A theory of extinction is derived which is valid within the limit of the Darwin intensity transfer equations. An expression describing the effect of n-fold rescattering within an ideal crystallite is derived, which differs from the equation given by Zachariasen because independent coordinates x1 and x2 based on an external coordinate system have been used, rather than the coordinates t1 and t2 which are only mutually independent if the crystal is a parallelepiped with faces parallel to the incident and diffracted beams. Furthermore, the derivation of the earlier expressions is based on a generally unjustifiable reversal of the direction of the diffracted ray (interchange of t2 and t'2). An exact expression is derived for the diffraction cross section σ(ε1) in the perfect crystallite, which contains a factor sin 2θ neglected in the earlier work. As a result, the previously used classification of crystals into type I and type II becomes less well …