CHAP. XIII.] OBTAINING LONGITUDE 295 



important factor of change of temperature. If, however, we 

 can return at once to A, and obtain the Error again, we can 

 positively say that the chronometers have gained or lost 

 so much between the first and second observations at A. 

 Assuming this loss or gain to have been uniformly carried 

 on throughout the interval, we shall have a travelling rate 

 which will give a far nearer result than by using rates obtained 

 at either end of our required base. By tliis means we only 

 obtain one meridian distance for our double run forwards and 

 backwards, but it will be of more value than two separate 

 meridian distances obtained by fixed rates. 



Even if we have to stop at B a few days, by observing Modifica- 

 on arrival, and immediately before departure, we can eliminate Travei- 

 the gain or loss of the cln-onometers during the stay there, by ling Rate, 

 subtracting it from the total gain or loss during the time of our 

 absence from A, and dividing the remainder by the number 

 of days actually travelling. We shall thus still get a fair 

 travelling rate, if the clu'onometers are at all trustworthy as 

 timekeepers. 



This, then, is the system of travelling rates, which can be 

 generally, and always should be, if possible, used in deter- 

 mining difference of longitude for the scale of a chart. 



Whatever be the system of rates employed, good observa- 

 tions must of course be regarded as the foundation of all of 

 them. We cannot control the irregularities of our clu-ono- 

 meters, but we can, to a certain extent, make sure of getting 

 fairly correct time by using the proper means. 



To ascertain the Error of the clnonometer as exactly as we Eiimina- 

 can with sextant and artificial horizon, we must endeavour to Errors by 

 get rid of the atmospheric and other errors, as we do in observa- Equal 

 tions of stars for latitude, which in this case is attained by 

 observing at equal altitudes east and west of the meridian. It 

 will be evident that, whatever be the instrumental and other 

 errors (excepting those of observation), supposing them to 

 remain unaltered, the middle time between the observations 

 will be the same, as whatever tends to make the observed 

 altitude more or less in the forenoon will act in the same 

 manner in the afternoon, and as we do not want to know 

 at all what that altitude is, but merely to ensure that it is 

 equal, a.m. and p.m., the amount of the errors is immaterial. 



