MUSEUM OF COMPAEATIVE ZOOLOGY. 



45 



In this table the first column gives the number of the generation, the 

 second the whole number of individuals in the generation, and the third 

 column the increase per cent of individuals in each succeeding genera- 

 tion over the last. In this specimen the increase underwent a very- 

 regular diminution. 



With larger colonies so great a regularity as that just shown is hardly 

 to be expected, nor is it found. The following table is based on 

 Figure 64, and is like the preceding; but in addition the percentage 

 increases have been averaged — i. e. the means of successive increases 

 taken in pairs have been given — to eliminate what may be called 

 accidental variations. 



Hence we conclude, There is a diminution in the rate of increase of in- 

 dividuals in the "fan" as it groivs older. 



In searching for an explanation of this phenomenon, I first drew 

 a line from the centre of the primary individual of the fan to the 

 periphery, and divided it into four equal parts. I then described 

 arcs with the primary individual as a centre, and with radii equal to 

 \, I, f , and I of this line respectively. Counting the number of in- 

 dividuals cut by these arcs respectively, and dividing those numbers 

 by the length of the corresponding arcs, I found that there is almost 

 exactly the same number of individuals per unit of arc for each of the 

 four arcs. (Rule 7.) The previous conclusion, that there is a dim- 

 inution in the rate of increase of individuals in the fan as it grows 

 older, may then be considered as a corollary to this rule, as it ob- 

 viously follows from it. 



