a species, means the latitude of the Equator, and 4,200 means lat. 70° N. 

 in minutes ; therefore, the latitudinal value of a locality shows how 

 much the faunal distribution inclines towards the north or south from 

 the central locality at lat. 35° N. It has been observed that there 

 exist some correlations of the coefficient of closeness or of the latitudinal 

 value with the latitude. Here in this paper a formulation has been 

 attempted in these correlations and an appropriate expression has been 

 given to the mixed geographical distribution of the northern and 

 southern fauna from the relation between the two indices. 



When the coefficient of closeness in the marine Mollusca calculated 

 by Otuka (1936) are plotted against the latitudes, each locality being 

 a centre, in regard to the localities of the Pacific coast, there exists the 

 following relation, 



log y = a X -\- b (1) 



where 3' is the coefficient of closeness, x the latitude, and a and b constants. 

 Putting Xq to the latitude of the central locality, in which the coefficient 

 of closeness necessarily becomes 1 and b = —axo, accordingly from 

 the aboye equation (1) 



log V = a {x — Xq) 

 where {x — Xq) means a latitudinal difference between the central locality 

 and a locahty comparable with it, and a means the decreasing rate of 

 log y with the latitudinal difference. Practically in the Pacific coast the 

 values of a deviates from ±0-0602 to ±0-3098. Among the groups 

 of localities having a respective centre, the uniformity of the mean values 

 of a given by a ^I!{^{log y)/{x — .ro)}/N, has been tested by the 

 statistical method for small number of observations (1), with the result 

 that no significant difference has been recognized. In the Japanese 

 -coast, as it may be considered that the shore-lines are nearty linear 

 along a north-south projection, and that the environments change 

 monotonously with the latitude from north to south, it can be supposed 

 that the values of a are nearly equal if an}^ locality is the centre. Thus, 

 in the above relation (2) a = ^ 0-134 is obtained, taking the mean of 

 the total values, where the sign (-f-) is taken in the case southwards from 

 the central locality and (— ) northwards. 



. When Xq = 35° N. — that is, when Enosima or Misaki and their 

 vicinities are taken as the central locality, the theoretical values of 

 coefficient of closeness drawn at intervals of 0-1 on a map are shown 

 in Fig. 1, from which it can be perceived that the MoUuscan fauna in 

 Enosima or Misaki and their vicinities decreases their common species 

 with the distance from these localities to the north or to the south, and 

 the ratio of faunal mixture with these localities can be read from the 

 expression of coefficient of closeness in this map. 



The latitudinal value contains a similar conception to the coefficient 

 of closeness, and the fiat fishes and MoUusca are the groups bearing a 

 similar ecological type as a kind of bottom fauna, and therefore a parallel 

 relation is expected between the two indices. Then, the distribution of 

 points as shown in Fig. 2 are obtained when the latitudinal values of the 

 flat fishes in every locality calculated by Kuronuma are plotted against 



(1) In this paper the statistical methods have been followed by Masuyama, 

 MoTOSABUR0^1943 : Syosurei no Matomekata to Zikkenkeikaku no Tatekata 

 (Statistical Methods for Small Observations and Design of Experiments), Tokyo, 

 .and Tokeikagaku-kenkyukai (Society of Statistical Science Research) ; 1943 : 

 Tokeisutihyo I (Statistical Numerical Tables I), Tokyo. 



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