Abstract
The mathematical theory of water-exit and -entry is critically reviewed. A detailed examination of each of the principal methods of analysis available shows that none of them yields even a uniformly valid approximation to the solution during surface crossing. It is concluded that, due to mathematical difficulties inherent in the problem, the best hope for obtaining a reliable estimate of the loads felt in crossing lies with a numerical analysis. Specific recommendations are made as to the formulation of practical numerical methods.

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