CHAP. xii.J LATITUDE BY STARS 281 



stars, a constant log of 0-002000 added to the other parts of 



the equation will give a close approximation to the exact 



reduction. 



In working out the circum-meridian observations of a star, Caicuia- 



it is not necessary to calculate the reduction for each individual ^efyc^^ 



Vers HA . . tion. 



observation. As is the only variable quantity in the 



Sin 1" "^ ^ ^ 



equation, and as it varies with the hour angle, by taking 



this out for each observation, and meaning these quantities, 



Vers H A 



we obtain a mean value of , which we insert in the 



Sin 1" 



equation, and add the mean reduction so found to the mean 



of the altitudes. If working with Raper's tables, we take out 



Vers H A 



the whole quantity, ; if without them, we look out 



^ ^ Sin 1" 



the Vers H A only, and introduce the log Sin I" into the 



calculation with the other logarithms. 



Knowing then the error of the watch used on mean time of 



place, and the approximate latitude and longitude, the rule for 



working out circum-meridian observations of stars will stand 



thus : 



1. Calculate Greenwich date. Rule for 



2. Correct right ascension of mean sun (sidereal time of Caicuia- 

 " Nautical Almanac ") for this Greenwich date, and subtract it duction. 

 from the right ascension of the star, which will give the mean 



time of star's meridan passage. 



3. Apply to tliis the error of the watch, which will give the 

 time shown by the watch at the star's meridian passage. 



4. Mean the observed altitudes, correct this mean for index 

 error, and divide it by two. To this apply refraction (cor- 

 rected for thermometer and barometer), wliich will give true 

 altitude. 



5. Write down the times of each observation in a column, 

 and taking the difference between each, and the time shown 

 by the watch at meridian passage, we get the hour angle at 

 each observation, which place in atnother parallel column. 



6. Take out for each of these hour angles the quantity from 

 Raper's Reductiqn Table, or, if we have not got that, the 

 natural versine. 



