In order to explore the internal relationship between Gauss and transverse Mercator projections on the sphere,the cylinder in normal Mercator projection is rotated right to touch the sphere at one meridian,and the formula of transverse Mercator projection is obtained on the basis of spherical triangle theorems.Considering transformation of power series expansion is not easy to be realized,expression of Gauss projection by complex numbers is derived.Based on the definition of complex variables and regular elementary functions,strict verification of equivalence between Gauss and transverse Mercator projections on the sphere is carried out via a series of mathematical analysis.%为探寻球面高斯与横墨卡托投影间的内在联系,将墨卡托投影中的圆柱旋转90°,与某一子午线相切,并根据球面三角形定理得到横墨卡托投影的一般表达式；考虑到高斯投影实数型级数展开式不易于进行公式变换,推导出球面高斯投影复变函数表示式；根据复变函数及常用初等函数的定义,从高斯投影复变函数表示出发,经过一系列数学分析过程,给出球面高斯投影与横轴墨卡托投影等价性的严格证明.
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