What does the copper pointer and the scaled piece over which it travels control? The scale has the word "longer" stamped into it, but it's not clear to me exactly what effect it has on the operation of the thermostat.
I am not sure about that particular thermostat, but that sounds like the anticipator control. Longer will mean the heat will stay on longer each time it comes on. That usually translates to slightly wider temp swings and slightly higher efficiency. The thermostat is guessing how long to leave the heat on, knowing that if it waits until the temperature at the thermostat gets up to the set temperature, and turns it off when that is sensed the temperature is going to end up hotter than intended.
Usually you can just leave it were it came and not worry about it. That is likely the best setting.
That is called the heat anticipator, and yes..it does indeed effect the stat. You set the anticipation setting to that setting that the furnace states, and leave it alone. It influences the spring stat and will prevent your furnace from overshooting, or short cycling.
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