700 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



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lated their orbital velocities. The agreement of this series of six 

 satellites with those derived from theory, is, iintler the circum- 

 stances, remarkable; and indicates that the observations of astron- 

 mers are not far wrong. 



There are two other and more distant satellites in this system, 

 the 7th and 8th from the primary (A. and B.. Avhich the elder 

 Herschell announced that he saw through his telescope, and 

 althoujrh he recorded their elements, no other astronomer has since 

 been able to find them: it is consequently supposed that Herschell 

 was mistaken. He puts down the velocities of these doubtful satel- 

 lites, (See Larduer's Hand Book of Astronomy,) one as 3,816 miles 

 per hour, and the other as 5,398 miles per hour. If the law of 

 common difference may be relied upon, Herschell was certainly 

 mistaken, either in his record or in his calculations. But it is pos- 

 sible that he was not mistaken in his observations. He may actually 

 have seen both of them, but committed an error in regard to their 

 positions. Applying the law of common difference, we find that 

 these two satellites, if they exist, have, one a velocity of 4,036, 

 (instead of 3,816), and the other 5,236, (instead of 5,392), miles 

 per hour. 



Table 14. 

 Satellites of Ueanus. 



Theoretical velocities. Actual velocities. 

 Miles per hour. Miles per hour. 



Velocity of A, a doubtful satellite 4,036 3,816(?) 



Add 600 -f 2= 1,200 



Velocity of B, a doubtful satellite .... 5,236 5,398(?) 



Add 600 -j- 4= 2,400 



Velocity of C, a known satellite 7,636 7,636 



Add 600 600 



Velocity of D, a known satellite 8,236 8,178 



Add600 600 



Velocity of E, a known satellite 8,836 8,828 



Add 600 + 2= 1,200 



Note. — I have, in the above table, put down the actual velocity of A, as 3,810, and of 

 B, 5,398, but I only mean that these are their actual velocities according to the calculation? 

 of Sir William Herschellj which arc probably erroneous. 



