VOL. LVI.") PHILOSOPHICAL TRANSACTIONS. 353 



But the other is a much better way of supplying the want of correspondent 

 observations; viz. by the help of a calculation made for the given meridian, and 

 corrected by adding or subtracting for the error of the tables, which error will 

 be deduced from the other observations, made in the same month or near it: 

 for in this way all the observations, made in the place to be determined, will 

 contribute partly to confirm the required longitude. And the certainty of this 

 method which Mr. W. means chiefly to explain, depends principally on this, 

 the error, to which the tables are liable, may be rightly corrected for any mo- 

 ment. This can easily be done if the error be constant for some years, or even 

 for months. But experience shows that observations made about the same time, 

 though deemed almost equally good by their observers, yet differ unequally from 

 calculation ; nay even the same immersion or emersion, as noted by different 

 astronomers, often gives an error of calculation differing by many seconds or a 

 whole minute, not wholly to be ascribed to the fault of the tables, but partly to 

 the observations themselves. In this case it is very often hard to find out the 

 true error of the tables; for even expert observers often inadvertently slip into 

 errors, and note down as true, observations that are erroneous. If therefore, as 

 is often the case, there be only one observation selected for finding out the error 

 of the tables, it is easy to fall into error. From all these reasons it appears how 

 necessary it is to examine the observations themselves, before they are employed 

 for determining the longitude, by any method whatever. And that may be done 

 as follows : 



Dispose all the useful observations of the same satellite, especially of the first, 

 made about the same time, as well in the place to be determined as in the ob- 

 servatory before sufficiently known, in a table according to the order of their 

 times. Assume for the present the required difference of meridians, as far either 

 as the observations, if there be any, offer immediate correspondents, or as an 

 incorrect calculation of one observation may require. Then examine exactly all 

 the observations by the tables, and mark, the errors of calculation so found. 

 Which done, and having attentively examined the series of errors, it will suffi- 

 ciently appear, 1st, which, among the selected observations made at the fixed 

 observatory, are the best and most deserving of confidence: 2d, what may be 

 the error of the tables at the middle time : and lastly, whether the difference of 

 meridians sought be greater or less than that which was assumed in the calcula 

 tion ; and how much it must be either augmented or diminished, to produce 

 nearly equal errors of calculation. Then it will be very probable that such im- 

 mersions as appear to be the most too early, and the emersions too late, are to 

 be esteemed the least certain, though they may have been deemed good ones by 

 the observers themselves, for the theory of Jupiter's satellites, especially of the 

 two nearest, is now so perfected, that it can hardly be doubted that all the im- 



VOL. XII. Z z 



