Section III, 1919 [139] ■ Trans. R.S.C. 



The Analysis of Simple Periodic Curves hy a Projection Method, with 

 Special Reference to Estuary Tidal Problems 



By A. Norman Shaw, D.Sc. and Violet Henry, M.Sc. 



with an Introduction by 



Dr. Bell Dawson, F. R.S.C, Superintendent of Tidal Surveys 



FOR Canada 



Presented by Dr. Bell Dawson, F.R.S.C. 

 (Read May Meeting, 1919.) 



§1. Introduction (by W. B. D.) The question discussed in this 

 introduction is the problem of dealing with estuary tides by the method 

 of harmonic analysis. This analysis is now very generally adopted as 

 the best means of arriving at the tidal constants by which the tides of 

 a future year can be calculated and published as a tide table. The 

 importance of estuary tides is evident, as a large number of the prin- 

 cipal harbours of the world are situated in estuaries, owing to the 

 fact that ocean traffic may penetrate further inland on account of 

 these tides. The tides in an estuary have features of their own, which 

 necessitates special treatment in the analysis in a way that is entirely 

 empirical; and the present endeavour is to improve upon this. 



Characteristics of Estuary Tides. On an open coast of the ocean, 

 the tide consists of an undulation which is fairly symmetrical in form, 

 and has a period of about 123^ hours; the summit of the undulation 

 occasioning high water, and the trough, low water. When this un- 

 dulation enters an estuary, it is opposed by the outflow of the river; 

 and in consequence the rise of the tide becomes more rapid and the 

 fall longer. 



In the outer part of the estuary, the undulation occasions an 

 inflow and outflow alternately; but further up the river a point is 

 reached where the river-flow overcomes this, and the current is al- 

 ways in one direction with only a fluctuation. But the river volume 

 meeting the incoming undulation still causes a rise and fall. Gradually 

 however, the river slope, up which the undulation has to travel, 

 together with bottom and side friction, combine to reduce the amount 

 of the undulation till its amplitude falls to nothing. 



In the actual analysis, all these physical and hydraulic features 

 of the progress of the tide up the estuary, as well as the horizontal 



