The probabilistic theory of the structure invariants ϕ_h + ϕ_k + ϕ_l + ϕ_m in P1

Probability distributions associated with the third and fourth neighborhoods of the structure invariant φ_lm = φ_h + φ_k + φ_l + φ_m are described. These distributions yield estimates for the invariants φ_lm (not merely the cosine invariants cos φ_lm) which are consistent with a specified enantiomorph. The estimates are particularly good in the favorable case that the standard deviations of the distributions are small.