272 BULLETIN OF THE BUREAU OF FISHERIES 



detoi-mined readily by a comparative studj' of the finer structures of tliese scales. 

 This is the only example of a disagreement in the number of annuli of easily read scales 

 of the same fish I have found in my material. 



These irregularities in the structure of scales do not invalidate necessarily the 

 scale method but emphasize the necessity of examining several scales from each 

 individual. 



SCALE METHOD AND ITS APPLICATION 



By a study of the scales we may determine the age of a fish in years, the approxi- 

 mate length attained by it at the end of each year of its life, and its rate of growth for 

 each year of life. The age in years is found by counting the annuli. The length at 

 the end of each year of life is computed from a series of measurements of a scale of a 

 fish of known length. Given the total length of a scale, the length included in its 

 annulus of year X, and the length of the fish from which the scale is taken, the length 

 attained by the fish at the end of year X is determined by the use of the following 

 formula, in which the third term is the unknown: 



Length of scale included in annulus of year X _ Length of fish at end of year X 

 Total length of scale Length of fish at time of capture 



Repeating this formula for the annulus of each year, the length attained by the fish 

 at the end of each successive year of life is computed. From these lengths the rate of 

 growth for each year is obtained by a simple subtraction. The assumptions upon 

 which this formula rests are discussed in later sections. 



METHODS OF MEASUREMENTS AND COUNTS 



BODY MEASUREMENTS 



Many of the fish used by me were preserved in formalin, transferred to 70 pen- 

 cent alcohol, and brought to the laboratory before they were measured or scales 

 removed from them. Others were measured in the field while fresh and discarded 

 after removal of scales for study. The method employed in measuring fish in the field 

 previous to 1924 consisted in laying a steel tape along the curvature of the body and 

 reading, to the nearest millimeter, the distance from the tip of the snout to the caudal 

 margin of the last perforate scale of the lateral line.^ In making measurements in the 

 laboratory it seemed best to get the length, not along the curvature of the body but, 

 in the usual way, parallel to the long axis of the body, and between verticals from that 

 axis through the tip of the snout and the posterior margin of the last perforate scale. 

 The fish was straightened, if need be, laid on its right side in a wooden tray, with its 

 snout lightly touching a pin driven into the tray. The measurement was made v/ith 

 the steel tape in a straight line between this pin and another stuck into the tray just 

 behind the last perforate lateral-line scale. The field measurements obtained before 

 1924 thus exceeded those made in the laboratory, for two reasons: They were made 

 along the curvature of the body instead of in a direct line and they were made on 

 fresh fish not shrunk by preservatives. To obtain the true length of the fresh fish 

 along its axis it is necessary to correct the field measurements, which are too high 



3 In 1924 and thereafter length measurements were made in the field, not along the curvature of the body, but in a direct 

 line—the steel tape was held parallel with the long axis of the body. No corrections were made for lhe.se fish. 



