A. MATHEMATICS AND ASTRONOMY. 61 



ceed two hundred. 3. The number of variable stars increases 

 vvith astonishing rapidity among the higher magnitudes. 



THE NATURE OF THE KIXGS OF SATUEN. 



M. G. A. Hirn, -well known for his investigations into the 

 dynamical theory of heat, has published a mathematical 

 memoir on the riuo-s of Saturn, and discussed the various con- 

 ditions that have been suggested as possibly contributing to 

 maintain the dynamical stability of that system. 



Although M. Hirn's results do not materially differ from 

 those already demonstrated by Peirce and Maxwell, yet we 

 recognize the importance of having this additional and per- 

 fectly independent investigation of so difficult a subject. 



In a recent popular exposition of this subject, M. Hirn gives 

 the present state of our knowledge as follows: 1. Solid rings 

 can not exceed a certain size without breaking. 2. Solid 

 liomogeneous rings are unstable, and must break up into sat- 

 ellites. 3. Non-homogeneous or weighted solid rings are 

 stable, but must have an enormous (imaginary) strength, and 

 therefore can not be permanent. 4. Gaseous or liquid rings 

 can exist ; and such was very probably their original condi- 

 tion ; but. their existence can be only ephemeral, and they 

 must fall toward and join the planets; if Saturn's rings were 

 once fluid, they must long ago have thus disappeared. 5. The 

 rings can only endure as solid fragments of limited size, and 

 separate from each other. Bull. Soc. iVIIist. Nat.^ 1872, 448. 



THE PLANET VULCAN. 



This hypothetical planet, in whose existence many still 

 believe (though we understand the evidence on Avhich Le 

 Verrier sought to establish its existence to be very much 

 shaken), has recently appeared, if we may credit Mr. Cowrie, 

 of Hong-Kong, who thinks he saw it on the occasion of its 

 transiting the sun's disk. Singularly enough, there comes 

 from two scood amateur astronomers of the Manchester Phil- 

 osophical Society a note recalling an observation made by 

 them both on the afternoon of the 12 th of March, 1849, when 

 they watched for half an hour the passage of a small black 

 spot across a portion of the sun's disk. The number of ob- 

 servations of this character seem to have slowly increased 

 until, whether or not we believe in Yulcan, we are at least 



