ARBANGMMENT OF THE BUDS 67 



comes to his hand, but note the conditions under 



which it grew. To begin with, he might try 



alders, and birches, and sedges. Here he will 

 find the fourth leaf normally over 



the first. He can easily construct ^ -^ ^ 



the numerical cycle. 'Ix . 



■ 69. Let us go back to the ap- 

 ple, or take up the plum (Fig. -^ j 

 65). Here 6 is over 1, and the 1 a 

 mark passes twice about the stem. j. 

 The angular distance between the ' ' m 

 buds, therefore, must be two-fifths I'^vi I 



of a circumference. We will cut ,r ^ i 



1*1 ' I 



the bark loose in a straight line ^ ' ' 



from 1 to 6, and peel it off (Fig. H \j^ j 



66). If the strip of bark were one i , I 



inch wide, then each bud would ^ [ 



be two-fifths of an inch at one ^j;^ I 



side of the neighbors above and ' * j , | 



below it, if the branch were j 



straight and symmetrical. Now turn fig. 66. 



back and see if the artist has Showing the arrange- 



correctly drawn Figs. 1, 3, 28, 35. ^^l l'^^^ "^^^ 



70. We have now found arrange- 

 ments represented by the fractions one-half, one- 

 third, two-fifths. The last fraction can be made by 

 adding the numerators and denominators in the first 

 two. Can we, then, add the last two and prophesy a 



