922 ON LEAF-ARRANGEMENT [ch. 



and we find them to be 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 arrangements grade into one another 

 on different parts of one and the same cone. Among other cases 

 in which such spiral series are readily visible we 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 which 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; and the 

 scales on the little cone of a Cypress shew the same numerical 

 simplicity. 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 sunflower. 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 cones of the 



