VOL XV.] PHILOSOPHICAL TRANSACTIONS. 247 



augmented were additional, add them to; if subductive, subtract them from, 

 each the time of its proper satellite's eclipse; so you have very nearly the appa- 

 rent times when each satellite last past over the axis of Jupiter, viewed from 

 the earth. 5. Subtract each of the times thus obtained from the time proposed, 

 the remainders are the intervals of the motion of each satellite from Jupiter's 

 axis. 6. Extend the thread from the centre over each of these intervals of 

 motion, numbered severally in the divided circles belonging each to its proper 

 satellite, where it cuts the proper orbit of that satellite, whose interval was 

 numbered in its peculiar circle; it shows among the parallels how many semi- 

 diameters of Jupiter that satellite is distant from him, and on which side of him 

 it is posited. 



; Note further, that the thread, as it lay extended over the parallax of the orb 

 numbered in the small arch, where it cut the several proper orbits of each 

 satellite, showed among the parallels how many semidiameters of Jupiter the 

 centre of the shadow was distant from the centre of Jupiter viewed from the 

 earth. And that if the parallax of the orb were additive, the shadow lies on the 

 right hand from Jupiter ; if subductive, on the left. 



To explain these precepts, I shall give two brief examples. Let it be then 

 proposed to know how far each satellite appears distant from Jupiter on the 26th 

 of December, l685, at l6h. 52m. p. m. when the 3d satellite falls into the 

 shadow; also on July J 6, J 686, at lOh. p. m. when there is no eclipse. i 



Anno l685, Dec. 26, ]6h. 52m. p. m. the parallax of the orb, is 9° 20'. - 

 additive. Therefore, 1. 2. 3. 4. f 



d. h. rn. d. h. m. d. b. m. d. h. m. 



The simple parallactic intervals add 1 5.. 2 10. . 4 25.. 10 20 



The half duration of the eclipses to be added ... . 1 10. . 1 30. . 1 18. . 



The parallactic intervals augmented 2 15.. 3 40.. 5 43. . 



Last immersions and conjunctions, Dec 25 9 37.. 25 5 47.. 19 12 58.. 10 30 



Times of last passing Jupiter's axis, Dec 25 11 52 .25 9 27.. 19 18 41.. 10 10 50 



Subtracted from the time proposed, Dec 26 l6" 52. . 26 I6 52. . 26 16 52. . 26 16 52 



Leaves the intervals of motion 1 5 0.. 1 7 25.. 6 22 11..16 6 2 



Over which, numbered in their peculiar circles, 



the thread being severally laid, cuts the proper semid. semid. semid. semid. 



orbit ofeach at their visible distances from Jupiter. 5right 6ileft 3right 4^right. 

 See pi. 8, fig. 3. 



Again, 1 686, July l6d. lOh. p. m. the parallax of the orbit is 10° 46' sub- 

 ductive. Hence, 1. 2. 3. 4. 



The simple parallactic intervals subd 1 12.. 2 35. . 5 19. . 12 



Half duration of the eclipses add 110.. 1 30, . 0. . 



The parallactic intervals augmented 2 22.. 4 5.. 0.. 



The next last emersions and passing the axis of the 



shadow. July 15 5 55.. 15 22 2..K 9 19.. 15 17 52 



