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With an appendix b y Douglas R. Hartree An ex ample of n um e rica l integra t ion is given tha t shows ve ry systematic effects ill the less signifi cant d igits . This lack of rand omne,s g ives round ing-off errors t hat exceed the predicted standard dev iation by a racto r of t hree.Th e ex am pie co nsidered in t hi s paper s holl's that system.atic round ing-off errors can occu r in num eri cal in Leg ration , irres pect ivc of Lhe nllm be r of d igiLs kept in t he cont ribut ion s to the in teg rill. In the appendix this ph eno me no n is examined, and cri ter ia are set up Lo detect t he cases i n whic h iL may a ri~e Lo a se ri ou s exte nt .

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