170 
PACIFIC SCIENCE, Vol. VII, April, 1953 
(3) Can the regression of body length on 
scale length be expressed by a straight 
line when fish of successive ages are 
considered? 
(4) If the regression is linear, does it have 
its origin at 0.0? (If so, the actual pro- 
cess of calculating lengths at previous 
ages may be greatly simplified.) 
Answers to these four questions are neces- 
sary in order to decide if, for back-calculation 
of lengths, a given body of data should be 
treated as a unit or grouped by year-classes, 
by regions in which the fish were captured, 
by age groups, or by groups combining two 
or three of these categories. 
Acknowledgments 
I wish to thank Mr. John C. Marr, Dr. 
Frances E. Felin, and Mr. Theodore M. Wid- 
rig of the U. S. Fish and Wildlife Service for 
making the material used in this study avail- 
able to me and for other assistance. 
SOURCE OF DATA 
Material with which to investigate these 
questions consists of records of scale readings 
for the Pacific sardine on file at the laboratory 
of the South Pacific Fishery Investigations, 
U. S. Fish and Wildlife Service, at Stanford 
University. The material was obtained as a 
result of a co-operative program between the 
U. S. Fish and Wildlife Service, the California 
Department of Fish and Game, the Fisheries 
Research Board of Canada, the Washington 
State Department of Fisheries, and the Fish 
Commission of Oregon. The methods of col- 
lecting samples, examining scales, and record- 
ing data are explained by Felin and Phillips 
(1948). In brief, each fish is represented by a 
card which contains information on fish 
length, sex, date and locality of capture, and, 
on a printed scale, the relative position, of the 
focus, annuli, and margin of the fish scale. 
The data are, in general, representative of the 
populations commercially fished along the 
Pacific Coast of the United States and Canada 
(with the exception of bait fisheries in south- 
ern California). 
From the material available (about 60,000 
cards), the data for the 1938 through 1942 
classes for fish caught off Canada, Washing- 
ton and Oregon, San Francisco, Monterey, 
and San Pedro during the fishing seasons of 
1939-40 through 1947-48 were selected in 
order to have (1) a series of year-classes repre- 
sented, (2) all the commercial ports repre- 
sented (3) for each year-class, fish with one to 
five annuli represented. 
METHODS 
To reduce this material (about 40,000 cards) 
to workable proportions and still have a repre- 
sentation of the fish taken by the commercial 
fishery, a sample was taken in the following 
manner: 
(1) All the cards belonging to the material 
selected were considered as a single 
"population” without regard to year- 
class, port of landing, age, or season 
of the year in which the fish were 
caught. 
(2) One thousand one hundred and ninety- 
nine bibliographic cards (about 3 per 
cent of the above population) were 
marked with numbers taken from a ran- 
dom nurhbers table (Table 1 in Dixon 
and Massey, 1949) using five-digit num- 
bers. The cards were arranged in as- 
cending order. Three percent was cho- 
sen because, after some trials, it was 
seen to be the minimum number of 
cards likely to include every category 
in the sample. 
(3) The scale reading cards were counted, 
and, when the count coincided with the 
number on the first bibliographic card, 
the latter was removed, and the corres- 
ponding scale card was taken as part 
of the sample. This process was re- 
peated, without interrupting the orig- 
inal count, until all the bibliographic 
cards were removed. 
(4) The sample so obtained was then sub: 
divided into all possible year-class and 
port combinations. By chance, the 
