VOL. LXiir.] 



PHILOSOPHICAL TRANSACTIOKS. 



will be = 0.59602 and O.99884; consequently ek = 0.40282. 

 value of EK instead of a — h, in the expression 



427 

 Substitute this 



?H X r (a — b) 



and you will have 



2Rr X 0.40282 



= 2" 18', and r =z 5"^ 23' of time. 



d ' —J~" - d 



will be the semidiameter of the satellite, or the whole diameter will be 22' 34" 

 (of the satellite's orbit, considered as a circle, or would be seen under an angle 

 of this quantity, from Jupiter's centre). In this observation, as I have already 

 said, I used a diaphragm with too great an opening (c), for the first disappear- 

 ance. Take then a 2d observation. On the first of August I771, there was an 

 emersion of the 3d satellite, about 15™ after 9. I marked the instant of this 

 emersion ; then I furnished my telescope with a diaphragm of 8 lines. The sa- 

 tellite disappeared, and did not begin to appear again till at the end of 6" 24*. 

 Some minutes after, when it was quite come out of the shadow, I measured the 

 diaphragm, which would make it disappear, and found it of 7 lines. These 7 

 lines give a segment abd of 0.08507. Then saying 8' : 24^^ :: 0.08507 : ar; x, 

 or the segment anm, comes out =0.76562, ae = 0.27994, ap = I.43098, 

 and EP = 1.15104. Therefore '^'"' ^ ^•'^^"'' ^ = gm 24% From this equation r 

 comes^out 5™ 20^, and the whole diameter 22' 22", (in parts of the circular orbit). 

 These two conclusions agree so perfectly well with each other, that, if I am not 

 too fond of my own work, I may venture to say, the method I have invented 

 may be carried to great exactness. I hope you will have the goodness to give me 

 your opinion of it, which I have the greatest respect for, and will be very useful 

 to me, especially if you have leisure to repeat the observations. I shall take the 

 liberty to subjoin a few hints, on the manner of making them, at the end of 

 this letter. The diameter of the Isl satellite I have determined by 3 observations 

 as follows: 



An Immersion 

 Emersion 

 Emersion 



1771, ■) 

 una 30 ( 



June 



57"" 17' 

 1 Aug. 1 ( save < J 3 



Sept. 2} 17 1 



m time or 



You see, sir, that this agreement is likewise very satisfactory. Mr. Messier 

 took part in these observations, and found the application of them very easy. 

 He himself observed the diameter of the 2d satellite, by the emersion of the 30th 

 of August; but it emerged at so small a distance from the 1st, that this circum- 

 stance may have vitiated the observation; the diameter of this satellite must 

 therefore be verified by fresh observations. However, the result of Mr. Mes- 

 sier's makes it 7" 2» in time, or 29' 42" seen from Jupiter ; and a former obser- 

 vation of mine, of the 11th of July, gave the same quantity precisely. Thus, 

 by means of the tables given in my paper, which I had the honour of mentioning 

 to you, it will be possible to compute the invisible segment, for all the observa- 

 tions which have been hitherto made, and the diameter of the satellite being 



3 I 2 



