304 PROCEEDINGS OF THE AMERICAN ACADEMY 



tion is in visible contradiction with the remarkable theory of " waves," 

 by Mr. Airy, the works of Whewell, and others ; but I will immediately 

 show that it would be highly important to apply the solutions given in 

 these works to the explanation given in my former notice. There I 

 particularly endeavored to explain the origin of tidal currents of great 

 rate, and then I said, in short, that we should have to investigate the 

 propagation of tidal currents in bays. Mr. Whewell, in his numerous 

 works, having acquainted us with the geography of the phenomena, 

 and shown many details, as well as many empirical laws of the tides, 

 avails himself also of the idea of " cotidal lines " in explaining the pecu- 

 liarities of the tides. As is well known, the cotidal lines are curves 

 drawn through the points of simultaneous high waters ; their position 

 on the map is associated with the idea of the propagation of tidal mo- 

 tion. The phenomena of tides in the ocean being fully determined by 

 the theory, it is evidently impossible to draw the cotidal lines across 

 the ocean, in the same way as the question is impossible, — "Whether 

 high or low water will occur at the transit of an attracting body." 

 It would be highly important to make use of the theory of cotidal lines 

 to explain the propagation of tidal currents, in which case the cotidal 

 lines will be the direct expression of the physical law. The cotidal 

 lines connecting the points, at which the greatest velocity of tidal cur- 

 rents is being simultaneously observed, are necessary for the study of 

 tidal phenomena in large bays (as e. g. White Sea and German Ocean). 

 Notwithstanding this, the explanation of the phenomena is still very 

 difficult when they occur in rivers, and where the tide rises gradually ; 

 whereas the superficial currents are very irregular and slack. In these 

 cases, starting from the theory developed by Mr. Airy in his work 

 " Tides and Waves," we arrive at the laws of the phenomena. If, in 

 fact, the pressure of the ocean in its progress meets with great resist- 

 ance in the system of waters in a quiescent state, or running in the 

 opposite direction, then the propagation of this pressure will be observed 

 as taking place in the form of waves (positive). 



The general description of the phenomena of tides was given by me 

 in the more simple case when the bay is immediately connected with 

 the ocean. The observations of tidal currents made by many eminent 

 American, English, and French observers, and also the full investiga- 

 tion of tidal currents in the White Sea by the Russian hydrographer, 

 Risnecke, have been taken by me as authorities. From the foregoing 

 remarks we can infer how complicated the phenomena will be in many 



