350 ' Astronomical and Xaulical CoUertiom. 



ii. A comparative View of the Principal Methods of correcting 

 Lunar Observations, with a new Construction. 



The practical eligibility of the different methods of correcting 

 lunar observations must depend, in great measure, on the means 

 which may be in the computer's possession ; and it will be con- 

 venient to consider, first, the methods which may be employed 

 with the simplest means, and to proceed afterwards to those 

 which are more refined in their details, and which are calculated 

 to comprehend the minuter quantities concerned in the results. 



I. Without either Tables or Instruments. 



The son of an illustrious statesman, now a young midship- 

 man, is said to have astonished his shipmates, by working out 

 the correction of a lunar observation, unassisted by books or 

 instruments of any kind. It is right that so brilliant an exhi- 

 bition of mathematical talent should be recorded with some 

 deo-ree of authenticity, as well for the honour of the individual, 

 as for the credit of the Naval Academy at Portsmouth, through 

 which this Nelson or Newton in embryo has passed, without 

 favour, in less than half the regular time. But it is not to be 

 expected that such a method of correction will become very 

 ■jniversal, even in the British navy, and we must therefore be 

 contented to examine some of the processes adapted to humbler 

 capacities. 



II. By the line of Chords. 



1. Draw a circle, and a radius for the lunar line, equTil to 

 the chord of 60°. 



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 line of chords, for the correction, 

 which will be subtractive when the intersection is on the same 

 side of the lunar radius with the solar radius, and additive 

 when on the opposite side. 



