280 HYDROGRAPHICAL SURVEYING [chap. xii. 



increases rapidly \\ ith the hour angle, so that we are confined 

 in using this method to about twenty minutes of the time of 

 meridian passage in ordinary latitudes ; but in observations 

 such as we are discussing now, which have for their object as 

 correct a determination of the latitude as we can obtain, we 

 must not observe more than about ten minutes from the 

 meridian, and perhaps less. 



The best method to use in reducing observations to the 

 meridian is that known as Raper's, in which the principle is 

 to add on to the observed latitude the amount necessary to 

 make it equal to the meridian altitude, and then to calculate 

 the latitude as in a meridian observation. 



This amount is known as the " Reduction to the Meridian," 

 and is so called because it is subtractive from the observed 

 zenith distance. 



The formula used by Raper is* — 



Reduction inl „ , ^, , ,, , Vers hour angle 



-; r = Los dec. xCos lat. x Sec alt. x 



sees, of arc J gin i" 



Vers H A 

 Raper gives a table of : — -^- for every minute and 



second of hour angle up to thirty minutes from the meridian, 

 wliich is very convenient, and is given in Appendix M. It 

 saves a considerable amount of figiu-es in the calculation, and 

 thereby diminishes the chances of clerical errors ; but the 

 formula, as given above, can be ^^'orked out if Raper's table 

 is not at hand. 

 Sidereal The hour angle as marked by a watch beating mean time, 

 ^^g or nearly mean time, will not be strictly correct either for a 

 star or the sun, as, for the former, it shoidd be taken by a 

 watch beating sidereal time, wliich gets over its twenty-four 

 hoiu-s wliile a mean solar watch has only advanced 23*^ b^^ 04* 

 nearly ; and apparent solar time varies from day to day as the 

 speed of the earth in her orbit varies ; but, within the limits 

 we observe, the difference in ordinary latitudes is scarcely 

 perceptible, and if we observe the stars of a pair about the 

 same distance from the meridian, any little discrepancy will 

 disappear in the mean. 



If it be desired to correct for the difference when observing 

 * For proof, see Appendix D. 



