Definition of "alternately"

All night Katerina and I watched alternately, though, I shame to say, I slept more than I watched; and, having first ascertained that there was no change, I came directly hither.

1834, L[etitia] E[lizabeth] L[andon], chapter IX, in Francesca Carrara. […], volume II, London: Richard Bentley, […], (successor to Henry Colburn), page 102

Tired with the heat and my walk, I threw myself down on the grass in the shadow of the house, where I lay half-asleep enjoying a quiet rest, when I was startled by an unpleasant clamour, the jarring voice of a woman, who was trying by alternately scolding and using pet names to pacify a litter of grunting pigs on the farm.

1886, Peter Christen Asbjørnsen, translated by H.L. Brækstad, Folk and Fairy Tales, page 278

Well, I can't help noticing that you insult me and then you're polite to me alternately.

1970, “The Butcher Who is Alternately Rude and Polite”, in Monty Python's Flying Circus, season 2, episode 5, spoken by Customer (Michael Palin)

The 2025 timetable would feature two trains per hour, alternately routed via Kirkcaldy (with 11 intermediate stops) and Dunfermline (14 stops), with journey times ranging between 65 and 81 minutes.

2023 November 1, Robert Drysdale, “Leven is nearly back on track...”, in RAIL, number 995, page 58

Downstairs, he was informed. That is, down the escalators, where there is both a women’s room (often with a line) and a men’s room (almost never with a line). Or alternately, he could ask the station master to buzz him into the “family” bathroom. He opted to go downstairs.

2008 July 18, Jennifer 8. Lee, “A ‘Women Only’ Restroom Renovation Tips the Balance at Grand Central”, in New York Times‎