of the Fishery Hoard for Scotland. 193 



from 12mm. to 40mm. were secured. The differences between the two 

 series on 28th December and on 1st April are these : — 





Smallest. 



Largest. 



Arithmetic 

 Average. 



Geometric 

 Mean. 





Mm. 



Mm. 



Mm. 



Mm. 



28th December, - 



97 



104 



105-5 



100-5 



1st April, - 



84 



108 



94-5 



96-0 



If the mean of the average sizes be taken for the two hauls, the 

 difference between the first series and the second series is, for the 

 arithmetic average, 100 0mm., and for the geometric, 98'3mm — and thi? 

 might be taken as approximately representing the increase in growth in 

 length in the witch at this stage in one year, i.e., about 3g inches. It 

 will be seen, however, as is the general rule, that the average difference 

 in length is greater at the earlier date than at the later ; in other words, 

 that the younger fishes increase in length more rapidly than those one 

 year older. The annual increment is therefore better represented on 1st 

 April than on 28th December ; and since 1st April is two or three 

 months anterior to the height of the hatching season, and the more 

 rapid growth in length of the smaller fishes continues, the true difference 

 in length between witches which are one year old and those which are 

 two years old is probably under 90mm. (3| inches). The average length 

 of a one-year-old witch appears to be about 3| inches, and that of a two- 

 year-old somewhat under 7 inches. 



The above Tables also furnish information as to the growth of the first 

 and the second series between the dates of the collections. Thus, in the 

 ninety-five days between 28th December and 1st April the increments of 

 the first series of witches was as follows : — 



Smallest. 



Largest. 



Arithmetic 

 Average. 



Geometric 

 Mean. 



Mm. 

 20 



Mm. 

 21 



Mm. 

 26-9 



Mm. 

 19-5 



In the period mentioned, therefore, the young witches grew a little 

 over 20mm. longer— about § of an inch. The second series of older 

 fishes grew less rapidly. Comparison of the sizes at the various dates 

 shows the following increases : — 



[Table. 



