i,j:ssojys witb plants 



are flat because of this distichous (or 

 two-sided) arrangement. This arrange- 

 ment, then, in which the third ^ 

 bud is directly over the first, 

 and in which the buds are 

 half a circumference apart, may 

 be represented by the fraction 

 one-half. If we were to make a 

 mark from 1 to 3, passing over 



2, we should make one revolution 



ll 



"*< 



of the stem, and this fact is ex- ♦ 

 pressed by the numerator of the 

 fraction. We should also pass 

 over two buds (counting the 

 first, but not the last), and this 

 fact is represented by the de- 

 nominator. 



68. All this suggests a new ^' 

 subject of inquiry. The pupil 

 will now profit by an examination 

 of any twig. If he desires to 

 work out the mathematics of the 

 cycles, let him secure straight 

 growths, preferably from up- 

 ward-growing branches, where 

 light is equally diffused ; but if 

 Fig. 64. ^® wishcs to scc things exactly as they 

 Twig of ^^"6) l^t tiim take the first shoot which 



elm. 



Fig. 65. 

 Twig of plum. 



