These data have been fitted with nomal pi'obability curves, according 

 to a graphical method devised by 0. E. Sette (unpublished manuscript). A 

 single normal curve fits the data for July-August and for September-October. 

 This group is assi;^ned to year class 1936. It obviously persists thi'ough 

 the season, retaining certain consistencies, namely, first, a mode v/hich 

 advances slightlj'', indicating slov; autumnal scale grov/th; second a standard 

 deviation v/hich remains constant. For November-December, and for January- 

 February, it V7as necessary to add a second, overlapping, c^irve on the left. 

 This group is assigned to year class 1937. As in the right-hand group, 

 this too -has the characteristics of a mode v;-hich advances, as is to be ex- 

 pected, from scale growth, and a constant standard deviation. 



To measure the degree to vrtiich the selection and placing of these hy- 

 pothetical curves fit the empirical data, comparison was made by the chi- 

 square method. A P value of .06^/ was obtained, (chi-square = 30. U; degrees 

 of freedom, 19), of borderline significance. 



Chief contribution to the chi-square comt^: from the sixth to ..jjith 

 classes. It appears, then, that the low P valu i first obtained was due 

 to minor irregularities of the data, rather than to selection and placing 

 of the hypothetical curves. If these be combined, the seventh class with 

 the sixth, the ninth with the eighth, P becomes .^6 chi-square 1$.^9; de- 

 grees of freedom 17). 



This, then, is an objective means of allocating proportions of new 

 to old rinf3;s v/here the marginal J.ncrements overlap. In the four-ring 

 series (Fig. 1) allocations were made as follows for^ November-December: 

 To the older agu, l/6 the specimens in size-class 7, 3A i" size-class 8, 

 3U/35 in size class 9. The remainder in these classes were assigned to 

 the younger age. In January -February, to the older age were allocated 

 9/26"^ of the specimens in size-class 8, 31/33 in size-class 9. The remainder 

 in these classes wore assigned to the younger age. 



The assignment of ages to individuals in these critical cases by the 

 method just described, precludes using those indi'/iduals for other studies 

 involving sizes, ages or growth, and the statistical cards vrere marked 

 accordingly. 



This method of solving the problem of distinguishing between^ new and 

 old rings has been incorporated into the routine of age analysis in pilchard 

 research. 



evidence bearing on the validity .of scales for 

 deTjiRI-HNING the age of adult Pilchards 



The forugoing section has dealt exclusively with the question of how 

 correctly one or more scale readers can assign a given age to a given fish, 

 or to the measurement of the "reader error". la the following discussion 

 the effect of this error plus that of the scale error (cf. page U ) will 

 bo examined. 



-^ I.e., the probability is .06 that a second series of empirical data 

 vrould differ as much or more from this theoretical series of curves, by 

 chance . 



107 



