictures you used to hold, look them squarely in the face, and then deliberately replace them with others that you can obtain--the strange law of periodicity will be in motion and, if you have only will enough, gradually the pictures that can be yours will unconsciously have taken the place of the old ones which have caused you pain.

Is it not much better to do that than just to let yourself grieve--surely it is more like a man ?" Henry looked at her, a little startled.

This idea had never presented itself to him.

Yes, it was certainly more like a man to try any measure than "just to grieve," and what if there should be some truth in this suggestion--?
What did the "law of periodicity" mean?
What an American phrase! How apt they were at coining expressive sentences.