【摘要】 本文首先根据习认为的泥沙粒径的对数值1nd服从正态分布的假设,导出粒径d的对数正态分布式及其相应的均值和方差计算式,与此同时,从理论上指出天然沙的平均粒径d_pj恒大于其中值粒径d₅₀;其次,给出一种确定混合沙全沙代表粒径d_j以及任意粒径组泥沙的代表粒径（中值粒径）d_j50的方法和计算公式;最后,从数学上证明并指出目前有些河流动力学教科书中关于与正态分布有关的诸如平均粒径d_pj、几何平均粒径d_?、均方差σ或σ_d以及四分差σ_q等几个表达式的正误。更多还原

【Abstract】 Based on the law of normal error of the logarithmic value of particle size for sediment composition, the expression of logarithmic normal distribution of particle diameter is derived, and the formulas calculating the mean diameter of the composition and the standard deviation are also given. By theoretical analysis, the mean diameter of the sediment mixture is always larger than the median diameter. Finally, a few mistakes in some textbooks are pointed out.更多还原