444 PHILOSOPHICAL TRANSACTIONS. [aNNO 1773. 



contains 3 unknown quantities, viz. the versed sines a and b, of the two invisible 

 segments, and the semidiameter of the satellite's disc: for you know, sir, that 

 there is nothing to be depended on, in all that has been done on the diameters of 

 the satellites by Cassini, Whiston, and Maraldi. The following is the way 

 which 1 have taken, to determine these unknown quantities. I observe, first 

 of all, that 2 of them, a and b, are reducible to one; because, as you will see 

 presently, the 1 segments are always in a known proportion [to the whole disc 

 of the satellite, as well as to each other] ; and consequently the proportion of 

 their versed sines Ai, ab, may be obtained, either by calculation, or by a table 

 made for the purpose. In order to discover it, considering that when the satellite 

 disappears, it is from the diminution of its light, I conceived, that one might 

 contrive to imitate, at any time, what happens in the eclipses, by diminishing 

 the light. I have an acroamatic telescope of 5 feet length, and 24 lines aperture. 

 I made some diaphragms of pasteboard, which I could apply on the outside of 

 my object glass, the openings of which lessened, by half lines successively, from 24 

 lines down to 3. In fine weather, I applied these successively to my object glass, 

 and endeavoured to find out, whether, by trying from the greatest to the less, 

 some one of them could not be found, that would make the satellite dis- 

 appear. My success in this gave me great satisfaction. One day, for instance, 

 the 3d satellite disappeared, when the opening was reduced to 3 lines, and the 

 1st, when it was reduced to 6 only; and as, in the telescopes, the quantity of 

 light is in the proportion of the squares of the apertures, I concluded, that the 

 '64th part of the light of the 3d satellite, and the l6th part of the 1st, were 

 insensible; whence it follows, that if, at the instant of an eclipse of the 1st 

 satellite, the l6th part of its light is insensible, the invisible segment abd will 

 be likewise a l6th part of the disc; and thence it will be easy to compute the 

 versed sine ab. In these first observations, I took care to chuse the time when 

 the satellite was at its greatest elongation; for the insensible part increases pro- 

 digiously, and sometimes amounts to a 3d of the disc, when the satellite is very 

 near the edge of Jupiter. This variation is much larger than that which takes 

 place in consequence of the distance of Jupiter from the opposition to the sun, 

 and contrary to it. As it is scarcely possible to estimate the law of the varia- 

 tions of this segment, occasioned by the proximity of Jupiter's disc, I judged 

 that they ought to be determined by observation. Accordingly, I followed the 

 satellite from the edge of Jupiter's disc, to the furthest limit of its eclipses, that 

 is, with respect to the 1st, to the distance of 2 semidiameters oi Jupiter. 

 Having thus several points by observation, I got the rest by interpolation, and 

 made a table of the variations of the invisible segment, which depend on the 

 distance from the edge of Jupiter; a similar table I likewise made for each of the 

 first 3 satellites; but have not yet been able to make suflScient observations on 



