THEIR ARRANGEMENT. 



141 



most stable and certain, as well as the easiest to observe. In the 

 higher forms, the exact order of superposition often becomes uncer- 

 tain, owing to a slight torsion of the axis, or to the diificulty of 

 observing whether the 9th, 14th, 22d, S5th, or 56th leaf is truly- 

 over the first, or a little to the one side or the other of the vertical 

 line. Indeed, if we express the angle of divergence in degrees and 

 minutes, we perceive that the difference is so small a part of the 

 circumference, that a very slight change will substitute one order for 

 another. The divergence in Jj = 138° 24'. In all those beyond, 

 it is 137° plus a variable number of minutes, which approaches 

 nearer and nearer to 30'. Hence M. Bravais considers all these as 

 mere alterations of one typical arrangement, namely, with the angle 

 of divergence 137° 30' 28", which is irrational to the circumference, 

 that is, not capable of dividing it an exact number of times, and con- 

 sequently never bringing any leaf precisely in a right line over any 

 preceding leaf, but placing the leaves of what we take for vertical 

 ranks alternately on both sides of this line and very near it, approach- 

 ing it more and more, without ever exactly reaching it. These 

 forms of arrangement he therefore distinguishes as curviseriaJ, be- 

 cause the leaves are thus disposed on an infinite curve^ and are 

 never brought into exactly straight ranks. The 

 others are correspondingly termed rectiserial, 

 because, as the divergence is an integral part 

 of the circumference, the leaves are necessarily 

 brought into rectiUneal ranks for the whole 

 length of the stem. 



249. A different series of spirals sometimes 

 occurs in alternate leaves, viz. J, -i, |, -f^ ; and 

 still others have been detected; but these are 

 rare or exceptional cases. 



250. Opposite Leaves (237, Fig. 210). In 

 these, almost without exception, the second pair 

 is placed over the intervals of the first, the third 

 over the intervals of the second, and so on. 

 More commonly, as in plants of the Labiate 

 or Mint Family, the successive pairs cross each 

 other exactly at right angles, so that the third 

 pair stands directly over the first, the fourth 

 over the second, &c., forming four equidistant vertical ranks for the 



FIG. 210. Opposite leares of the Strawberry-bushj or Euonymus Americanus. 



