LONDON — It was 2:30 in the morning, and Marc and Jo Stephens were at home in Redruth, Cornwall, when Ms. Stephens realized that their fourth child was about to be born, three weeks early.

The next thing Mr. Stephens knew, his wife was on all fours, the baby’s head was showing and events were moving inexorably along. Rather than having a panic attack, grabbing a large bottle of gin or running screaming into the street, Mr. Stephens, a 28-year-old navy engineer, applied the lessons he had learned earlier in the evening when, after his wife began labor, he typed “how to deliver a baby” into the Google search engine on his computer.