RECORD AND REDUCTION OF THE TIDES. 75 



in 1857, '58, '59. Referring to Bellot Strait: "As in Greenland, the night tides 

 are much higher than the day tides." Speaking of the ice motion, and remarking 

 that the tides are the chief cause of it, he says: "Now we know that the night 

 tides in Greenland greatly exceed the day tides." Also, when near Buchan Island, 

 north of Upernavik, and in the vicinity of Cape Shackleton: "We had grounded 

 during the clay tide, and were floated off by the night tide, which on this coast 

 occasions a much greater rise and fall." By the labors of Dr. Kane we now know 

 that the diurnal inequality extends as high up as 79° of latitude on the north- 

 western coast of Upper Greenland. In a report of Mr. Sonntag's to Dr. Kane, 

 dated Godhavn, Sept. 12, 1855, he says: The mean height of spring tides is 12.8 

 feet, and at the time of new and full moon high water is at 12 h m ; the highest 

 spring tide is three days after full moon, and the night tide is at this time fully 

 three feet higher than the day tide. At Northumberland Island, Sept. 10, 1854, 

 at (after) the time of full moon high water was at IP P. M., and the night tide 

 rose three feet more than the day tide. These statements, crude as they necessarily 

 are, show that the attention of the party was fully directed to the phenomenon. 



A cursory examination of the Plates (I, II, and III) shows that the diurnal 

 inequality extends without exception over the whole series of observation, that it 

 is well marked in the difference of the height of high water, but very little or 

 irregularly in the height of low water; that sometimes the day tide, at other times 

 the night tide is the higher of the two occurring in a lunar day ; further, that it 

 vanishes a day or two after the moon's crossing the equator, and that it amounts 

 in maximo to about three feet some time after the moon attains her greatest 

 declination. There is but one instance where the inequality approximates to the 

 production of a single day tide. See curve for Nov. 23, 1853. 



We may now enter somewhat more fully into the discussion of this inequality, 

 which is produced by the interference of two independent waves, the diurnal and 

 the semi-diurnal, the former depending for its size chiefly on the moon's declina- 

 tion. For a complete study of these compound waves, they require to be examined 

 in their separate parts, and it would therefore be our first object to effect their 

 separation into the diurnal and the semi-diurnal ; a process which, when graphically 

 performed, is neither too laborious nor lacking in accuracy ; it is nevertheless a 

 process of some nicety, and requires observations of standard excellence. Upon 

 trial, I found the less rigorous method employed by Mr. Whewell in his discussion 

 of the Plymouth and Singapore tides, was better suited to the general mass of the 

 observations at Van Rensselaer, and that the above described process of separation 

 had better be reserved to that portion of our observations which are apparently 

 of the best character. 



The observed heights of high and low water were laid down graphically, and a 

 line was drawn by the eye, cutting off the zigzags of the successive high waters, 

 leaving equal portions above and below the intermediate curve. These differences 

 from the mean height were then set off from another axis, and those belonging to 

 the hi<di water next following the moon's superior transit were marked by a curve 

 of dashes ; those following the moon's inferior transit were marked by a curve of 

 dots. These curves, without exception, were found to have alternately, as the 



