CORPORA ALBICANTIA, CORPORA ABERRANTIA AND CORPORA ATRETICA 377 



0-206, and the ratio between the mean numbers of 'young' and 'medium' corpora albicantia is 

 therefore 1 : 2-085. We will assume that it is 1:2. 



'Young', 'medium' and 'old' corpora albicantia represent consecutive stages of regression and, if 

 the sampling is representative, the average duration of these stages should be proportional to the 

 frequency of each group, since they do not disappear. The 'medium' corpora albicantia are twice 

 as common in the samples as the ' young ' corpora. 



The antarctic pelagic whaling season for fin whales lasted 58 days or 0-16 years in 1956, and 69 days 

 or 0-19 years in 1957, 1958 and 1959. It is, therefore, reasonable to suppose, for present purposes, that 

 sampling is instantaneous and at yearly intervals. The majority of corpora albicantia are formed 

 several months before the sampling period and very few actually during the sampling period (see 

 below, pp. 450-53). If the average duration of the 'young' stage extends over x sampling periods, 

 then the 'medium' stage, because it is twice as frequent, persists over 2X sampling periods. If 

 sampling were not restricted to a short annual period then the actual ratio of ' young ' to ' medium ' 

 corpora in the samples might be very different from 1 : 2, and the actual duration of ' young ' corpora 

 (in terms of months, rather than sampling intervals) may be much less than half the duration of the 

 ' medium ' stage. 



An example will make this point clearer. Suppose the average month of formation of corpora 

 albicantia is August. Then the average sampling date (in February) is some 6 months later and for 

 'young' corpora albicantia to be fully represented in the samples they must, on average, persist in 

 this stage for over 6 months. In the simplest case, in order to fit the data a corpus albicans formed 

 in August must be present as a ' young ' corpus albicans only in the first sampling period, and as a 

 ' medium ' corpus albicans in the two succeeding annual sampling periods. Whereas, on average, the 

 'young' stage need last at a minimum for just over 6 months (less than 18 months at a maximum) in 

 order to be represented in only one sampling period, ' medium ' corpora can last as long as 35 months 

 (but not less than just over 12 months) in order to be represented in two sampling periods. 



It is, however, known that 'young' corpora albicantia do not disappear during pregnancy and 

 because ovulations do not occur during pregnancy the average duration of this stage of regression must 

 be at least 10 or 11 months, though the rate of regression may be more rapid during lactation 

 (see p. 434). 



In estimating the average annual increment of corpora it is not, therefore, the absolute duration of 

 each stage, but the relative duration in terms of the number of sampling periods that occur during 

 each stage which is important. 



Because the relation between the average numbers of ' young ' and ' medium ' corpora approximates 

 to a simple ratio, in the equation below t must approximate to a whole number. 



Let n= observed average number of 'young' corpora albicantia; 

 t = duration of this regression stage in sampling intervals ; 

 a = annual increment (to be ascertained). 



Then a = njt, and the shorter the duration the larger must be the annual increment (or vice versa) 

 to provide the observed value of n. 



The parameter n is known ; t must be sought by trial and testing with other evidence but is assumed 

 to be a whole number (not a fractional value), for the reasons given above. 



If t = 1 then a = 1-544 ±0-104; 

 t = 2 then a = 0-772 ±0-052; 

 t = 3 then a = o-5i5±o-035; 

 t = 4 then a = o-386±o-026. 



Values of t higher than 2 are excluded by virtue of the sexual cycle of the mature female and the 



