Methods of correcting Lunar Obaervations. 351 



5. In order to reduce the oorrertion, multiply it by the hori- 

 zontal parallax, and divide it by 62° when it is subtractive, and 

 by 53° when additive, and apply the reduced correction to the 

 observed distance. 



This method is published in Dr. Kelly's Spherics ; it is very 

 expeditious, and its result is generally within about a minute 

 of the truth, corresponding to half a degree of longitude, and 

 often still nearer. But the construction may be rendered much 

 more accurate by the assistance of the sector and a scale of 

 equal parts. 



III. By the Scale and Sector. 



1. With a radius equal to the horizontal parallax, taken 

 from any scale of equal parts, draw a circle, and a line for the 

 lunar radius. 



2. At an angular distance equal to the observed distance, 

 draw another radius for the solar line. 



3. Set off the zenith distances on each side of the respective 

 radii, and draw the chords of the double arcs. 



4. Measure the distance of the intersection of the chords 

 from the lunar radius, on the scale of equal parts, for the paral- 

 lactic correction. 



5. Draw a radius through the intersection of the chords, 

 measure its angular distances from the two former radii ; and 

 take, from the table of refractions, the refractions answering 

 to these two angles as zenith distances, for the effects of the 

 respective refractions. 



6. When the observed distance is small, take its tangent 

 with respect to the given circle, from the sector, or otherwise ; 

 apply this tangent within the circle, from the intersection of the 

 two chords, so as to make one of the segments of a new chord, 

 and measure the other segment of this chord by means of the' 

 sector, setting the radius of the circle to the horizontal parallax 

 in minutes, diminished by 28', on the line of lines ; the result 

 will be the correction for obliquity in seconds. If the tangent 

 is too short to reach the circle, take its double or quadniple. 

 and double or quadruple the number found accordingly. 



