A more concise formula of the meridian arc length was obtained by introduced two new parameters:the third flattening and the Gauss hypergeometric function.From another perspec-tive,the simplified formula is also can be explained by a Taylor series expansion.By this,we got error estimate of the formula in terms of the Lagrange form of the remainder.For numerical verification of the error estimate theory,application example was presented by using the WGS84 data.The results show that experimental data are consistent with the error estimate theory and the simplified formula is more precise than the standard one.%通过引入椭球的第三扁率及高斯超几何函数,导出子午线弧长解算公式的简化形式,并给出其泰勒级数解释,进而根据拉格朗日余项理论估计其误差.以WG S-84椭球参数为例进行验证分析,结果表明简化后的子午线弧长公式精度提高显著,误差估计理论正确.
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