76 THE TRANSATLANTIC LONGITUDE. 



observed times of these three stars the correction +' 0'.020, and repeating the solu- 

 tion for two unknown quantities, we shall find the azimuth correction A to be 

 changed by 4- O'.Oll, and the clock-correction At by — 0'.()09. This increases the 

 interpolated values for the Valencia clock-corrections during the period of the tele- 

 graphic exchanges by only O'.OOl, making the resultant longitude larger by this 

 amount, and the subtraction of 0\02() from the result refers the whole series to the 

 observations of Mosman at Valencia, and Dean at Newfoundland, as foUows : — 



1866. Oct. 25 



2" 51" 56^457 



28 



.468 



Nov. 5 



.455 



6 



.481 



9 



.460 



The sum of the squares of the deviations of the several values from their mean 

 is thvis slightly reduced. An equal weight seems fairly attributable to all the deter- 

 minations, excepting the first, in which there is a regular increase in the values 

 deduced from the successive sets, which possibly indicates a variability in the clock- 

 rate. This, together with the want of experience necessarily attendant upon the 

 first trial, leads me to assign to it but half the weight given to the other four, and 

 we thus attain the mean value of the longitude. 



X = 2" 51" 56.465 



which, corrected for the personal equation in determining time Dean — Mosman = 

 + OMl, and for that of noting signals Dean — Gould = + 0\03, becomes 



;i = 2" 51-" 56.54. 



2. Heart's Content and Calais. 



The time-observations from which the longitude between Heart's Content and 

 Calais is deduced were made by Mr. Boutelle for the second and third series of ex- 

 changes, and by Mr. Chandler for the first and fourth. The resultant values on 

 the 11th and 16th December require, therefore, the subtraction of the correction, 

 Boutelle — Chandler = — 0'.04 ; after which the several determinations may be 

 combined, to obtain the value which would have been found, had all the Calais obser- 

 vations been made by Mr. Boutelle alone. 



The result of the exchanges, Dec. 12, is very far from trustworthy, as a glance 

 at the computation of the time will show. During the three hours Avhich were 

 reqiiisite for obtaining the transits of seven stars at Calais, the clock lost 1'.28, 

 although it had gained 0'.4 during the eleven hours preceding, and gained again 

 during the two hours following. Some serious disturbance to the clock evidently 

 occurred about this time. The unfavorable weather prevented Mr. Boutelle from 

 detecting it, in spite of his best endeavors ; but the fact is not surprising in a clock 

 so old, and so ill adapted for transportation. It would seem as though the fault 

 were in the compensation ; but examination has shown the teeth of the seconds- 

 wheel to have been in bad order, so that a "jump may have occurred during the 

 course of the observations, without detection at the time, or recognition in the 



