680 PHILOSOPHICAL TRANSACTIONS. [aNNO 1683. 



it might be: after I had finished the tables of their mean motions, I set 

 myself to calculate others for finding the true times of their return to the 

 heliocentric conjunction of % in all places of his orbit, with some other which 



1 foresaw requisite for the easy calculation of their eclipses: having this in 

 readiness, and being encouraged by the late success of my endeavours, I re- 

 solved to calculate all the eclipses of the following year l684, and to impart 

 them to the public in the tracts, for the use of foreigners as well as ourselves; for, 

 if these eclipses be observed, it will certainly show the difference of meridians 

 between them and us. And I must confess it is some part of my design, to 

 make our more knowing seamen ashamed of that refuge of ignorance, their 

 idle and impudent assertion that the longitude is not to be found, by offering 

 them an expedient that will assuredly afford it. Such of them as pretend to a 

 greater talent of skill than others, will acknowledge that it might be attained 

 by observations of the moon, if we had tables that would answer her nootions 

 exactly ; but after 2000 years experience, we find the best tables extant erring 

 sometimes 12 minutes or more in her apparent place, which would cause a 

 fault of half an hour, or 7-I- degrees in the longitude, deduced by comparing 

 her place in the heavens with that given by the tables. I undervalue not this 

 method, for I have made it my business, and have succeeded in it, to get a 

 large stock of good lunar observations, for the correction of her theory, and as 

 a ground work for better tables ; but the examination will be a work of a long 

 time ; and if we should afterwards attain what we seek, the calculation will be 

 so perplexed and tedious, that it will be found much more inconvenient and 

 difficult than that I propose by observing the eclipses of Jupiter's satellites, 

 which however at present I must prefer. 



For I am persuaded that the eclipses of the first will scarcely be found above 

 4 minutes differing from my calculation in the catalogue, nor those of the third 

 above twice as much ; now an error of 4 minutes cannot cause a fault of more 

 than 1 degree in the longitude, collected by comparing an observed ingress of 

 the first satellite into l/'s shadow, or emersion from it, with the time given in 

 the catalogue; and I hope it will scarcely ever be found to err so much. But if 

 the same eclipse may be observed in 2 distant places at the same time, or com- 

 pared with an observation of the same satellite made within a week elsewhere, 

 the difference of meridians will be had something better than by comparing 



2 observations of the same phasis of a lunar eclipse made in distant places. 

 For whereas it is somewhat difficult, by reason of the penumbra, to deter- 

 mine the true time of the application of either of the moon's limbs to the sha- 

 dow, the satellites eclipses, especially those of the first, are almost momentary. 

 And as there can seldom be 4 eclipses of the moon visible the same year, those 



