On the measuring errors of non-normal distribution and the limits of run error

Besides the normal distribution errors,there are other varieties of measuring errors,such as,the uniform distribution errors or the errors subjected to the distribution of the sum of a uniform distribution and a normal distribution.This paper is intended mainly to discuss the distribution of the sum of a uniform distribution and a normal distribution.The formulas of the distribution density and the probability of this distribution are derived and a comparison between this distribution and the normal distribution is made.Then the author analyses the sighting error of a precision theodolite or level influenced by the run error of the micrometer and points out that this error subordinates to the distribution discussed above.The limit of the run error is suggested as 2β=3σ,where σ is the standard deviation of the sighting error Finally opinions are expressed for the revision of the current official specification for the run error limit of the then dolits J₀₇,J₁ and the level S₀₅.