224 Part Il] —-Twenty-fourth Annual Report 
At the ‘ Doghole,” off Aberdeen, on 30th July, 26 measured from 
29-3cem. to 46cm. (114-183 inches) ; on 21st August, 12 ranged from 
36°4cm. to 48°7em. (144-193 inches) ; on 3rd September, 8 taken at the 
“ Doghole” were from 39°4cm. to 45cm. (154-17? inches) ; 5 on 31st 
October measured from 39°5cem. to 53°5em. (153-21; inches) ; 5 on 5th 
November were from 46°4cm. to 52cm. (183-204 inches) ; and on 28th 
and 29th November, 33 measured from 39'2cm. to 57-3cm. (15,4-223 
inches). On 12th December, 35 measured from 43°7em. to 61°6cem. 
(174-244 inches), the mean size being calculated at 49:°5cm., or 194 
inches, and the age at 32 or 33 months. 
Comparatively few were taken in the Moray Firth. On 12th November 
16 ranged from 44°8cm. to 6lem. (173-24 inches) ; on 19th December, 
15 were from 46cm. to 60cm. (18-233 inches); on 20th to 25th 
December, 40 measured from 40°3 to 59°8cm. (153-233 inches) ; on 17th 
January, off Dunbeath, 41 measured from 41‘9cm, to 62°5em. (164-243 
inches). 
In May, off the Shetlands, when they had begun their fourth year, 141 
measured from 41°8cm. to 61:6cm. (16-247 inches). The mean in this 
ease is about 50cm., and the arithmetical average 50°'9cm., or exactly 20 
inches. 
The average size of the cod on the east coast of Scotland when three 
years old may be placed at from between 19 and 20 inches, and the 
probable range of sizes from about 16 to about 24 inches. 
' The number of cod older than this in the collections was very small, 
and their distinction into groups problematical. In the haul on 12th 
November, in the Dornoch Firth, I have placed ten, measuring from 
66'4cm. to 76cm. (254-30 inches), as approaching their fourth year. 
And on 20-25th December, in Burghead Bay, six measured from 61:2cm. 
to 73:4cm. (24-28 inches), which are assumed to be about the same age. 
It is now desirable to compare the differences in the average length of 
the different groups, which represents the extent of the growth in a year 
from one annual series to the next. Considering first the means of the 
first and second series, as given in the Table, there are twelve cases in 
which this comparison can be made. The difference between the means 
varies in different collections from 14'5cm. to 19cm., and the average 
amounts to 16°57cm., or 64 inches. Some are better than others, and if 
we select the nine cases in which the number of fishes in either of the 
series does not fall below 20, we find that the variation is from 14°5cm. 
to 18:5cm., and the average of the lot is 16°2cm., or 62 inches. If the 
comparison is limited to the cases in which more than 70 fishes are 
represented in each series, and the numbers are fairly equal—and these 
cases are three in number—the differences are respectively 15cm., 15:5cm., 
and l5cm., the average being 15°2em., or almost exactly 6 inches. 
There is another method by which comparison of the differences between 
the groups can be made, viz., by comparing the differeuce between the sizes 
at which the maximum numbers of fishes occur—between the maximum 
ordinates, ‘‘modes,” or apex, of each curve. As might be expected from 
these collections, which contain only moderate numbers of fishes, the 
members of any given group are not duly represented throughout; in some 
instances the larger fishes predominate in numbers, in others the smaller, 
and soon; and thus in asingle collection of this kind comparison of the modes 
or maximum ordinates of two groups may be far from showing the true 
differences between these groups. Thus, in the fourteen cases in which 
such comparison can be made between the cod in their first year and those 
in their second year, the distance between the maximum ordinates varies 
from llem. to 22cm, or exactly double. The mean of these numbers, 
