276 PHILOSOPHICAL TRANSACTIONS. [ANNO 1 798. 



planet; from which he deduces the following remarks on those observations. 

 From the observations of Jan. 14, Feb. 10, March 6, 1787, and Feb. 13, 1792, 

 it appears, that all very small stars, when they come near the planet, lose much of 

 their lustre. Indeed, every observation that has been recorded before, of supposed 

 satellites that have been proved to be stars afterwards, has fully confirmed this cir- 

 cumstance ; for they were always found to be considerable stars, and their being 

 mistaken for satellites was owing to their loss of light when near the planet. This 

 would hardly deserve notice, as it is well known that a superior light will obstruct 

 an inferior one ; but some circumstances which attend the operation of the affec- 

 tions of light on the eye, when objects are very faint, are so remarkable, that they 

 must not be passed over in silence. After having been used to follow up the sa- 

 tellites of Saturn and Jupiter, to the very margin of their planets, so as even to 

 measure the apparent diameter of one of Jupiter's satellites by its entrance on the 

 disk, I was in hopes that a similar opportunity would soon have offered with the 

 Georgian satellites : not indeed to measure the satellites, but to measure the planet 

 itself, by means of the passage of the satellite over its disk. I expected also to 

 have settled the epochs of the satellites, from their conjunctions and oppositions, 

 with more accuracy than I have yet been able to do, from their various positions 

 in other parts of their orbits. A disappointment of obtaining these capital advan- 

 tages deserves to have its cause investigated ; but, first of all, let us cast a look on 

 the observations. 



The satellites, we may remark, become regularly invisible, when, after their 

 elongation, they arrive to certain distances from the planet. In order to find what 

 these distances are, we will take the first observation of this kind, as an example. 

 Feb. 22, 179I3 the first satellite could not be seen. Now, by my lately constructed 

 tables, its longitude from the apogee, at the time of observation, was 204.5 degrees ; 

 that is, 24.5 degrees from the most contracted part of its orbit, on the side that 

 is turned to us, which, as its opposite is called the apogee, I shall call the perigee. 

 By my tables also for the same day, we have the distance of the apogee from the 

 planet, which is .60 ; supposing the greatest elongation distance to be 1. This 

 being given, we may find an easy method of ascertaining the distance of the satel- 

 lite, when it is near the apogee or perigee : for it will be sufficiently true for our 

 purpose to use the following analogy. Cosine of the distance of the satellite from 

 the apogee or perigee is to the apogee distance from the planet, as the greatest 

 elongation is to the distance of the satellite from the planet. When the ellipsis is 

 very open, this theorem will only hold good in moderate distances from the apogee 

 or perigee ; but when it is a good deal flattened, it will not be considerably out in 

 more distant situations : and it will also be sufficiently accurate to take the natural 

 cosine from the tables to 2 places of decimals only. When this is applied to our 

 present instance, we have .91 for the natural cosine of 24.5° ; and the distance of 



the satellite from the planet will come out , : 6 x 33 = 21 // .8. By this method, it 



