a Greenwich lunar transit, /i and I2 the lunitidal intervals at the two 

 stations, ii and Lo their longitudes in degrees west of Greenwich, *S' 

 the longitude of the standard time meridian of the localitj^, and Ti 

 and T2 the standard time, in hours, of high (or low) water at the two 

 stations. Then: 



ri=(?+ (2.1/60) {L,llb) + {L,-S)llb+h 



= 6^+(4.14/60)ii-.S/15+/i 

 T2=6^+(4.14/60)Z2-;S/15+J2 



Whence: 



ri-T2=/i-/2+ (4.14/60) {L,-L,) (1) 



The correction for longitude is therefore 4.14 minutes of time for 

 each degree of difference between the longitudes of the two stations, 

 due regard being had to the algebraic sign of the correction resulting 

 from the application of the formula. Obviously for easterly longi- 

 tudes the sign of the correction would be reversed. 



For example, the high-water interval at Portland, Oreg., long. 

 122°40' W., is 6M3°^, and at Astoria, near the mouth of the Columbia 

 Eiver, long. 123°46' W., the high-water interval is OMl'". The dif- 

 ference in the time of high water between Portland and Astoria is 

 therefore 6M3'"-0'^41'"H-4.14 (122.56- 123. 77)'° = 6^02°'-05'" = 5^57'". 

 High water at Portland is therefore 5'^57™ later, on the average, than 

 high water at Astoria. 



11. Since the time of high water cannot be determined from 

 observation within a range of several mmutes, the correction for the 

 difference in longitude between two stations may be neglected unless 

 it exceeds 1 minute of time. The corresponding difference in longi- 

 tude is about 15' of arc. No correction for longitude need be made 

 therefore unless the two stations are at least 10 miles apart in an east 

 and west direction. 



12. Greenwich lunitidal intervals. — A Greenwich high- (or low) 

 water interval at a station is the interval from a transit of the moon 

 over the meridian at Greenwich, as given in the Nautical Almanac, 

 to the Greenwich time of the following high (or low) water at the 

 station. For convenience, high- and low-water intervals usually are 

 computed by subtracting the tabulated Greenwich times of upper or 

 lower transits from the time of the next ensuing observed high and 

 low waters, as recorded on standard time at the station. The average 

 differences so found are then converted to Greenwich intervals by 

 adding the west longitude, in hours, of the standard-time meridian. 

 If the result exceeds the average interval of 12.42 hours between 

 successive lunar transits, that interval is subtracted. The local luni- 

 tidal intervals may then be found by subtracting the product of the 

 west longitude of the station, in degrees, times 0.069 hours (4.14 



