Here's what Nicky wrote for Alexei's birth:
"30 July, 1904 - Peterhof
A great and unforgettable day for us, during which we were clearly visited by the grace of God. At 1.15 in the afternoon Alix gave birth to a son, whom we named Alexei as we prayed. Everything happened remarkably quickly - at least for me. In the morning I went to visit Mama as usual, after which I went to find Alix for lunch. She was already upstairs, and half an hour afterwards the happy event occurred. There are no words to thank God enough for sending us this comfort in a time of sore trials!
Dear Alix felt very well. Mama arrived at 2 o'clock and sat with me for a long time before her first meeting with her new grandson. At five o'clock I took the children to a Te Deum, which all the family present. Wrote a mass of telegrams. Misha came from the camp; he said he was now 'in retirement'. Dined in the bedroom."
And this message was found in Alix's notebook:
"30 July 1904
Weight 4660; length 58. Measurement of the head 38; chest 39
The Heir Tsarevich Alexei Nikolaevich was born on Friday 30 July 1904 at 1.15 in the afternoon."