Generally, on the birth of an Imperial child there were celebrations and such. If course if it was a boy, it became a bit more to say the least. If it was a boy more political stuff was done, and it was basically a celebration for everybody. For a daughter, it was obviously less, especially a fourth daughter were it was generally hoped and expected there would be a son, an heir. I suppose he made promises that there would these sorts of things it was a son, and everbody in general expected it, he didn't need to say that such things would be. And I believe that in the case of Alexei everything that happened when an heir was born happened, especially a long awaited heir. But someone should check the stats on Alexei's birth just to make sure. The New York times is certainly a valuable source of info on the Romanovs from a contemporary, foreign viewpoint.