642 ON LEAF- ARRANGEMENT [ch. 



on the whole very constant in number, according to the 

 species. 



Thus in many cones, such as those of the Norway spruce, we 

 can trace five rows of scales winding steeply up the cone in one 

 direction, and three rows winding less steeply the other way; in 

 certain other species, such as the common larch, the normal 

 number is eight rows in the one direction and five in the other ; 

 while in the American larch we have again three in the one direction 

 and five in the other. It not seldom happens that two arrange- 

 ments grade into one another on different parts of one and the 

 same cone. Among other cases in which such spiral series are 

 readily visible wye have, for instance, the crowded leaves of the 

 stone- crops and mesembryanthemums, and (as we have said) the 

 crowded florets of the composites. Among these we may find 

 plenty of examples in w^hich the numbers of the serial rows are 

 similar to those of the fir-cones ; but in some cases, as in the daisy 

 and others of the smaller composites, we shall be able to trace 

 thirteen rows in one direction and twenty-one in the other, or 

 perhaps twenty-one and thirty-four ; while in a great big sunflower 

 we may find (in one and the same species) thirty-four and fifty-five, 

 fifty-five and eighty-nine, or even as many as eighty-nine and 

 one hundred and forty-four. On the other hand, in an ordinary 

 " pentamerous " flower, such as a ranunculus, we may be able to 

 trace, in the arrangement of its sepals, petals and stamens, shorter 

 spiral series, three in one direction and two in the other. It will 

 be at once observed that these arrangements manifest themselves 

 in connection with very different things, in the orderly interspacing 

 of single leaves and of entire florets, and among all kinds of leaf-like 

 structures, foliage-leaves, bracts, cone-scales, and the various 

 parts or members of the flower. Again we must be careful to 

 note that, while the above numerical characters are by much the 

 most common, so much so as to be deemed "normal," many 

 other combinations are known to occur. 



The arrangement, as we have seen, is apt to vary when the 

 entire structure varies greatly in size, as in the disc of the sun- 

 flow^er. It is also subject to less regular variation within one and 

 the same species, as can always be discovered when we examine 

 a sufficiently large sample of fir-cones. For instance, out of 505 



