MUSEUM OF COMPARATIVE 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, 
Gene | N | > | Genera- |Number of) Increase 
hei Fa ee Average. tion. Individ. | per Cent. Average. 
Ren | | 
1 1 29 
VIII. 28 27 . 
II 2 100 23 
100 IX. 33 18 
III. 4 100 18 
100 Sg 39 18 
IV. 8 100 16 
88 XI. 44 13 
Y 14 75 
49 XII. 20 ! 
VI. 17 22 Incomp lete. 
26 || XIII 4 |) 
VII 22 30 
Hence we conclude, Zhere is a diminution in the rate of increase of in- 
dividuals in the “ fan” as it grows 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 
ares with the primary individual as a centre, and with radii equal to 
4, 2, 3, and 4 of this line respectively. Counting the number of in- 
dividuals cut by these ares respectively, and dividing those numbers 
by the length of .the corresponding ares, I found that there is almost 
exactly the same number of individuals per unit of are for each of the 
four ares, (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. 
