ON HARMONIC PREDICTION OF TIDES. 323 



It is quite certain that the chief cause for the failure of harmonic methods for 

 shallow- water ports has been the incompleteness of analysis, and the absence of a 

 reliable method of dealing with the shallow-water constituents. This is under 

 investigation. 



Regarding the differences in predictions, it is necessary to consider four possible 

 causes : 



(1) differences in the values of harmonic constants used by the two authorities 



furnishing the predictions, 



(2) differences in the number of harmonic constituents that can be taken into 



account on the machines used for the calculation, 



(3) application of corrections, as at Liverpool, 



(4) uncertainty in the behaviour of machines. 



It will be admitted that the choice of harmonic ' constants ' that can be made ought 

 not to be a serious matter, especially where there are lengthy series of observations, 

 as in the first four examples quoted. 



In the case of Balboa, it is believed that the harmonic constants used are identi- 

 cal, and that no corrections have been made to the machine results, so that one 

 seems driven to assign the fourth cause. Theie is evidence from other sources 

 which tends in some cases to throw a certain amount of doubt on the behaviour of 

 predicting machines, but this also is under investigation by the Committee. 



The machines used for the purpose of predicting tides differ considerably in the 

 number of constituents that can be taken into account, but it is not much palliation 

 even to know that a machine is as accurate as it can possibly be, when important 

 constituents have necessarily to be treated as non-existent. Investigations at the 

 Tidal Institute point to the conclusion that the number of constituents required to 

 deal adequately with the shallow-water problem is considerably greater than that 

 allowed for in the building of tide-predicting machines. It is partly for this reason 

 that corrections by non-harmonic methods are sometimes applied, though their 

 success is very doubtful. 



The whole problem of the harmonic prediction of tides is being investigated by 

 the Committee, in collaboration with the Liverpool Tidal Institute and other 

 bodies interested in tidal work, and further information concerning progress will 

 be presented in their reports to the Association. 



2. Eeport on Harmonic Analysis of Tidal Observations in the British 



Empire. By J. Peoudman. 



I. The following report was undertaken for the Association through Prof. Lamb, 

 who has collected information from all the authorities concerned, and has been in 

 consultation with the author during the whole time of its preparation. 



It is based on information very kindly supplied by the Admiralty, the National 

 Physical Laboratory, Messrs. Roberts, Prof. D'Arcy Thompson, the Survey of India, 

 the Tidal Survey of Canada, Prof. R. W. Chapman of Adelaide, the Government 

 Astronomer of Western Australia, and the Tidal Survey of New Zealand, as well as 

 on the published literature of the subject. 



In the first place an indication is given of the origin of the various harmonic 

 constituents, which aims at explaining more than the customary popular accounts, 

 while avoiding the heavy mathematical formulae required for the analysis itself. 



In the second place a table is given of the results of analysis, the inconsistencies 

 in which show that the subject is in an unsatisfactory state. 



In the next place an account is given of the various methods of analysis that 

 have been used hitherto, with the object of making prominent their essential 

 features, and providing the basis of a critical examination of them. To complete 

 this critical examination requires a large amount of computative labour. 



Finally, a complete historical account is given, with bibliographies and lists of 

 analyses made. 



It is to be remarked that the principle of the harmonic analysis is part of the 

 theory of the small oscillations of a dynamical system, and its application becomes 

 less accurate as the range of tide becomes a larger fraction of the depth of the 

 water, or as the tidal currents become greater. It yet remains to be found to what 



