82 COMPOUND ORGANS OF PLANTS. 



inspection of the young shoots of the larch, which by their 

 rapid growth do not admit of any fascicular development of 

 their leaves. On these shoots the young leaves of the larch 

 will be found to be scattered, not fascicled, clearly showing 

 their natural arrangement, and proving that the fascicles are 

 the result of the development of the leaves and the non-de- 

 velopment of the nodes of the stem. 



The spired growth of the leaves. This is most readily 

 perceived in such plants as have their leaves distributed 

 alternately on either side of the stem. If a thread be wound 

 about the stem so as to touch the basis of the first, second, 

 third, fourth, and succeeding leaves, it will be found to de- 

 scribe an ascending spiral around the stem, and with such 

 accuracy that the law may be expressed numerically. The 

 observations of Dr. Gray, on leaf arrangement, are too 

 interesting to be omitted in this place. " If we write down 

 in order the series of fractions which represent the simpler 

 forms of leaf arrangement, as determined by observation, viz. : 



3> i> l> T 5 s> 2 8 T> il> we can nar dly fail to perceive the 

 relation that they bear to each other. For the numerator of 

 each is composed of the sum of the numerators of the two 

 preceding fractions, and the denominator of the sum of the two 

 preceding denominators. Also, the numerator of each fraction 

 is the denominator of the next but one preceding. We may 

 carry out the series by applying this simple law, when we 

 obtain the farther terms, T 5 3, a^vj}, fj, &c. Now these 

 numbers are those which are actually verified from observation, 

 and, with some abnormal exceptions, this series comprises all 

 the cases that occur/' 



That the interest which attaches to the above extract may 

 be fully appreciated, I remark, that the fractions severally 



