72 RECORD AND REDUCTION OF THE TIDES. 



The ratio 1 of the solar to the lunar tide is deduced with more exactness from the 

 inequality in times, and the above value is certainly greater than the average value 

 deduced at more southern stations. One of the reasons why this ratio is not con- 

 stant, and which probably applies here, is given in (538, (3) (Tides and Waves), 

 viz. : If tides are communicated by different channels to the same port, the pro- 

 portion of the solar and lunar waves will depend on the length of those channels. 

 This explanation would require a polar tide to enter through Kennedy Channel, 

 to combine with the principal tide which passes up Baffin's Bay, and enters by 

 Smith's Straits. According to the equilibrium theory, there should be no tide at 

 the pole, and but a small tide in latitude 78 £° ; but it is the tide wave propagated 

 from the Atlantic, which is felt in this part of the polar regions. With regard to 

 a, its value as found by the heights is more accurate than that found by the times; 

 the latter gave a = 9°, the former 15° (the same from high and low waters). 

 Adopting 15°, the retard or age of the tide becomes li day, by which interval the 

 spring and neap tides follow the syzygies and quadratures, respectively. The time- 

 value of a is here smaller than the height-value, which is more in accordance with 

 theory than the opposite, as observed at a number of places on the coast of England 

 (543 and 546, Tides and Waves). Compared with other values of a, the Van Rens- 

 selaer value appears somewhat smaller than an average at more southern stations. 



AVe have further, mean rise and fall of tides at Van Rensselaer Bay 7.9 feet, 

 range of spring tides 11.1 feet, and range of neap tides 4.7 feet. These numbers 

 are averages from the discussions of 9 h lunations, and obtain without regard to the 

 diurnal inequality, which will be investigated further on. 



Effect of the Changes in the Moon's Declination and Parallax on the half-monthly 

 Inequality, in Time. — In reference to the investigation of the half-monthly inequa- 

 lity, it is comparatively of little consequence which transit of the moon is taken 

 for comparison ; it is otherwise in the investigation of the effect of a change in the 

 moon's declination and parallax, as well as for a similar effect due to the sun, which 

 latter, however, cannot become a subject of investigation for the tidal series in 

 hand, on account of its short extent; for the same reason, the variation in the ine- 

 quality, in height, will have to be passed over. To ascertain the effect due to the 

 moon's declination and parallax, an anterior value, corresponding to a certain age 

 of the tide, is to be taken in the comparison ; the preceding investigation gave for 

 the retard li day, each lunitidal interval, minus its corresponding mean value for 

 the respective hour of the moon's transit, was therefore tabulated in respect to the 

 moon's declination and parallax (separately for each), corresponding to one day ante- 

 rior to the time of high or low water, thus referring the results to transit E. The 

 present investigation can only furnish an approximation to the true results ; the 



an 



1 For comparison of different values for this ratio, the following have been selected : — ^ for London, 



0.370; for Plymouth, 0.401 ; from the discussions of the Superintendent of the U. S. Coast Survey, for 

 Key West, 0.325 ; San Diego, 0.39 ; and San Francisco, 0.342. (Annual Rqnrls of 1853 and '54.) 



— for Dundee, 0.277 ; fa- Brest. 0.346 : for Plymouth, 0.294. 

 M'" 



