A reconciliation of extinction theories

The differences between previous theoretical treatments of extinction based on the Darwin intensity equations arise because of the different functional form chosen for the coupling constant σ. When the same function is used these theories make closely similar predictions. It is shown that a limiting condition on integrated intensity as the crystal size increases puts restrictions on the functions which may be used. A Lorentzian or Fresnellian function can be used for primary extinction while secondary extinction requires a Gaussian, rectangular or triangular function. An analytical expression is given for the variation in the value of the extinction factor with scattering angle.