ASTRONOMY AND METEOROLOGY. 343 



fractions with the successive approximations of the common series for 

 leaves is rendered still more significant by the fact, that one of those 

 two which differs most from the common series, namely, the ratio 

 between the year of Venus and that of the Earth, is one of a series 

 which, in vegetable life, cannot be distinguished from the common, 

 except by the spiral running in the opposite direction; the series, 

 namely, beginning with -|, , -f, f, , -fa, &c. The year of Venus dif- 

 fers by only about one hour and a half from fa of the Earth's. 



" Among the periods of Jupiter's moons, also, we find three ratios, 

 among those of Saturn six, among those of Herschel four, which 

 are nearly approximations in these series. They do not, however, 

 follow the proper order of approximation as they approach the pri- 

 mary planet. 



"Here, then, are two problems, one in astronomy, the other in bot- 

 any, and both solved by the same arithmetical law. The botanical 

 problem is, to distribute the leaves, buds, petals, &c. of plants in such 

 wise as to secure a graceful variety of symmetry. The astronomical 

 problem is, to proportion the years of the planets in such wise as to 

 render the conjunction of any considerable number a rare occurrence; 

 to secure, that is, the system from too great mutual interference, by 

 keeping the planets scattered round the sun. This is done by mak- 

 ing the years incommensurable, and nearly in the ratio which is meas- 

 ured by approximations to an aliquot part of the difference between 

 some odd number and the square root of five. The botanical problem 

 is solved by setting the leaves at an angle, which is to the whole 

 circle in a ratio measured by the same approximations. And, in both 

 cases, the odd number usually employed is three, and the aliquot part 

 is one half. The ratio between the Earth's year and that of Mars does 

 not conform to this rule." 



SECOND COMET OF 1849. 



IT now appears that the telescopic comet discovered in April, 1849, 

 by Geo. P. Bond, of the Cambridge (Mass.) Observatory, was de- 

 tected the same night by M. Schweizer, of Moscow. Its elements 

 agree quite well with those of the second comet of 1748, so that it 

 may be another instance of the return of a comet after a lapse of a 

 certain period. 



CONNECTION OF COMETS WITH THE SOLAR SYSTEM. 



THE following is an abstract of a paper presented to the American 

 Association, by Prof. Peirce, on the connection of comets with the 

 solar system. Prof. Peirce stated that there had been a century of 

 exact observations upon comets, so that it seemed worth while to in- 

 quire if we could not now ascertain whether they are component parts 

 of the solar system, or strangers visiting us from other systems. He 

 believed that the facts were sufficient to decide this question. 



