J. W. Jenkinson 
449 
Iu the second place the growth-rate differs considerably — both initially and 
finally — in the various parts. The maximum observed is 73'28 for the second 
stage of the length of the caudal fin, the minimum 5'59 for the last stage of the 
breadth of the caudal fin (the negative values obtained for the two last stages of 
the anterior dorsal, and of the ventral fins, are due to the excessive value given to 
the means, owing to an error in measurement, in the two previous stages). And 
lastly, the rate of decline of the growth-rate differs. Thus between Stages II and 
III there may be a decrease of 10 (total length), 11 (head, anterior dorsal fin, 
ventral fin), 15 (breadth of caudal fin) or 25 (length of caudal fin). Similarly the 
decrease in the final stage varies from 5 to 16. 
Apart from the irregularities exhibited in the cases alluded to there is no 
evidence that in the period under observation more than one growth cycle is 
involved. 
We turn next to the variabilities of these various dimensions (Table II, in 
which both standard deviations and coefficients of variability are given). The 
coefficient of variability (C. V.) may be taken as giving the best measure. 
Two things are at once evident. First there is a regular decrease during the first 
four stages (length of anterior dorsal fin and length of ventral fin must be ruled 
out for the reasons already given). Like the decrease in the growth-rate this 
decrease of variability is also more rapid at first than later on, at least this is 
generally so. There are however exceptions. In the posterior dorsal fin (length), 
caudal fin (length) and caudal fin (breadth) there is nearly as much or even more 
difference between the variabilities in the third and second stages as there is 
between the variabilities in the second and first. It is not easy to associate these 
anomalies with anomalies in the change of the growth-rate of the corresponding 
parts. It is true that the growth-rate changes irregularly in the posterior dorsal 
fin : but in the caudal fin length and breadth the difference between the growth- 
rate from the first to the second stages and that from the second to the third stages 
is very great. Again, the growth-rate in the eye increases temporarily between 
Stages III and IV, but there is no corresponding increase in the variability. 
Secondly, in respect of all characters except the number of spots there is a 
slight increase of variability in the final stage, an increase which is not, as a rule, 
associated with any increase in the growth-rate. This slightly increased variability 
never however becomes as large as the variability in the first stage and is usually 
a good deal smaller. The question is whether this general decrease of variability 
in the whole period is to be ascribed in whole or in part to the decrease in the 
growth-rate, for, since there was a certain mortality, it may be reasonably con- 
tended that this was selective and caused the diminished variability. 
The 5°/ D that, as stated, died in the first fortnight, need not be considered, 
but some attempt must be made to make an allowance for the 5% that died 
between Stages I and II. 
Biometrika vm 57 
