You say 1 second, I always thought we gain or lose two minutes a day. One minute at sun rise and one minute at sun set.
http://www.timeanddate.com/sun/usa/springfield-ma?month=6Here's where I got my info. It states the biggest difference from one day to another, in the spring, is 2 mins 51 secs.
You can adjust it to the largest city near you.
Cool site that gives info on sun distance, angle and a bunch more.