LONGITUDE FROM OCCULTATIONS. 27 



The vertical interval between the first and last wires is 734" '3; if t be 

 the interval in seconds of time required by the Moon's limb to pass over this 

 space during vertical transit, and z l ~ z 2 be the difference between the two 

 tabular zenith distances corresponding to the two assumptions of longitude, 

 the correction to the longitude always positive in seconds of time is found 



from the expression 



734-3 X o s 'Q74 X 60 



t X ( Zl ~ Z 2 ) 



The mean value of t and z : ~ z 2 for the day has been used. 



The weights in the seventh column are approximately proportional to the 

 square of the quantity z t z. 2 . "When the zenith distance of the Moon at 

 the time of observation is near 80, and also when the corrections to the 

 tabular place of the Moon have been unsatisfactorily determined, only half 

 weight has been allowed. The observations on three days have been rejected, 

 there being no data for correcting the tables. 



The resulting longitudes of the Altazimuth pier are : 



J I. No. of Days Obs. j II. No. of Days Obs. Mean. 



Mean 10.31.27-3 



(3.) Longitude of Honolulu from Occultations of Stars by the Moon. 



For the reduction of the observed occultations, the corrections to the 

 Tabular Geocentric R.A. and N.P.D. of the Moon's center have been taken 

 as follows : 



Correction Correction 



toK,A. toN.P.D. 



The Moon's R.A. and N.P.D. were interpolated with second differences 

 from the hourly ephemeris in the Nautical Almanac, on two assumptions of 

 longitude. The parallaxes were then computed from the formulae 



-r, T, T> A a. sin A i a 3 sin 2 A a 3 sin 3 h 



Parallax m R.A. = -g^-p'" "" s in 2" ' sin 3," ' 



where 



a = sin p . cos <fi . sec 8 



/ sin p . sin </A sin h 1 



tan 8 1 = ( i '-^ r tan 8. 



\ sm 8 / sin h 



