Was the Day of Atonement in the fall or in the spring?
The Day of Atonement was observed in the fall, not the spring. In Leviticus 16 it is distinguished from Passover, which was the spring feast. The Day of Atonement is known in English as Yom Kippur, and it was instituted shortly after Israel came out of Egypt.
Les explains that the Day of Atonement began back in the days shortly after Israel came out of Egypt, the same as all the other Feast Days such as Passover, First Fruits, and Unleavened Bread. He points out that Passover was the Feast in the Spring, the memorial of the Night of the Passover in Egypt when the death angel flew over and they were protected by the blood. But Atonement was in the Fall. Its present English name is Yom Kippur, which Les says is a far better definition than Atonement. He notes that in Leviticus 16 the word Atonement is really a misnomer because there was no atonement; animal blood could not take away sin. He also mentions you can split the word into At-one-ment, which is a good definition.