January i i, 1906] 



NA TURE 



249 



influence of the rotation in the restricted problems 

 dealt with, by no means appear to justify this 

 course. 



If, however, a complete tidal theory which should 

 adequately account for all the phenomena of observ- 

 ation has hitherto been found wanting-, at least con- 

 siderable advance in the coordination of observed 

 phenomena has been obtained by the introduction 

 of the harmonic analysis for the discussion of tidal 

 ob ervations, while tidal records suitable for such 

 analysis have accumulated. These, so far as they 

 are accessible at all, are scattered through various 

 scientific publications, and the author has rendered 

 a valuable service to all interested in tidal phenomena 

 in collecting them in tabular form in a single memoir. 

 The tables given on pp. 664-677, part iv. A, and pp. 

 342-351, part iv. B, contain the results of the 

 harmonic analysis of tidal observations taken at more 

 than four hundred stations distributed throughout the 

 world, and probably contain almost all information 

 of a precise character in relation to the tides at 

 present available. These tables give the amplitudes 

 and phases of the principal types of oscillation as 

 derived from observation alone, and only involve 

 theory in so far as it enables us to assign the periods 

 in advance by means of exact astronomical data. It 

 is to be regretted that in no case is any indication 

 given of the degree of precision with which the 

 analysed results reproduce the actual observations 

 from which they are derived, or of the extent to 

 which they confirm the theory on which they 

 depend. 



A considerable portion of the memoirs is further 

 devoted to an attempt to coordinate the results 

 derived from different stations so as to form a com- 

 prehensive picture of the general progress of the tide- 

 wave over the surface of the ocean, and the results 

 are exhibited in a series of charts indicating the 

 position of the wave crest at each successive cotidal 

 hour. 



The construction of these charts is, unfortunately, 

 but vaguely indicated. As already stated, no ready 

 means is provided of estimating the value of the 

 material used for the purpose, or of the methods used 

 for its combination. 



In so far as these charts are based on the results 

 of observation alone we are prepared to believe that 

 they give a fairly accurate representation of the 

 actual tides in the regions where observations are 

 sufficiently numerous to supply the necessary informa- 

 tion, but, as is well indicated in the cotidal chart due 

 10 Berghaus and reproduced bv the author, there 

 will remain very considerable tracts of the ocean 

 surface about which no observational information is 

 available, and which are left blank on the charts 

 prepared by Berghaus. In fact, as tidal observation 

 is almost of necessity confined to the neighbourhood 

 of the coast lines, the only method of filling in such 

 blanks is to have recourse to theory, and the correct- 

 ness or otherwise of the charts prepared by the 

 author must therefore depend to a very considerable 

 extent on the correctness of the theory which he has 

 put forward, which forms the principal subject erf 

 Part iv. A. 



This theory has already been the subject of adverse 

 criticism in Nature (September 4, 1902, p. 444), and 

 we cannot but regret that we have to adhere to the 

 objections to it previously raised. 



Without reverting to these objections it is rather 

 our purpose here to examine the particular applica- 

 tions of it now dealt with in part iv. B, which con- 

 stitute the chief purpose for which it was designed. 



NO. 1S89 VOL - 73] 



The object Of the author, as he himself expresses it, 

 is " to obtain through theoretical consideration- . . . 

 a first approximation to the times of the principal 

 ocean tides," i.e. the phases of the oscillations in 

 relation to those of the disturbing forces which 

 produce them. The times in question are deduced 

 from a theorem based on the analogue of the com- 

 pound pendulum which asserts that in maintained 

 simple harmonic motion under the action of friction 

 " the virtual work of tin- external periodic forces is 

 zero at the instant of elongation." If we rightly 

 understand the significance of this theorem, it would 

 appear to imply that, at the instant of elongation, the 

 disturbing forces which give rise to the type of 

 motion under consideration form an equilibrium 

 system.. We conclude either that they are in equi- 

 librium throughout the motion or that they are in equi- 

 librium at this instant in virtue of the fact that their 

 resultant, which is ex hypothesi of a simple harmonic 

 character, is passing through its zero phase. The 

 former hypothesis may be dismissed as giving rise 

 to no permanent oscillation ; the latter indicates a 

 phase difference of a quarter of a period between the 

 phase of the oscillation and that of the resultant 

 disturbing force. 



The application of the theorem in question to the 

 lidal problem is somewhat obscure, but the illustration 

 of the simple pendulum presented by the author 

 enables us at once to recognise an essential condition 

 under which it is applicable. The phase difference 

 in this case is correctly expressed by equation (297), 

 which indicates in general a phase difference of zero 

 or half a period when friction is slight. When, how- 

 ever, friction is sufficiently great the phase difference 

 may amount approximately to a quarter of a period, 

 and the same will be true even with small friction 

 when there is an exact coincidence between the period 

 of the disturbing force and the " natural " period of 

 vibration of the pendulum. 



Thus the fundamental theorem on which the deter- 

 mination of the phase depends only holds good if 

 we regard friction as sufficiently large to control the 

 phase, and unless the relative influence of friction in 

 comparison with other causes which influence the 

 phase is in some way known, the phase will remain 

 quite indeterminate. Of course it may be contended 

 that in the case of the tides the conditions necessary 

 to render friction the controlling factor exist, but 

 this contention is nowhere put forward explicitly by 

 the author, and we are of opinion that it could not 

 6e substantiated. We are further of opinion that 

 the effects of friction on phase will be everywhere 

 comparatively insignificant, so that we should expect 

 to find the phases of the oscillations, so far as they 

 ca 1 be resolved into separate simple harmonic types, 

 approximately in agreement with (or differing by 

 half a period from) those of the disturbing causes 

 instead of, as the author's theory requires, differing 

 from them by a quarter of a period. We conclude 

 that the author's theory ceases to be available even 

 to lead to a " first approximation " in the deter- 

 mination of the phases. 



We can thus only regard the charts produced, 

 except in so far as they are controlled by direct 

 observations, as a speculation on the part of the author 

 unsupported by scientific evidence, and regret that an 

 otherwise painstaking and far-reaching research on 

 our existing: knowledge of the tides has been marred 

 by the intervention of an unsatisfactory theory which 

 we feel bound to regard as not merely inadequate, 

 but for the purposes to which it is applied actually 

 misleading. 



S. S. H. 



