THE BAHAMA ISLANDS 91 



_ 21/4 sin {23P^ — 3r^) + S3I, sin (3J/.° — J/g) + 



tan V - ^,jj^ _j_ 22 jy^ ^^g {2Ml—3Pi) + S'Wg cos (3Jf § — M^) + 



_ 231, sin (23/ ■'?— i/») — S3I, sin (3itf.^ — i/g) + 



tan i^ - _ pjj^ _^ 2^'J/4 cos {2if2" — 3fl) — 3^Jf e cos (33/.^ — Ml)-{- 



From (1) and (3) we obtain 



HWI = 7h. 21.om. LWI = lli. 09.4ni. 



The corresponding values from the First Reduction were 



HWI = 7h. 22.8m. LWI — Ih. 11.8m. 



which, considering tlie great difference in methods, is regarded as a very fair 

 agreement. 



The sun's effect upon the time of tide is sometijnes to accelerate and some- 

 times to retard its occurrence, according to the moon's phase or the relative 

 positions of the moon and sun. The 'priming of the tides is the period when the 

 tides occur sooner than the average, which roughly speaking usually occurs 

 from new or full moon to the quadratures; and the lagging of the tides is the 

 period during wliich they occur later than the average, which is approximately 

 from the quadratures to new or full moon. The theoretical limits of this 

 variation in lunitidal interval due to priming and lagging of the tide are 

 given by the following formulas : 



Mean minimum HWI = HWI -^^—^ (3) 



" maximum £fIF7= /rPr/+-^^^ (4) 



Extreme minimum HWI = HWI— -J^M^'^ (5) 



" maximum HWI = HWI + M^—l^k ' <^^) 



For Nassau we obtain from (3), (4), (5), and (6), the following values: 

 Least lunitidal intervals due to phase or priming of the tides. 



Mean Minimum Extreme minimum 



HWI = 7h. 01.3m. ' 77117 = 6h. 53.6m. 



Greatest lunitidal intervals due to phase or lagging of the tides. 



Mean maximum Extreme maximum 



HWI = 7h. 44.3m. 77117 = Th. 52.0m. 



The extreme values for priming and lagging occur when the moon is in 

 apogee at the time of the equinoxes, and the moon is between three and four 

 days from the new or full. 



