Predicting tracer responses and E curves

Caqui O may be obtained by summing all the system responses to these individual inlet impulses. Now consider the tracer which emerges from the system at a time t in the shaded area 2 of Fig. 8. That portion of it which derives from the shaded element 1 of will equal the total tracer 

Fraction of tracer staying in the system for a time between (t — t ) and (t — t + At) units of time. 

In the limit, as the rectangle width At shrinks to zero, this discrete summation becomes equivalent to the integration of eqn. (26) with the second bracketed term of eqn. (25) being the definition of E(f — t )dt (see Sect. 3.1). 

Equation (26) involves the dummy variable t which will disappear on integration. Analagous arguments enable the convolution integral of eqn. (26) to be expressed in the alternative form. 

From eqn. (A.2) (Appendix 1), CA , (t) can also be defined through Laplace domain analysis by the equation 

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