How does Dalton's law apply to atmosphere?

Dalton's law simply states that the total pressure is equivalent to Pressures1 + Pressures2 + Pn and so on...

In regards to what relationship it has to the atmosphere this law can be applied to the various layers of the atmosphere and the individual pressures that each layer exerts upon the earth's surface.

Hypothetical Example:
Ionosphere's pressure = 0.01lb/insq
Lithosphere's pressure = 0.04lbs/insq

add these together and you will have the combined pressure exerted upon the earth.

You can also find the density of each of the individual layers by this pressure and figure out which gas(es) preside with in each of them.

This law is typically used to find the pressures of pure gases such as hydrogen or helium via in the chemistry lab. Each gas exerts a varied amount of pressure under different environmental circumstances such as Temp, elevation and whether or not it is in a sealed system.