Harmonic Analysis of Tidal Observations. 561 



Governor's Island, New York Harbour. 



In an appendix to the ' Report of the United States Coast Survey ' 

 for 1885, Professor Ferrel gives the results of harmonic analysis 

 applied to tidal observations at this station. A map shows the sites 

 of the tide-gauges at Governor's Island and at Sandy Hook. 



Mr. Ferrel's treatment of the tide M x differs from that recom- 

 mended in the Reports of the British Association, and his entry for 

 Mj is therefore here omitted. 



In the preface to the previous collection of results a memorandum 

 by Mr. Ferrel, about the phases of the tides, was quoted. In a foot- 

 note, added after the paper had been presented, I remarked that it 

 was not easy to accept Mr. Ferrel's memorandum as conclusive of the 

 identity of treatment of the American tides with the procedure 

 recommended by the British Association. The same reason, which 

 then caused me to feel this doubt, applies to the present series of 

 results, and it will therefore be well to state the case somewhat more 

 fully than was possible in the footnote referred to. 



In the ' British Association Report for 1883 ' the equilibrium theory 

 of tides is developed so that each tide is represented by a positive 

 cosine. Now, there are two of the tides, viz., those initialled L and 

 X, in which the development naturally leads to a negative cosine, and 

 if these terms are to appear as positive cosines, 180 must be added to 

 the argument. It follows, therefore, that if Mr. Ferrel retains the 

 cosines in the negative form, the angles K for L and X, as tabulated 

 by him, must be augmented by 180, in order to bring his results into 

 accordance with ours. Now, it may be observed that in all the results 

 tabulated by the U.S. Coast Survey, the tides L and X are apparently 

 in diametrically the opposite phase from that of all the other semi- 

 diurnal tides. "I 



That this is actually the case appears physically so improbable that 

 I conjecture, even in the face of Mr. Ferrel's memorandum, that he 

 uses a different convention as to the tides L and X, and that to read 

 his results in our notation his values of K should be augmented by 

 180. I here tabulate, however, the values as I find them. 



Whilsb speaking of this point, it is impossible not to refer to the 

 very remarkable peculiarity of the tide K 2 in the results for Sandy 

 Hook in the previous collection, and for Governor's Island here. It 

 is obvious that all the semidiurnal tides of true astronomical origin 

 should be nearly in the same phase, but here we have a single tide 

 exactly inverted as compared with the rest. Is it possible that by 

 some accidental change of sign 180 can have been erroneously 

 imported into the result ? 



