GROWTH AND MATUEITY OF SALMON IN THE OCEAN 
49 
observed changes in size during the season would be less than the actual growth 
occurring within a single race. It might even occur that fish of the same age group 
taken late in the season would be actually smaller than others taken earlier in the 
season, although they had had several additional months of life in the ocean dur- 
ing which time they were feeding and growing rapidly. The reverse condition 
might also be found, in which smaller races were running early in the season and 
larger ones later. The effect of this would be to augment the true effect of growth. 
In the case of fish taken outside, however, it seems probable that the observed 
changes in length quite truly represent the effect of growth, since fish of the same 
race presmnably remain within the fishing area over the entire fishing season. 
That this in general is true is indicated by the fact, demonstrated above, that there 
is comparatively little change in the composition of the outside schools as regards 
age groups, and particularly the main types of nuclear growth, while at the same 
time very conspicuous changes are taking place in the composition of the runs 
in the river. The details of the growth process are necessarily lost unless they 
can be worked out for single races. A mixture of several races, such as we have 
in the collections available, will show only certain of the general features of growth 
that are common to at least the majority of the races represented in the collections. 
The restdts of the study of such mixed material give a composite picture, which 
may not exactly represent the true condition in any one of the races represented. 
Fraser (1920) has made an intensive study of the growth of all five species of salmon 
as found in the Straits of Georgia, where, as in the present study, it was impossible 
to segregate accmately the various races. The results of his study are interesting 
as showing the general trend of the growth, but it would seem that such material 
can not be relied upon to show the finer details of the growth process. 
In order to reduce to the simplest terms the observed changes in length, the 
trend of these changes during the fishing season, from the 1st of May to the end of 
September, have been calculated. The data on fish taken in the ocean have been 
kept separate from those relating to fish taken in the river, and separate trends have 
been calculated. An examination of the data showed that the rate of change in 
length was, in most age groups (and by inference in others), practically constant 
during the season, and it was therefore assumed that the trend would be best shown 
as a straight line. The trends were therefore calculated on the basis of the formula 
y = a + l)x, in which y is the observed length (the average of all individuals of a single 
age group found in any one collection) , x is the day of the fishing season on which 
the collection was made (beginning with the opening of the fishing season on May 
1), and a and & are constants, a represents the most probable average length 
of the age group in question on the 1st day of May, and h the most probable daily 
increment in length. The calculations were made by the method of least squares,^ 
and the "observation equations" were weighted according to the nimaber of indi- 
viduals found in each age group in the various collections. This method of direct 
weighting is recommended in some of the texts on the method of least squares. 
The mathematical work of calculating these trends was accomplished in most 
cases by the use of logarithms, and the results were checked by means of a 20-inch 
' See any of the numerous texts on the method of least squares. 
