assumptions and there is also agreement with 

 the rate based on assumptions A, B, and C. 

 Looking at the problem in this way, we can 

 come up with the interpretation that assump- 

 tions A, B, and C and assumptions H, I, J, 

 and K are analyses of the same phenomena 

 from different starting points and that both are 

 reasonable from their respective standpoints. 

 As for the reality of assumptions A, B, and C 

 and assumptions H, I, J, and K, 



(1) Assumptions H, I, J, and K in conn- 

 par is on with assumptions A, B, and C apply to 

 very particular cases, and in view of this fact 

 and in the absence of other concrete facts sup- 

 porting these assumptions, it may probably be 

 concluded that their reality is very slight. 



(2) As is clear from the considerations 

 brought forth under (a) and (b), with regard to 

 the establishnnent of the relationships (ajAj 



»-A'b' — *~ B2) and (a2A2 ^A"b" — »-B3) 



for assumptions A and C, the reasonableness 

 of these assunnptions was positively promoted 

 by the intervention of A'b' and A"b". And it 

 may be said that this fact shows a greater 

 validity in assumptions A, B, and C, where the 

 schools which appear respectively in even- 

 nunnbered and odd-numbered years are con- 

 sidered directly, than in assumptions H, I, J, 

 and K, where these schools are considered 

 indirectly. 



In conclusion, if lor hypothesis (3) we 

 postulate cyclical migratory phenomena with a 

 2-year period, it is possible that this can be 

 the dominant factor in the fluctuations of the 

 modes from year to year. However, if we 

 consider the fact that assumptions A, B, and 

 C, which are of a more general nature, also 

 apply to the same identical phenomena, it i » 

 thought that it may be decided that in the pres- 

 ent stage of studies this hypothesis has very 

 little reality. 



From the foregoing considerations, it has 

 been shown that the applicability of hypothesis 

 (1) is strengthened by assumptions A, B, and 

 C, that hypothesis (2) can be judged to be at 

 least not a controlling factor, and that there is 

 room for the application of hypothesis (3) 

 through postulating the existence of an 

 alternate-year cycle in the migratory 

 phenomena. No determination can be made 

 under present conditions as to the problenn of 

 whether the elements which essentially control 

 the phenomena are produced in accordance 

 with hypothesis (1) or (2), or whether they 

 arise f r o nn entirely different factors, or 

 whether they are the effect produced by a 



complex intermingling of a number of factors, 

 but in any case they must be said to be 

 extremely interesting phenomena, 



III. A Consideration of the Mechanism of the 

 Alternate -year Cycle 



We shall here attempt a consideration of 

 the mechanism of the alternate -year cycle based 

 on assumptions A, B, and C, which are thought 

 to have the strongest reality. If we try to point 

 out the most outstanding points of difference 

 between the even-nunnbered years and the odd- 

 numbered years as shown in the phenomena, in 

 figure 3, (1) we can detect a tendency for the 

 length group corresponding to a to be numerous 

 in even-numbered years and scarce in odd- 

 numbered years. However, its abundance in 

 the even-numbered year 1952 differed hardly at 

 all from that of odd-numbered years; (2) the 

 length group corresponding to A appears as a 

 conspicuously predominant mode in odd - 

 numbered years but presents no such predomi- 

 nant mode in even-numbered years. A tendency 

 can be seen for the position of this mode to be 

 displaced to the left in even-numbered years 

 and to the right in odd-numbered years; (3) the 

 length group corresponding to B appears as a 

 conspicuously predominant mode in even- 

 numbered years, but in odd-numbered years it 

 appears as an inconspicuous mode sonnewhat to 

 the left in a position corresponding to b; (4) the 

 length group corresponding to C appears as a 

 mode only in odd-numbered years and in even- 

 numbered years does not form any particular 

 mode; (5) the length group corresponding to D 

 appears as a very small mode only in even- 

 numbered years and no nnode appears for this 

 group in odd-numbered years. In all cases the 

 length groups larger than that corresponding to 

 D show very unclear differences between odd 

 and even years. 



According to assumptions A, B, and C the 

 length groups a. A, B, C, and D mentioned 

 under (1) to (5) are assumed to be 1 year apart, 

 so hereafter they will be handled as year 

 classes a. A, B, C, and D. As is clear from 

 (1) to (5), the factor contributing to themecha- 

 nisnn of the alternate-year cycle is principally 

 the relative abundance as between years seen 

 as separate ages, and at the sanne time it 

 can probably be judged that this tendency is to 

 be detected also in the displacement of the 

 modes seen as separate ages. 



(a) Concerning relative abundance: 



The age groups that appear conspicuously 

 in even-numbered years correspond to a, B, 



32 



