118 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



Table 63. — Constants for position of secondary branches. 



[Unit = 1 node.] 



From tables 60 and 61 the following points may be noted: 



(a) The first secondary branch does not usually occur at the first 



node of the primary branch. The average position of first branches is 



at about the third node. 



(6) Roughly speaking, about 50 per cent of first secondary branches 



arise at or below (i. e. , proximad of) the third node of primaries, and 50 



per cent at or above (distad of) this node. 



(c) There is a close agreement between all the series in respect to 

 the position of origin of secondary branches. 



(d) There is a wider range and higher degree of variation in this 

 character than would have probably been predicted. Series I is very 

 remarkable in this respect, there being one first branch occurring on 

 the 19th node of the primary axis. All the series had first branches 

 occurring as far out as the 9th or 10th node. 



(e) In table 60 it is to be noticed that there is apparently a tendency 

 for first branches to occur more frequently at odd than at even nodes, 

 at least at the beginning of the primary axis. In all the series (except 

 III, where the numbers are small) there is a high frequency at the 

 first node, a decided drop at the second node, and a more or less consid- 

 erable rise again at the third. Beyond this point the numbers are so 

 small that one can not make a safe judgment. So far as the data go it 

 of course looks as if we might possibly have the start of a Fibonacci 

 series here, but there is no evidence whatever of a relatively high 

 frequency at the 5th and 8th whorls as compared with the 4th, 6th, and 

 7th, which we should expect to find if we were really dealing with such 

 a series. 



Having seen how the position of origin of first branches is distributed 

 on the axis from which they spring, we may examine into the same 

 matter in the case of the succeeding branches (second, third, fourth, 

 and fifth). It is not worth while to go beyond the fifth on account of 

 the small number of observations. The data are given in table 62. 



