74 RECORD AND REDUCTION OF THE TIDES. 



The empirical values for the groups of small and middle values of parallax appear 

 systematic; the values in the last column for large parallax are less regular. The 

 maximum correction on the average is somewhat greater than one-fourth of an hour. 



The corrections to the mean establishment for changes of the sun's declination 

 and parallax may be taken as one-third of the corresponding lunar values, and in 

 the present case will probably not exceed five minutes of time. 



The means of each column, containing the non-periodical part, are small, and 

 appear rather irregular; they are variable with the transit or the moon's age 

 adopted in the discussion. 1 



Diurnal Inequality. — We now proceed to the examination of a prominent feature 

 in the Rensselaer Harbor tides, namely, the diurnal inequality. This inequality 

 is well marked in the diagrams, Plates I, II, and III. Although the existence of 

 this inequality, in height and times, has long been known to practical men, it was 

 not until about twenty-five years ago that its laws were understood and reduced to 

 ((imputation by Mr. Whewell. 2 The subject has since been taken up by the 

 present superintendent of the TJ. S. Coast Survey. Prof. Bache; 5 his researches 

 commenced about nine years ago, and resulted in a further extension of the method 

 of discussion as well as in the recognition of the geographical limits of the pheno- 

 mena on our own coast ; further, the discussion of single day tides, produced by 

 this inequality in extreme cases, and here complicated by an extremely small rise 

 and fall of the tides, was now successfully accomplished. According to the equi- 

 librium theory, the diurnal tide ought to be very small in latitude 79° ; but viewing 

 the Rensselaer Harbor tide as a wave, produced principally in the Atlantic, and 

 propagated through Davis's and Smith's Straits, the existence of the diurnal 

 inequality in so high a northern latitude cannot surprise us. The following notes 

 were extracted from Captain McClintock's narrative of the voyage of the " Fox," 



' On this point the reader may consult Whewell's 9th series of tidal researches : " Laws of the Tides 

 from a Short Series of Observations," Phil. Trans. 1838; also Airy, "Tides and Waves," articles 552 

 and following. 



a Researches on the Tides, sixth series. On the Results of an Extensive System of Tide Observations 

 made on the Coasts of Europe and America in June, 1835. By the Rev. W. Whewell. Phil. Trans. 

 Roy. Soc. 1836. 



Researches on the Tides, seventh series. On the Diurnal Inequality of the Height of the Tide, espe- 

 cially a1 Plymouth and Singapore. By the same author. Phil. Trans. 1837. 



Researches on the Tides, eighth series. On the Progress of the Diurnal Inequality Wave along the 

 Coasts of Europe. By the same author. Phil. Trans. Roy. Soc. 1837. 



Note on a Discussion of Tidal Observations at Cat Island in the Gulf of Mexico, by Prof. A. D. 

 Bache. Coast Survey Report for 1851, App. No. 7; Additional Notes thereto, Coast Survey Report 

 for L852, App. -No. 22. 



On the Tides a1 Key West and of the Western Coasl of the United States. Coasl Survey Repor) foi- 

 l's;,:;. App. \os. 21 and 28. By Prof. A. I>. Bache. 



Comparison of the Diurnal Inequality of the Tides at San Diego, San Francisco, and Astoria, on the 

 Pacific I loa I of the I nited Slates. Coasl Survey Report for is.vi, App. No. 26. By Prof. A. D. Bache. 



Approximate Co-Tidal Lines of Diurnal and Semi-Diurnal Tides of the Coast of the United Slates 

 on the Gulf of Mexico. Coast Survey Report for 1856, App. No. :;:>. By Prof. A. D. Bache. 



For the theoretical investigation of the diurnal tide, see also Airy's Tides and Wave-, articles 46 and 

 following ; and articles 562 and following. 



