Abstract
The correlated probabilities of lateral and angular displacements of cloud-chamber tracks, resulting from multiple small-angle scattering, have been calculated for several cases of interest. The results are applicable to curvatures and other measurements taken in the presence of a magnetic field. The usual Gaussian-type scattering law has been used in the form of the fundamental correlated distribution function derived by Fermi. One direct application of this function is to the effect of scattering on angle measurements in nuclear "stars."A "three-point formula" is derived, involving a correlated distribution of two successive lateral displacements with the resultant angular displacement. The distribution of scattering-produced curvatures, originally derived by Bethe, is calculated. A "four-point formula" allows a quantitative discussion of the tendency of scattered tracks to appear circular rather than skewed or S-shaped.Finally, a formula is derived for the distribution of the successive chord angles for a track observed at several points, and used to discuss the best method of averaging the observations to reduce scattering-produced curvature errors. The error produced by scattering is not appreciably diminished by taking the best mean for an observation of the track at a large number of points, instead of a single observation of chord and sagitta (three points).
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