where v/ = v — vc. The argument of the exponential is just the optical thickness of the layer between p1 and p2 , and to keep the notation simple we will assume the integral to be taken in the sense that makes it positive. The double integral and the nonlinearity of the exponential make this a hard beast to work with, but there are two limits in which the result becomes simple. When the layer of atmosphere between p1 and p2 is optically thin even at the center of the line, where absorption is strongest, the line is said to be in the weak line regime. All lines are in this regime in the limit p2 ^ pi, though if the line is very narrow or the intensity is very large, the atmospheric layer might have to be made exceedingly small before the weak line limit is approached. For weak lines the exponential can be approximated as exp(—St) « 1. — St, whence
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