The duty of the moment is what you should be doing at any given time, in whatever place God has put you. You may not have Christ in a homeless person at your door, but you may have a little child. If you have a child, your duty of the moment may be to change a dirty diaper. So you do it. But you don’t just change that diaper, you change it to the best of your ability, with great love for both God and that child…
There are all kinds of good things you can do, but whatever they are, you have to realize that there is always the duty of the moment to be done. And it must be done, because the duty of the moment is the duty of God.