Why did James say the drought in the time of Elijah was 3.5 years long?

Both Jesus (Luke 4:25) and James (James 5:17) refer to the 3.5 year drought in Elijah’s day.  In 1 Kings 18:1, we read

After many days the word of the LORD came to Elijah, in the third year, saying, “Go, show yourself to Ahab, and I will send rain upon the earth.”

This is the only reference I can find to a three year drought in 1 Kings 17-19.  According to R.A. Torrey in Treasury of Scripture Knowledge:

This form of expression, both in Hebrew and Latin, means “after the third year,” ie., some time between the third and fourth year

If R.A. Torrey is correct, this explains the apparent discrepancy in the time periods given.