152 RECORD AND RESULTS OF 



2 95 

 dependixig on the ratio of solar to lunar tide ^-- = 0.376, which is preferable to the 



7.85 



value (0.367) given in the text (p. 71), the spring range being 10.8, and the neap 

 range 4.9 feet, values which approximate closer to the Port Foidke results. 



In the notation of Art.'s (536) to (540), Tides and Waves, we have from the time 



on Q//r 



inequality, for Port Foulke ^^77=^ 0.364, and from the height inequality -p77,=0.329; 



the heights generally give the smaller value, but that deduced from the times is 

 theoretically the more correct one. The retard of the tide from the time-inequality 

 is a = 10° 3', and from the height-inequality a= 11° 0', the latter is, theoretically, 

 the preferable value. The average daily separation of the sun and moon is 48'".8;- 

 hence the time in which the moon moves through this angle or the age of the tide 



equals , ^ ^ . q or 0.9 of a day (21| hours); by this interval the spring and neap 



tides foUow the syzygy and quadrature respectively. The retard, as found at Port 

 Foulke and Van Rensselaer Harbor, is comparatively small. 



Effect of Changes of the Lunar Parallax on iJie Half-monthly Inequality. — From a 

 short series of observations, like the one now under consideration, we can only 

 deduce approximately the changes which the half-monthly inequality undergoes in 

 consequence of variations in the lunar parallax, and the same remark applies to the 

 changes produced by variations in the moon's declination. The method followed 

 in this discussion is nearly the same for the parallactic and declination effects, and 

 appHes for high and low water and for times- and heights. The hmi-tidal intervals 

 and corresponding heights were rearranged with reference to small and large values 

 of the parallax ; it is, however, not the parallax belonging to the epoch of high or 

 low tide which was employed, but one anterior to that time, the retroposition 

 depending on the retard of the tide as determined in the preceding article. As the 

 average age amounts to nearly a day, the parallax preceding the leffect by that inter- 

 val was used in the tabulation. No distinction is required for upper or lower tran- 

 sits. The first group consists of intervals and heights for parallax between 54' and 

 57', the second for parallax between 57' and 60'. The means being taken for each 

 hour of the moon's transit, the following tables were obtained. The letter P stands 

 for parallax; the inequality for the average parallax (57') is added from the pre- 

 ceding investigation. 



