50 



NATURE 



[September 9, 1920 



therefore the discontinuity serves to mark out the 

 winter growth, because the discontinuity becomes 

 permanent, and leaves on the scales the blank 

 spaces or broken lines which are the characteristic 

 winter rings of certain species in addition to the 

 narrowing of the spaces between the lines. 



By counting the rings formed on the scale, the 

 age of any individual fish can be ascertained. 

 VVhen large numbers of any one species are exam- 

 ined they can be grouped into "age classes" or 

 "year groups " according to the number of rings. 

 The average size of each group can be determined, 

 and the difference between these sizes gives the 

 first approximation to the amount of annual 

 growth. 



This general theory has been confirmed for 

 several species, first by an examination of the 

 growing edge of tlie scale throughout the season, 

 when the rings have been seen in the course of 

 development, and secondly by marking experi- 

 ments on the fish (salmon, plaice, cod, etc.), when 

 additional rings corresponding in number to the 

 winters elapsed in the interval between marking 

 and recapture have in every case been seen to be 

 formed on the scales. 



Fig. 2. — Proportional growth of a fish and its scale. 



In practice there are, however, certain modifica- 

 tions and exceptions to the general theory which 

 must be looked for and taken into account. What 

 are known as "false rings" may occur. These 

 bear a resemblance to winter rings, and are prob- 

 ably caused by sudden changes in environment, 

 such as a change of temperature, lack or abund- 

 ance of food, or even by the fish migrating from 

 one part of the sea to another. These rings can 

 generally be distinguished from true rings in the 

 scales of fishes the habits of which are known. 

 For instance, in salmon there is frequently a 

 grouping of close lines in the middle of the third 

 summer, known as a "summer check." 



In very old fish the rings are close together 

 near the edge, and it is difficult to make out their 

 number with exactitude. It may sometimes 

 happen that the latest rings become fused to- 

 gether, and the total number then appears less 

 than those shown on the bony and opercular struc- 

 tures of the same fish. 



Results of age determinations of many samples 

 of fish have been studied from the mathematical 

 probability point of view to ascertain whether such 



NO. 2654, VOL. 106] 



groups have a probable or natural variation of 

 size, and whether groups of fish of the same ascer- 

 tained number of rings taken under similar con- 

 ditions are suflficiently alike in size grouping to 

 give a high probability af being of the same age. 

 These mathematical tests have confirmed tne 

 theory that on the average the age determinations 

 of certain species of fish (salmon and herring) are 

 correct up to five or six years of life — that is, 

 those years when they are of most economic 

 importance. 



These methods of age determination enabled 

 observers to deduce the approximate growth rates 

 of fish by comparing the sizes of fish of known 

 age. Growth curves so deduced generally rose 

 rapidly from zero for the first two or three years 

 of life, and then the rate of increase fell off rapidly 

 as the fish grew older. 



Later researches have demonstrated that this 

 falling off in the growth rate in such fish as herring 

 and plaice and others is not wholly due to a 

 normal slackening in the development, but is made 

 greater by the fact that in several species a segre- 

 gation according to size takes place, the larger 

 fish of the youngest groups leaving their asso- 

 ciates and joining shoals of older 

 fish, generally in deeper water. 

 Such a segregation has been 

 found to take place at the onset 

 of maturity in certain species. 

 Thus it follows that the youngest 

 year groups in the samples are 

 represented only by the larger 

 individuals of those groups, and 

 their average length >is higher 

 than those of the complete year 

 group. 



When such selection of size oc- 

 curs, the average sizes of succes- 

 sive age groups are not strictly 

 comparable with one another. 

 Norwegian investigators developed the 

 method of ascertaining the growth of in- 

 dividual fish by measuring the comparative 

 distances between the rings on the scales, 

 on the assumption that the scale grows in length 

 in proportion to the length of the fish. Fig. 2 

 shows a fish of length L with an enlarged image 

 of its scale. The scale is measured from its centre 

 along the main axis, and also to the edge of the 

 winter rings, giving the values V (length of scale), 

 •z^i, •^2, etc. (lengths from centre to end of first, 

 second winter rings, etc.). If exact proportional 

 growth is assumed between the fish and its scale, 

 it is evident from the parallel lines in the diagram 

 that Zj : Wi : : L : V, and the lengths at previous 

 winters (Ij, \, etc.) are found from the simple 

 formulae 



'i — Y • ^> '2 



V 



L, etc. 



Such a method enables the data as to growth to 

 be multiplied to a very great extent, and should 

 therefore be most valuable in detecting good and 

 bad years of growth, which can be associated with 



