SEA-FISHERIES LABORATORY. 207 
3. Appendix on Statistical Methods. 
The following mathematical methods are well-known 
ones, but it interesting to consider their application to 
the data of fishery statistics. 
(1) Frequency Curves. 
Almost any one of the series of measurements of the 
lengths of the plaice composing a catch may be graduated 
in such a way as to give (apart altogether from the bias 
of the worker) a very regular series of figures, or a very 
smooth curve. Prof. Pearson’s now well-known proba- 
bility curve may be employed for this purpose and the 
method involves finding various moments of inertia, 
about the mean of the series, for each unit of length in 
the series. Constants obtained from these values can 
then be employed to determine the particular type of 
probability curve best fitting the rough data, and the 
constants to be used in the equation found are also so 
obtained. We shall see that not every series of length- 
frequency measurements can be so manipulated—at least 

with success—but many can. I give examples of three 
such theoretical frequency-distributions, and also charts 
which represent graphically the original data and the 
smoothed figures.* 
Three types of frequency curve have been found—- 
possibly there may be others. 
Types I, that is 
Teo Gl al (1-2) 
where Ma 
a, aA, 
The curve is asymmetrical about the mode, and it is 
limited in either direction. It rises steeply from the 
beginning (a,) and then falls more slowly towards the 
*It is proper that one should acknowledge with gratitude the very clear 
and practical summary of Pearson’s method given by W. Palin Elderton. 
—‘* Frequency Curves and Correlation.” OC. & EK. Layton, London, 1906. 
