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PROCEEDINGS OF THE 



[Jan., 1857. 



floating in the stream, &c. ? the following method might he prac- 

 ticed, by observations on the parabolas described by the cascades 

 at different points. Direct the centre of the cross wires of a 

 theodolite to the vertex V, of the curve of the cascade at a dis- 

 tance from the instrument known by survey, then turn the tele- 

 scope through a known horizontal angle to the point O, then de- 

 press the telescope through a known vertical angle, to a point P 

 in the stream of water proceeding from V, then from these known 

 angles, and the known depression of the points O and V below the 

 centre of the instrument and the distance of V, find the length of 

 O V and O P in feet, then will the required velocity v at the point 



4 X O V 



Y be given in feet by the equation v = The chief difficulty 



J * V o p J 



will be in determining the point V or vertex of the parabolic curve. 



The points I have sought to establish in this paper, on the 



supposition that the gorge is excavated by the action of the Falls 



themselves, are the following : 



1. That, from the sameness of direction of the sides of the 

 gorge above and below the American Fall, the main Fall has cut its 

 way to G independently of the existence of a lateral stream or 

 fall. 



2. That in consequence of the continuity of the line A D G to 

 F, it is probable that the abruption in the Canada Fall takes place 

 chiefly along the line F H, and that the recession of this Fall will 

 be in the direction of the line F I, so that finally the line of brink 

 of the two Falls, Canadian and American, will be nearly the same 

 along the line A I or one parallel to this. 



3. That the recession of the Canada Fall is not less than fifteen 

 times greater than that of the American Fail in the same time, and 

 therefore, that no deduction from the recession of the latter is 

 applicable to the former without modification. 



4. That it is probable that the ratio of recess in the two Falls is 

 greater than that of their volumes of water.* 



The two following gentlemen were proposed as Curators, 

 and unanimously elected:- 



Robert Hume, Esq. Dr. F. Peyre Porcher. 

 _ — . 



*Prof. Hall informs me that my letter to him has been entered on the list of 

 papers presented to the American Association at their last meeting, and that it 

 will appear in their proceedings, accompanied by his remarks. The above paper 

 may be regarded as a revised form of that communication, 



