Finding the Longitude from Lunar Distances. 89' 



owners. Those who wish to test the lunar method should 

 practise at a place whose longitude is well known. Tiie 

 index error should be carefully found at each observation. 

 The same dark glass or glasses should be always used for 

 the sun, the grading of the brightness being obtained by the 

 U]3 and down motion of the telescope, and the contacts 

 should be alternately made on and off The errors of the 

 resulting longitudes can then be tabulated or graphically 

 described, whence a table of corrections for the different 

 parts of the arc can be made. Some observatories contain 

 special apparatus for testing sextants, but an ordinary 

 observer would have more confidence in the former method. 

 To those who wish to study the general theory of the 

 sextant, I would recommend " Simms on the Sextant and 

 its Applications," published by Troughton and Simms, of 

 London, as the best work on the subject in our language. 

 It is not, however, an easy book to read, and the notation is 

 cumbrous and uninviting. For an example of finding the 

 errors of a sextant from astronomical observations, the best 

 work is the " Treatise on Practical Astronomy, as applied to 

 Geology and Navigation," by Professor Doolittle, of the 

 Lehigh University. The work was carried out by Professor 

 Boss, the present director of the Dudley Observatorj^ and 

 the various steps of the process are given with the minutest 

 detail. The greatest correction found was 38 seconds of arc, 

 which shows that the instrument was a very good one, for 

 Simms states in the work before referred to, that there are 

 few sextants in which the error which varies with th.e 

 reading does not amount at its maximum to 40 seconds of 

 arc. In many it exceeds I minute, and instances are to be 

 met with where it amounts to -5 minutes. 



For reducing a lunar observation, or clearing the distance 

 as it is technicall}' called, man}^ methods have been devised, 

 indeed, no other astronomical ])roblem has shown such a 

 fecundit}' of results, but their principles may be broadly 

 divided into two — one the absolute solution of the two 

 astronomical triangles ))resented by the problem, the other the 

 differential variations of the parts of these triangles. The 

 former of these is now seldom used, owing to the amount of 

 work and care necessary ; it iS; however, the only safe one to 

 u.se when the observed distance is very small. The shape in 

 which this computation is carried out, is generally some 

 slight modification of Borda's formula, published near the 

 end of the last centurv. The large tables of Mendoza Rios 



