The author proposes, in a series of memoirs on this subject, to investigate the different problems of Hydrodynamics, in a manner which shall carry theory along with experiment. From the great attention that has been of late years bestowed on the question of the motion of the tide-wave, any mathematical investigation which does not assume some process of approximation, is extremely interesting. Whilst the more recondite problems of motion derived from impulses, &c. have been carefully examined by the greatest philosophers of the present day, the more simple and easy ones have been left almost untouched.