HA RDWICKE'S SCIENCE- G OSS I P. 



29 



be said generally, that when we can count the number 

 of rows (vertical) of leaves as placed on the axis, we 

 have at once the den-ominator of the fraction ; for 

 the number of rows is identical with the number of 

 leaves in the cycle. 



One of the simplest arrangements is the distichous 

 (in two rows). This is found to be the normal plan 

 in all grasses, in the elm (Ulmus campestris) , linden 

 (Tilia), &c. The third leaf is immediately over the 



the angular divergence of the leaves may be expressed 

 in degrees. Thus in the pentastichous, or | arrange- 

 ment, each leaf is separated from its predecessor and 

 successor by two-fifths of the circumference of a circle, 

 i.e. two-fifths of 360 , or 144 . Thus in this case the 

 angular divergence is 144 degrees. In the distichous 

 plan the angular divergence is one-half a circle, or 

 180 degrees. The tetrastichous phyllotaxis has the 

 fifth leaf immediately over the first, and examples of 



Fig. 18. — Opposite phyllotaxis ot Lamiutn album. 



first, and there is one turn round the stem. The leaves 

 being arranged in two rows, one on each side of the 

 axis, it is obvious that on one side there will be the 

 1st, 3rd, 5th, 7th, &c, and on the other, the 2nd, 

 4th, 6th, 8th, &c. The fraction suitable to this case 

 will be \ — one turn and two leaves in the cycle. 

 Speaking mathematically, a circle contains 360 , and 

 by taking the number of degrees, represented by the 

 fraction, which indicates the phyllotaxis in question, 



the tristichous arrangement are seen in the elder 

 and in sedges. The following fractions represent 

 common forms of phyllotaxis : \, \, j, \, ^, 2 8 T , Jf. 



It may be noticed that the numerator of each 

 fraction is the denominator of the next but one 

 preceding, and that, after the first two of the series, 

 each numerator is the sum of the two preceding 

 numerators, and similarly with the denominators. 

 It will now be necessary to say something concerning 



