We can distinguish two limiting cases for Equation 7.15. When the time scale over which S' varies is slow compared to t, then the first term on the left hand side is negligible compared to the second, whence the solution becomes T' = tS'(t)/(pcpH) = S'(t)/a. In other words, the system acts as if it's in equilibrium with the instantaneous solar radiation at each time. In the opposite limit, the time scale of the solar fluctuation is rapid compared to t, in which case it is the second term on the left hand side that may be neglected. Thus,
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