408 SCIENTIFIC RECORD FOR 1883. 



twenty years ago that Jupiter exercised a peculiar influence over the 

 minor planets, tending to produce well-marked gaps amongst them at 

 certain well-defined distances. For if the period of any minor planet 

 were commensurable with that of Jupiter, the latter would exercise a 

 perturbing influence upon it which would eventually result in a com 

 plete change of orbit. Later on, in 18G8, Professor Kb kwood employed 

 the same principles to account for the great division (Cassini's) in Sat- 

 urn's rings. Maxwell had shown that the rings must be formed of sep- 

 arate particles moving round the planet to a certain extent as independ- 

 ent satellites. But a body moving round Saturn at the distance of Cas- 

 sini's division would have a period that was very closely commensur- 

 able with those of each of the six inner satellites, and it would therefore 

 be especially exposed to perturbation. Dr. W. Meyer, of Geneva, has 

 carried the principle yet further and has investigated every possible com- 

 bination of the commensurabilities of the revolution periods of the sat- 

 ellites, and he finds that, including the division of Cassini, there are seven 

 places where the satellites would unite to exercise a perturbing influence 

 on the members of the ring system. The first position is where the period 

 would be one-fourth of that of Mimas, and marks the inner boundary 

 of the dark ring. Particles moving at almost precisely the same dis- 

 tances would have their times commensurable with each of the other 

 five inner satellites ; thus for a period of one-quarter of that of Mimas 

 we have a distance of 10".56 from the center of Saturn, for one-sixth of 

 that of Enceladus 10".43, and for one-eighth of that ofTethys 10".G6. 

 Dr. Meyer sees a consequence of this close agreement in the well-defined 

 character of the inner edge of the dark ring. Next comes Struve's 

 division in the dark ring. One-fifth the period of Enceladus corre- 

 sponds to a distance af ll". 79; one-seventh that of Tethys 11".6G; the 

 three next satellites give a closely similar result. The position of 

 Struve's division is not very exactly known, and Dr. Meyer adopts 

 11". 79* as its distance, being the mean between the positions of the 

 inner boundaries of rings C and B. One-third of the period of Mimas 

 introduces a new series of commensurabilities in which all the six satel- 

 lites take a part, but the agreement is by no means so close as in the 

 first two cases, and Dr. Meyer regards the indistinct character of the 

 inner boundary of the bright ring B, which would about correspond to 

 the mean of the distances indicated, as connected with this less perfect 

 coincidence. The period of Enceladus is four times, that of Tethys six 

 times, that belonging to a particle at this distance. Cassini's division 

 corresponds, as already stated, to a period commensurable with each 

 of the six inner satellites, the period of Mimas being twice as long, En- 

 celadus three times, Tethys four, Dione six, Rhea nine, Titan thirty- 

 three. The commensurabilities in the case of the four nearest satellites 

 are of the simplest possible character, and we find that the inner edge 



* There is a misprint here in Dr. Meyer's j>aper ; the observed and calculated dis- 

 tances have been interchanged. 



