IV.—Note on the Number of Plaice at each Length, in certain Samples from the Southern Part of the North Sea, 1906. By T. EDSER.

IT

It appears that, within certain limits, the number of plaice at any length is directly related to that length by a formula of the type, log y = A + bx where y is the number and x is the length, that is to say, the number of fish of length n + 1 centimetres, say, is in a constant ratio to the number of length n centimetres, within these limits.

The relation is illustrated by the diagram given below, based upon figures for the year 1906. The data for the first nine months

of this year, are published on pages 87 to 90 of the Report on the Research work of the Board of Agriculture and Fisheries in relation to the Plaice Fisheries of the North Sea, 1905-06 [Cd-4227]; but for the last three months, I have been permitted to use figures which have not yet been published. For this illustration I selected the samples of plaice designated as "Lowestoft, trade category (4)

others," because these give, as nearly as possible, true samples of the plaice above a certain size in that part of the sea where the trawling took place.1

Practically all these samples were taken from that part of the North Sea south of 54°, and in water of from 20 to 60 metres in depth; but very little was obtained from the inshore grounds of less than 20 metres. Here the very small fish abound, and as these are largely able, by reason of their small size, to escape through the trawl meshes, their exclusion, as will be seen later, does not materially affect this question. Unfortunately, it has been impossible to include samples from the deeper northern portion of the North Sea, because the plaice caught there were sorted, from the trawl, into three categories-"large," "medium," and "small"-of which the limits are ill-defined, so that a considerable number of fish of certain lengths were nearly as frequently included in one category as in the next. Up to the present I have not been able to rearrange these into complete samples of plaice trawled. It was, therefore, impossible to include in this diagram samples comprising the whole life cycle of the plaice, but more recent investigations may supply figures which will be applicable for this purpose.

Table showing at each length, the number of plaice measured, together with the logarithm of the number.

The diagram is drawn from the figures given in the table; the abscissæ showing the length of the fish in centimetres, and the ordinates the logarithms of the numbers at each length; the number published at each length includes the fish measuring that centimetre and less than the next in length.

From the point where the curve begins to about the maximum two disturbing factors affect its form. They are

1. The trawl retains practically none of the plaice under 17 centimetres, and an increasing proportion of those measuring from 17 to 25 centimetres.

2. An artificial selection takes place after the fish is on board, some of the smaller sizes being thrown back into the sea; the extent of this selection depends largely upon the probable state of the market.

It will therefore be seen that deductions drawn from the frequencies of the smaller sizes would be of little interest, as they would be influenced by artificial, and, to some extent, arbitrary, sortings. From just beyond the maximum, i.e., from, say, 25 to 68 centimetres, within which range the measurements of nearly 170,000 plaice are recorded, it will be seen that the points lie fairly evenly about a straight line (the line in the diagram has been fitted by inspection). The most strongly marked divergence occurs from 34 centimetres to 40 centimetres, and Dr. A. T. Masterman points out that, as far as present data indicate, the rate of growth of male plaice shows a rapid decline at about 40 centimetres and that at about this length, the number of males in proportion to the females also diminishes rapidly. These reasons may explain this divergence from the straight line, and it is possible that, instead of one line, a better fitting will be obtained by two almost parallel straight lines, one for each sex. This point will, however, be better approached when figures for the sexes separately are forthcoming. From 48 centimetres on to the end, the points lie somewhat raggedly; but it is probable that errors of observation account for this, because here the numbers of plaice measured are, as will be seen from the table, considerably smaller, ranging from 145 at 48 centimetres to I at 68 centimetres. This diagram is one of a series of 27 which I have prepared on the 1906 measurements, and all of them bear out the conclusion drawn above, that the points lie about a straight line, neglecting those to the left of the maximum; and it is upon this experience that the law stated above is founded. An approximate evaluation of the law in this particular series of fish will be found to be 9 log y = 67 - x; that is to say, the number of fish of length n + 1 centimetres is approximately 77 per cent. of the number of length n centimetres for all values of n greater than 25.

This is the equation for the 170,000 plaice of 25 centimetres or more in length. If the number is larger or smaller it is clear that the frequencies will be represented by a straight line occupying a position to the right or left respectively, and parallel to, that shown in the diagram, the generalised equation being log y = k − x/9, where k is a constant to be determined so as to

give the correct total number of fish, P, exceeding 25 centimetres in length. The relation between P and k is readily found by summing to infinity the successive values of y corresponding to 25, 26, 27 centimetres. This gives k = 2'13131 + log P, whence 213131 + log P – x/9.

log y

=

V.-A Note on certain Tables in Part II of the Supplement to the Sixty-fifth Annual Report of the Registrar-General. By REGINALD DUDFIELD, M.A., M.B.

ON p. xx of part II of the last Supplement Dr. Tatham observes: "Of the total male population above the age of 15 years at the last census more than 94 per cent. (including students) were returned as following some occupation meaning thereby that he ranked them as "occupied." occupied." In the census tables of occupations, "students" are included in Order XXIII ("Retired or Unoccupied"). A comparison of the totals of "years of life" given on pp. 3 and 8 of the Report with the numbers enumerated (Census Report: Summary Tables, pp. 186 et seq.) as "occupied" and as "retired or unoccupied" shows that for the purposes of the Supplemental Report 48,087 males aged 15 years and upwards have been transferred from the "unoccupied" class (Order XXIII) to the "occupied." The numbers of the "retired" obtained from the Supplement, viz., 287,742 agrees with sum of the "retired from business" (262,175) and "pensioners" (25,567) of the census table, and it is presumed that the 48,087 males have been transferred from the student group ("others aged 15 years and upwards, including student) which numbered 290,395 at the census.

The differences in the numbers of "occupied" at each age, as given by the census and as deduced from the Supplemental Report, are set out below: