29C) 



HYDROGRAPHICAL SURVEYING [chap. xiii. 



Superior 

 and In- 

 ferior 

 Transit. 



Principle 

 of Equal 

 Altitudes. 



Equation 

 of Equal 

 Altitudes. 



The method of equal altitudes, therefore, must be used 

 whenever we wish to get Error exactly. The Error of watch 

 obtained by single altitudes, called " absolute observations," 

 will depend for its accuracy upon the corrections for each 

 source of error, wliicli, as we have before stated, can only 

 be considered as approximate. 



Equal altitudes of the sun can be taken either in the forenoon 

 and afternoon of the same day, so as to find the Error at noon, 

 called Error at "superior transit ; or in the afternoon of one day 

 and the forenoon of the next, by which means we obtain the 

 Error at midnight, or at inferior transit. Theoretically, these 

 are equally correct, but in practice it is better to get Error at 

 noon, if we can, as the elapsed time being less, gives less lati- 

 tude to the chronometers or hack-watches for eccentricity. 

 The alternative is, however, very valuable, and saves many a 

 day, as when, for instance, we arrive at the place we wish to 

 observe at an hour or two too late for forenoon sights. We 

 can then begin our set in the afternoon, and get away, if we 

 wish to do so, the next morning after forenoon sights, and 

 thus save several hours, a considerable consideration in running 

 meridian distances. 



The principle of finding the Error of a timekeeper by obser- 

 vation of equal altitudes is that, the earth revolving at a uni- 

 form rate, equal altitudes of a body, on either side of the 

 meridian, will be found at equal intervals from the time of 

 transit of that body over the meridian, and that therefore the 

 mean of the times of such equal altitudes A\ill give the time 

 at transit. 



In the case of a body whose declination is practically in- 

 variable, as a star, this is strictly true, and the calculation of 

 the Error of the watch is confined to taking the difference of 

 the time shown bj^ the watch, and the true calculated time of 

 transit. 



In the case of the sun, however, the declination is constantly 

 changing ; the altitudes are thereby affected, and an altitude 

 equal to that observed before transit will be reached after 

 transit, sooner or later, according to the direction of change in 

 the declination. 



It is therefore necessary to make a calculation of the correc- 

 tion resulting from this change of declination, to be applied 



