ON HABMONIC PBEDIOTION OF TIDES. 321 



Tidal Institute at Liverpool. — Report of Committee (Prof. H. Lamb, 

 Chairman, Dr. A. T. Doodson, Secretary, Sir S. G. Burraed, 

 Sir C. F. Close, Dr. P. H. Cowell, Sir H. Darwin, Dr. G. H. 

 Fowler, Admiral P. 0. Learmonth, Sir J. E. Petavel, Prof. J. 

 Proudman, Major G. I. Taylor, Prof. D'Arcy W. Thompson, 

 Sir J. J. Thomson, Prof. H. H. Turner). 



1. Report on Harmonic Prediction of Tides. By A. T. Doodson, D.Sc. 



The present state of heirmonic prediction of tides cannot be regarded as very satis- 

 factory, and this report has been written with the object of calling attention to 

 the matter. For some of the information the writer is indebted to the Hydrographic 

 Department of the Admiralty. 



While real accuracy in the prediction of tides is not obtainable at present, owing 

 to inability to predict effects of meteorological variations, yet one would expect that 

 the normal, or undisturbed, or periodic tide could be accurately given. That such 

 is not the case is well known to those who have compared observations with pre- 

 dictions ; there are periodic or systematic differences in height and time of high 

 water which are sufficiently serious in many cases to cause distrust. This is 

 especially the case with harbours in river estuaries or in comparatively shallow seas, 

 and, in fact, the distrust has led in many cases to the complete abandonment of the 

 method of harmonic prediction. Thus the Hydrographic Department of the 

 Admiralty report that the German and Netherlands tidal authorities have found 

 the methods of harmonic prediction so seriously in error that they have abandoned 

 them, and the experience of the Hydrographic Department for the North Sea has 

 also been very unfavourable to the continuance of this method. For many ports 

 situated in estuaries, and catered for by British authorities, it is customary to apply 

 non-harmonic corrections to the results of harmonic prediction. 



It is generally admitted, however, that harmonic predictions for oceanic ports 

 {i.e., ports open to the free influence of the deep water oceanic tide wave) reach a 

 high degree of accuracy. The general continuance of the harmonic method of 

 prediction, therefore, will depend very largely upon the solution of the ' shallow- 

 water problem.' This calls for scientific research, and, concerning it, reference may 

 be made to future reports of the Committee. 



That the method of harmonic prediction for river ports should be in danger of 

 discontinuance could be taken as sufficient evidence regarding the unsatisfactory 

 state of harmonic prediction, but a few figures may serve to show what degree of inac- 

 curacy is considered by authorities to be unsatisfactory. For instance, at Quebec 

 the average error, regardless of sign, is as high as 16 minutes for high water, and 

 28 minutes for low water predictions, though the harmonic constants for Quebec are 

 based on over 19 years' continuous observation. Again, a comparison of observa- 

 tions with predictions of high water at Liverpool shows a very marked oscillation 

 in the differences, of which the following is an example : — 



10, 6, 11, 3, 9, 4, 13, -1, 8, -7, 8, 2, 8, 2, inches ; 



thus successive high waters are alternately predicted too low or too high by as much 

 as seven inches. (The predictions are taken from the tables of 1918. It should be 

 stated, however, that these are not purely harmonic predictions, but are corrected 

 by non-harmonic methods.) This is probably due to incomplete or faulty analysis, 

 and, concerning this, reference may be made to Prof. Proudman's Report on 

 Harmonic Analysis, where comparisons between observation and prediction of hourly 

 heights are recorded for Liverpool, 1869 ; it has been shown that this represents 

 also the present day state. 



If, however, the above evidence were not g,vailable an estimate of the value of 

 1920 Y 



