CHAP. XIV.] CHRONOMETRIC MERIDIAN DISTANCES 335 



The performances of chronometers used dm'ing a chrono- Diagram 

 metric meridian distance may be shown graphically by the chrmu)^ 

 aid of a diagram on squared paper, the vertical ordinates repre- meter 

 senting the observed daily differences, and the horizontal * ®^ 

 ordinates the days during which the meridian distance was 

 carried out. 



A similar diagram will show the variation in the rates of 

 the different chronometers as ascertained from time to time. 



Supposing that we had had to stay at Mesale for a few Another 

 days before returning to Maziwi, we can still find a fair travel- Travei- 

 Hng rate. ling Rates. 



The formula for this is as follows : 



M = 3-a-n — ^- — —, 



m + n 



where, the other letters representing the same values, 



|3^ is the error at place B before leaving. 



Here the travelling rate is, 



( a--a)-(/3^-/3) 

 m + n 



This can be exemplified thus. We obtain sights at Maziwi 

 on 27th and at Mesale on 31st as before. Then sights again 

 at Mesale on the 4th noon, and again at Maziwi on the 6th 

 noon. 



From the difference of the errors on the 27th and 6th we 

 should deduct the difference of the errors on the 31st and 4th, 

 and divide the remainder by 6, the sum of the intervals from 

 the 27th to the 31st, and of the 4th to the 6th, or, in other 

 words, the number of days actually travelling, which will give 

 us the rate. We then proceed as before. 



The travelHng rate obtained in this instance will not be as 

 good as in the former case, as the chronometers will have had 

 two disturbances instead of one, and the rate they may settle 

 into on starting the second time, after four days' quiet at 

 anchor, may not be the same as before ; but it will still be 

 better than obtainable by any other method, and if circum- 

 stances of weather, sea, and temperature are nearly alike on 



