79 



log. sill, of, ait., the sums will be the -prop. logs, of the res- 

 pective parallaxes, i^i. 



2. Moon's par.— moon's rofrac.=:c®iTi!of alt. Take cliff, of 

 (corr. of altitude + star's or sun's refraction + moon's alt.j) 

 and star's : altitude (or sun's alt. + par.) This diff. is the dif}". 

 of true altitudes. Find also dilf. of app. altitudes. 



3. When the sun is observed, add together the numbers 

 in tab. 1, 2, 4, and 5. When a star is observed add the 

 numbers in tal). 1, 2, 3, and 5, log. ©f this sum (its index 

 being always 3 + number of figures) + log. (v. sin observed 

 dist. — V. sin diff. of observed altitudes), rejecting 10 from the 

 index -= log. of a number to be subtracted fi'om the above 

 diff. of versed sines. 



4. The remainder + v. sin difi'. of true altitudes = v. sin of 

 true distance. 



Observations. No distinction of cases occur. No pro- 

 portional parts but such as are taken out by inspection. 

 The versed sines may considered as whole numbers, the 

 radius being (1,000,000). In taking out the versed sines 

 of the observed distance, the seconds may be I'eserved and 

 added to the conclusion. Also in finding the log of (v. sin 

 observed dist. — v. sin diff. ob. alt.) the two last figures may 

 be considered as cyphers. 



For those conversant in contracted decimal multiplication, 

 the third precept may stand as follows. 



3. When the sun is observed, take the sum of the num- 

 bers in tab. 1, 2, 4, and 5. When a star, the sum of the 

 numbers in tab. 1, 2, 3, and 5. Find also the excess of the 



M 3 versed 



