FUNDAMENTAL RELATIONS OF ANIMALS 129 



In this series the Earth forms a break; but this apparent irregu- 

 larity admits of an easy explanation. The fractions ^, ^, §, |, ^, ^, |-|) 

 etc., as expressing the position of successive leaves upon an axis, by 

 the short way of ascent along the spiral, are identical as far as their 

 meaning is concerned ^vith the fractions expressing these same posi- 

 tions by the long way, namely, |, |, |, |, ^, ^, fi, etc. 



Let us therefore repeat our diagram in another form, the third 

 column giving the theoretical time of revolution. 



60,129 



30,687 



10,759 



4,333 



1,200 



687 

 365 

 225 



It appears from this table that two intervals usually elapse between 

 two successive planets, so that the normal order of actual fractions 

 is I", i, I, f , A' ^tc, or the fractions by the short way in phyllotaxis, 

 from which, however, the Earth is excluded, while it forms a mem- 

 ber of the series by the long way. The explanation of this, suggested 

 by Peirce, is that although the tendency to set off a planet is not 

 sufficient at the end of a single interval, it becomes so strong near the 

 end of the second interval, that the planet is found exterior to the 

 limit of this second interval. Thus, Uranus is rather too far from 

 the Sun relatively to Neptune, Saturn relatively to Uranus, and 

 Jupiter relatively to Saturn; and the planets thus formed engross 

 too large a proportionate share of material, and this is especially 

 the case with Jupiter. Hence, when we come to the Asteroids, the 

 disposition is so strong at the end of a single interval, that the outer 

 Asteroid is but just within this interval, and the whole material of 

 the Asteroids is dispersed in separate masses over a wide space, in- 

 stead of being concentrated into a single planet. A consequence of 

 this dispersion of the forming agents is that a small proportionate 



