fHE TRANSATLANTIC LONGITUDE. 75 



other times, and comparing likewise the transit-observations made by different 

 persons at the same station, during the present longitude-operations. 



The latter course seems preferable, and all the more allowable, inasmuch as those 

 values which careful, independent scrutiny has rendered the most probable are all 

 of them small, yet most of them distinctly indicated. And I propose to adopt, as 

 not altogether empirical, although obtained by an exercise of judgment quite as 

 much as of computation, values for the personal equations, deduced from other 

 sources than the special comparisons here described. It so happened that the 

 algebraic signs of the numerical values thus employed are the same as by the 

 special comparisons, although the magnitudes of these values are very much dimi- 

 nished. 



I cannot but believe that an explanation is here presented of the very perplexing 

 phenomenon, so often, and indeed so generally, encountered in the discussion of 

 personal equations, that the values, as found from the comparison of two observers 

 directly, differ so widely from the results obtained when a third observer is employed 

 as an intermediate standard. Different individuals are affected, by any unusual 

 circumstances attending their observations, in degrees differing with their nervous 

 organizations. 



Thus, in the present case, Mr. Mosman's observations were probably affected but 

 slightly by the stiffness of the key-spring, which apparently affected those of Messrs. 

 Boutelle and Chandler and myself to so great an extent. 



The following values have been adopted, as seeming most truly to represent the 

 personal equations between the different observers, while engaged in the regular 

 observations of the campaign: — 



Gould— Mosman = + 0».02 



Dean — Mosman = -\- 0.11 



Goodfellow—Dean = +0.02 



Boutelle—Goodfellow = —0.14 



Boutelle—Chaudler = — 0.04 



While adopting these values, I am far from believing that they are the same for 

 stars in different declinations, or even for stars of different magnitudes. But they 

 do seem to represent, with some approximation to the truth, the average differences 

 between the several observers in determining time. 



XI. 



FINAL RESULTS FOR LONGITUDE. 



1. FoUliommerum and Heart'' s Content. 



The longitude deduced from the signals of Oct. 25 depends upon time-observa- 

 tions at Valencia by myself, and may therefore be combined with those of the last 

 three nights on which Mr. Mosman determined the time, by subtracting the adopted 

 personal equation, Gould — Mosman = + 0'.020. But the longitude of Oct. 23 

 depends upon the transit-observations of Oct. 28 and 30, on the latter of which 

 dates three of the nine stars were determined by Mr, Mosman. Applying to the 



