54 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



branches having from 3 to 6 whorls is approximately the same for pri- 

 mary, secondary, and tertiary branches. 



In table 29 are given the constants for the variation in the size of 

 primary and secondary branches for the totals of the series. On 

 account of the relatively small numbers in most instances it is not worth 

 while to give separately the values for each plant, nor for the tertiary 

 branches. 



Table 2^.— Constants for variation in size of primary and secondary branches. 



Series. 



Order of branch. 



I 



II 



III 



IV 



V 



VI 



Primary 



Secondary., 

 Primary — 

 Secondary.. 



Primary 



Secondary. 



Primary 



Secondary. 



Primary 



Secondary. 



Primary 



Secondary. 



Mean 

 (unit = 1 whorl). 



7.085±0 



3.036± 



7.756± 



3.726± 



6.650± 



4.023± 



8.324± 



5.857± 



5.567± 



3.548± 



6.559± 



5.161± 



.427 

 .238 

 .411 

 .208 

 .622 

 .335 

 .313 

 .263 

 .392 

 .301 

 .367 

 .252 



From this table we see that: 



(a) There is surprisingly little difference between the different series 

 in respect to mean size of branches. 



(6) The mean size of primary branches is roughly twice that of 

 secondaries. 



(c) As was to be expected, the mean size of branches is the greatest 

 in the series which was collected latest in the growing season (Series IV) . 



{d) Both absolutely and relatively to the mean size the variation is 

 greater in primary than in secondary branches, with the single excep- 

 tion of Series IV, where, probably as a result of the great number and 

 relatively large size of secondary branches, we get a higher proportion- 

 ate variability in this group. 



SUMMARY OF RESULTS. 



Before taking up the discussion of the positional differentiation in 

 detail, it is desirable to put together in a connected way the results 

 which we have so far gained regarding the variation in leaf-number. 

 By taking separately the whorls borne on different axial elements of 

 the plant body we have found that there is a very sensible differentia- 

 tion of whorls in respect to their leaf -number when they are grouped 

 according to their general location on the plant. The nature of this 



