A Stable Atmosphere
As briefly descirbed previously, in a stable atmosphere an air parcel will tend to return to its original position if displaced upwards or downwards, if left to itself. If a parcel is displaced upwards it will sink back to its original level due to the colder air being more dense than the air it moved in to. If a parcel of air is displaced downwards it becomes warmer than the ambient air and will tend to rise back up. In both these cases the air parcel comes across a restoring force after its displacement. This force inhibits vertical mixing.
For stable stratification (stable atmosphere) in an unsaturated (dry) atmosphere the environmental lapse rate must be less than the DALR. Generally, the greater the difference between the two the larger the restoring force.
In a saturated (moist) atmosphere if the environemtal lapse rate is less than the SALR then the atmopshere is stable. In this case the atmosphere is absolutely stable, as it is stable for both a dry and moist atmosphere.
In the figure below, if an unsaturated parcel of air (a) of temperature 30 degrees C were lifted from the surface it would cool at the DALR as it rose. At 1000m it would 20 degrees C, 6 degrees cooler than the environment, which in this case has cooled at 4 degrees per 1000m. If this parcel continued to rise it would become colder than its surrounds, and thus more dense, and so would tend to sink back down to it's original level. If this parcel were displaced downwards it would become warmer than its surroundings, less dense and therefore rise back up. The same is true for saturated air (b). The rising air is colder and heavier than the surrounding air in both cases.
Diagram showing an absolutely stable atmosphere where the environmental lapse rate is less than the SALR

a)
b)