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中文摘要：
为提高精度、统一算法，应用拉格朗日级数理论和计算机代数系统，推导了经线弧长和等量纬度的计算公式，提出基于墨卡托投影的恒向线主题正反算法．该算法不需要迭代，应用数学上角度的定义解决了恒向线主题反解中方位角的解算问题，且不需要进行象限判定．结果表明，该算法计算精度高，具有通用性，特别适用于电算化，对船舶的航迹计算和电子海图中的航线设计具有一定的应用价值．
英文摘要：
To improve the precision and unify the algorithm, an arithmetic for forward and inverse solution of rhumb line problem based on Mercator projection was presented, and the meridian arc length and isometric latitude were derived by applying lagrange theory and the computer algebra system, The algorithm has solved the azimuth calculating question without iterative calculations, which need not to make the quadrant determination for the azimuth. Results show that the algorithm has high precision and accords with the arbitrarily special situations without loss of generality, which is suitable specially for the program implementation and can be applied in the area of sailing computation and sailing line design in ECDIS.
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