Observed d-^ 



Computed d^ 



Qm 



Qm 



42 



25 



41 



41 



48 



48 



27 



40 



24 



22 



TIDAL OBSEIIVATIONS. 159 



enough by the approximate formula cZ4'= 102 tan h', the declination of tlie moon 

 being taken for an anterior epoch of two days. 



J' 



13 

 22 

 25 

 21 

 12 

 



The curve thus computed is represented on Plate II; see bottom diagram. Cor- 

 responding to this curve the bottom diagram of Plate I shows the computed height 

 inequality for high water. 



Separation of the Diurnal and Semi-Diurnal Waves. — The compound wave actu- 

 ally observed consists of the diurnal wave; to Avhich the diurnal inequality is due, 

 and of the ordinary semi-diurnal wave which produces the ordinary tides. For a 

 complete study of these waves it is necessary to have them in their separate forms. 

 The manner in which this separation will be effected is the same as that employed 

 in the U. S. Coast Survey ; it was originally proposed by Assistant L. F. Pourtales, 

 in charge of the tidal party, about the year 1855,^ and has taken the place of the 

 more laborious analytical process previously employed; the graphical process of 

 Mr. Whewell's was applied only to observed high and low waters, and consequently 

 gave but few points of the diurnal wave.^ In Series II the high and low waters alone 

 were observed, which renders it quite unsuitable for the purpose of separation. I 

 was therefore obliged to select the least interrupted portion of the half-hourly obser- 

 vations of Series I. The compound (observed) wave, and its two component waves 

 from November 21 to December 11, 1860, are shown on Plate III. The graphical 

 process of separation is as follows : After the observations are plotted and a tracing 

 is taken, the traced curves are shifted in epoch 12 hours 24 minutes fonvard, 

 when a mean curve is pricked off exactly between the observed and traced curves ; 

 the same process is repeated after the paper was shifted 12 hours 24 minutes back- 

 wards, when a second pricked curve is obtained ; the mean pricked curve then 

 represents the semi-diurnal wave. To obtain the diurnal curve we have only to lay 

 off the differences between the observed curve and the semi-diurnal curve. The 

 process is simplified by blacking the under surface of the tracing paper with a lead 

 pencil and running in with a free hand the intermediate curve by the pressure of a 

 steel point which leaves a sufficient mark on the paper ; the average of the two 

 curves thus traced gives the semi-diurnal wave in quite an expeditious manner. 

 Nevertheless the discussion, by separate Avaves, of any lengthy series of observations 

 remains a laborious task. On Plate III the observed heights, reduced to the same 

 plane of reference or zero level, are shown by dots, and connected by a full line ; 

 some omissions in the observations are supplied by dots ; the average level reads 

 16.7 feet. The semi-diurnal wave is shown by a curve of dashes, and the diurnal 



' See my discussion of the Van Rensselaer Harbor tides, p. 78, where the method is first pub- 

 lished, by permission of A. D. Bache, Superintendent U. S. Coast Survey. 

 " See 8th Series of Researches of Tides. Phil. Trans. 1837- 



