72 tides and bench marks 



Eeduction of Eecoeds. 

 The tide follows the moon much more closely than it does the sun, so that 

 there is a tendency for the tide to occur when the moon is in a given position 

 in the heavens. The difference between the time of tide and the time of the 

 moon's transit or meridian passage, is called the hmitidal interval for the 

 station. Both upper and lower transits of the moon are usually compared with 

 the time of the first high water and first low water which follows the given 

 transit ; hence we may express the operation as follows : 



HWI = Time of HW — 3's transit 

 LWI = Time of LW __ 3's transit 

 where 



HWI ■= high water lunitidal interval 

 LWI = low water lunitidal interval. 

 The purpose of the tabulation given here, called " First Reduction," is to 

 compute the lunitidal intervals for high and low waters, and also to find the 

 mean range of tide and mean half-tide level. In this kind of work the time 

 of the moon's transits should have been reduced to the meridian of Nassau, but 

 in order to save work the unmodified Greenwich transits Avere used, and the 

 final result corrected by the general formula : 



x = 4: [0.035 (E — L)+S-— L] minutes of time, 

 where x = Correction to the lunitidal intervals, in minutes of time. 



E = West longitude of the meridian for whk-h the Ephemeris gives the 



moon's transits. 

 S = West longitude of the time meridian used for recording the obser- 

 vations, expressed in degrees and decimals. 

 L := West longitude of the station or local meridian expressed in degrees 

 and decimals. 

 In this case E = 0, as Greenwich transits are used. 



S = L=:77° 31' = 77°.35. 

 Substituting these values in the equation it becomes: 



x = — 0.14 L = — .UX 77.35 = — 10.83 minutes. 

 Hence the mean intervals for both high and low waters are diminished 

 by 10.8 minutes. If, for any purpose, lunitidal intervals in any portion of 

 the First Eeduction are required, they should be corrected by the same con- 

 stant. The mean lunitidal interval for high water at full and change of the 

 moon is called the Establishment of the Port, and tbe mean of all the high 

 water intervals is known as the corrected establishment of the port. For 



