I 



Methods of correcting Lunar Observations. 353 



from the tangent, on the sector, with the radius set to 55 — 28 

 =27, we have 27" for the effect of obliquity. The sum of the 

 last three corrections is 76", which, subtracted from 350 " , leaves 

 274"=4' 34", to be subtracted from the observed distance. 

 The true correction is 4' 41", differing only 7" from this ap- 

 proximation. The distance of the intersection, measured by 

 Dr. Kelly's method, is about 6°, making the reduced correction 

 317"— 5^', which is too great by half a minute only. 



IV. By common Logarithmic Tables. 



A. If we have only common tables of logarithms at hand, we 

 shall find the approximate methods of computation considerably 

 more expeditious than the direct, and sufficiently accurate for 

 all common purposes. It will be found one of the easiest ap- 

 proximations to follow the steps of the constructor by the scale 

 and sector, and the precepts will stand thus : 



1. To the logarithmic sine of the sun's altitude, add the 

 cosecant of the distance, and find the number corresponding. 



2. To the logarithmic sine of the moon's altitude, add the 

 cotangent of the distance, and subtract the natural number cor- 

 responding from the former number ; or, where the observed 

 distance exceeds 90°, take the sum instead of the difference. 



3. Subtract the logarithm of the difference or sum from the 

 proportional logarithm of the horizontal parallax, and the re- 

 mainder will be the proportional logarithm of the parallactic 

 correction. 



4. From the same logarithm of the difference or sum, sub- 

 tract the sine of the moon's altitude ; the difference will be the 

 tangent of the lunar refractional distance, which, subtracted 

 from the observed distance, will give the solar refractional dis« 

 tance. Find the refractions answering to these zenith distances 

 for the refractional corrections. 



5. Take the sum and difference of the same difference or 

 sum and the numerical cosine of the moon's altitude ; add to- 

 gether their logarithms, the cotangent of the observed distance 

 and the constant logarithm 8.4130, and the sum, subtracted 



Z 



