342 ANNUAL OF SCIENTIFIC DISCOVERY. 



below, of very recent discovery. The planets known from high an- 

 tiquity are Mercury, Venus, Earth, Mars, Jupiter, and Saturn. To 

 these, in 1781, was added Uranus, or Herschel, as it is sometimes 

 called, from the name of its discoverer. Early in the present century, 

 astronomers became convinced that a planet existed between Mars 

 and Jupiter, and an association of twenty-four observers was formed 

 to examine the whole heavens. But, early in January, 1801, the 

 present planet Ceres was accidentally discovered by Piazzi, in Sicily. 

 In March, 1802, Pallas was discovered by Olbers, in Bremen, and 

 this was followed, in 1804, by the discovery of Juno, and, in 1807, 

 by that of Vesta. On December 8, 1845, Astr&a was discovered by 

 Professor Hencke, and on July 1, 1847, he also discovered Hebe. 

 Iris was discovered August 13, 1847, and Flora, October 18 of the 

 same year, both by Mr. Hind. Metis was, we believe, discovered by 

 Mr. Graham, in Ireland, on April 25, 1848. The recent extraordinary 

 discovery of Neptune is familiar to all. The total number of primary 

 planets discovered, up to the present time, is, it will be seen, 18. Many 

 of them are never visible to the naked eye. Editors. 



INTERESTING ANALOGY IN BOTANY AND ASTRONOMY. 



PROF. PEIRCE described to the American Association a curious 

 analogy, which has been more fully developed by the Rev. Thomas 

 Hill, of Waltham, Mass., in a recent review. " If, on any twig of 

 a cherry-tree, we count the leaves from the bottom upwards, we shall 

 find that the sixth leaf is over the first, the seventh over the second, &c. 

 That is, two successive leaves, viewed from above, make an angle 

 with each other equal to two fifths of a circle, and it requires five 

 such intervals to make two complete revolutions. On a twig of 

 the elm, the third leaf is over the first ; or the angle between two 

 successive leaves, viewed from above, is half a circle. In the currant, 

 the angle is usually three eighths; that is, eight leaves are required 

 to make three turns, and the ninth leaf is over the first. The angle 

 which two successive leaves, viewed from above, make with each 

 other, in any plant, is generally found to be one of the following 



series of fractions of a circumference :, -^ |, -f, -^ -.*-, ^-f., -f 

 &c. Sometimes, however, this angle is one of the following : 

 "4> i"> "f tVi & c - '> an d occasionally we have found, in the golden-rod, 

 fractions of the series 1, ^ -^ -^ &c. Other fractions are found, but 

 we believe that, in a healthy plant, the fractions always belong to a sim- 

 ilar series, that is, to a series in which the two first fractions hare the 

 numerators each 1, and the denominators differing by I, and the terms of 

 any other fraction are formed by adding those of the two preceding. 

 Such a series, the higher it is carried, approximates more and more 

 nearly to an aliquot part of the difference between the square root of 

 five and some odd number. Now, if we divide the year of the planet 

 Uranus by that of Neptune, the year of Saturn by that of Uranus, that of 

 Jupiter by that of Saturn, &c., we shall obtain nearly the following frac- 

 tions :-i W> f i, if, if , ii, A, if Th e dose coincidence of these 



