WORLD- TRO UGHTS. 329 



from its predecessor by an interval or angular distance 

 equal to one half the circumference of the stem. We have 

 here, then, a spiral expressed by the fraction ^. The com- 

 plete series of fractions, therefore, is the following : \, J, J, 

 f, ^-, ¥ 8 T , etc. Now let it be borne in mind that these val- 

 ues are obtained by actual observation, and that there are 

 plants whose leaf-arrangements are known to correspond 

 to each of these fractions severally, as well as others in 

 the series farther continued. But notice the relation which 

 subsists between the successive fractions in the series. 

 Each numerator is equal to the sum of the two preceding 

 numerators, and each denominator to the sum of the two 

 preceding denominators. Knowing this law, we may con- 

 tinue the series to any extent ; and it has been so contin- 

 ued, and fractions obtained to which plants have subse- 

 quently been found to correspond, though we hardly know 

 how at present to interpret the unrealized possibilities in- 

 dicated by the higher terms of the series. Is all this the 

 result of chance ? Is it not rather mathematics, law, intel- 

 ligence ? 



We turn now our attention to the " infinite meadows of 

 heaven," where 



"Blossom the lovely stars, the forget-me-nots of the angels." 



Neptune, the remotest planet, revolves about the sun in 

 60,000 days — speaking in round numbers — Uranus, the 

 next, in 30,000 days, which is one half the preceding num- 

 ber; Saturn, the next, in 10,000 days, which is one third 

 the period of Uranus ; Jupiter revolves in 4000 days, which 

 *s two fifths of the period of Saturn. And so we go on 

 through the system, and find the law expressing the rela- 

 tions of the revolutions of the planets identical with that 

 which determines the arrangement of the leaves upon the 

 humble stem of a plant. 



