68 



Transactions. 



" relative rate " of column 6 to one of the comparisons (the 

 later one is taken to correspond to the sign of the rate) in order 

 to make it comparable with the other. Column 7 has been ex- 

 plained. The difficulties encountered with rate have already 

 been adverted to. They become very apparent when deducing 

 the transmission-time, especially when that quantity is very 

 small, as in the present instance. When we are dealing with 

 transmission -time of a third of a second, as is the case between 

 Fanning and Bamfield, one or two hundredths of a second vari- 

 ation affects but little the various transmission-times ; but it is 

 very different when the transmission-time falls near the limit 

 of certainty of the rate. The relative rate of the 18th December 

 was deduced as the others from the best available data, and the 

 result shows a negative value of a hundredth of a second for 

 transmission-time. This, however, does not affect the differ- 

 ence of longitude. Columns 8 and 9 give the deduced clock or 

 chronometer corrections respectively at the two stations for the 

 same instant, the mean of the times of the two exchanges. With 

 the three data then — the difference between the two clocks at 

 an absolute instant, and the respective clock - corrections for 

 that instant — we obtain column 10, the difference of longitude, 

 each with its respective probable error deduced from the pro- 

 bable error of the respective clock-corrections. 



We have then the following values 



Dec. 6 — Difference of longitude 



" 7 



„ 11 



„ 12 



„ 17 



„_ 18 

 Weighted mean 

 Personal equation 

 Difference of longitude 

 Doubtless Bay longitude 

 Wellington longitude . . 



