426 .^PHILOSOPHICAL TRANSACTIONS. [aNNO 1773. 



ment for any particular eclipse, the actual distance of the satellite from the edge 

 of Jupiter being known, look for the quantity of the invisible segment which 

 answers to that distance, in my table, and multiply this quantity by - 

 -rV X r X ^TT-. If two different observations, made in the same place, or 



p^q^ h k^ r ' 



rather two observations made in different places, by different observers, are to 

 be compared, the invisible segment must be determined, such as it was for each 

 observer ; ab and a/;, the versed sines of these segments must be computed, and 



in the expression ^ , the only remaining unknown quantity will be r. 



The following is the method I have hit upon for determining it. I considered, 

 that by trying different diaphragms successively, some few minutes before an 

 immersion, it would be easy to find out the particular size which would make the 

 satellite disappear ; and that the proportion of the invisible segment to the whole 

 disc of the satellite, for that instant, would by that means be determined. Sup- 

 pose then that I have found this diaphragm : my next step is, to cover the ob- 

 ject-glass of my telescope with a diaphragm somewhat larger, which suffers me 

 just to perceive the satellite, but so weak and small, that the least further dimi- 

 nution of its light must render it invisible. I wait till it actually disappears; I 

 write down this time, then take away the diaphragm, and the number of seconds 

 which pass between this first disappearance and the true immersion, giving me a 

 great part of the diameter, I easily compute the whole. The following is an 

 example of my method. On the 26th of June 1771j there was an immersion of 

 the 3d satellite, at 56™ after 9 in the evening. I found the diaphragm which 

 made the satellite disappear, to be of 12 lines. I then fitted my glass with a dia- 

 phragm of 17 lines; I might have taken one much smaller: presently the satel- 

 lite disappears. But removing the diaphragm, I see the satellite again, very 

 distinctly, for 2™ 18'; after which the true immersion followed. Now this is 

 my calculation. The aperture of the diaphragm, which made the satellite dis- 

 appear, being 12 lines by observation, the invisible segment at the instant of 

 the eclipse, must have been a quarter of the disc. Let abd be this quarter. I 



I know that, at the instant of the immersion, the sa- 

 tellite had entered the shade, by the whole part ep of 

 its diameter. I say then, if on an aperture of 24 lines, 

 the part abd is insensible, the insensible part, on an 

 aperture of 17 lines, will be larger than abd, in the 

 ratio of the square of 24 to the square of 17- Saying, 

 then as 17^ : 24^ :: 0.25000 :: x, x comes out = 

 - s^j. 0.49827, or near half the disc, represented by unity ; 



thence I see that, at the instant of the first disappearance, the satellite had not 

 gone in farther than k. Putting the radius ac = J, the versed sines ae, ak 



