The book A Mathematical Theory of Random Migration was written by author Karl Pearson Here you can read free online of A Mathematical Theory of Random Migration book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is A Mathematical Theory of Random Migration a good or bad book?
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On one side of a straight line there is supposed to be a uniform distribution of habitats ; on the other at starting no habitats. To investigate the distribution in the unoccupied area after one migration. Each individual is supposed to take n-fights to the new habitat. Let YYhe the straight line and a point at distance c from it on the unoccupied side of it. Let N be the average density per unit of area on the occupied side. Then after an n-flight migration, the contribution from P (co-ordinat...es r, ^) at will be Nrhyhr n (r 2 ), and integrating this all round a circle of radius r from A to C within the occupied area, we have for the quantity F n (c) at f 00 /"cos -1 c/r F n (c) = 2NJ e j o n {r*)rd x dr = 2 JV I cos -1 c/r n (r 2 ) r dr. @ = -2NJ y n jp^ - = -2NJy n (c* + tf)dy (xliv). Hence dF„ dc The evaluation of this integral needs a further consideration of the w-functions. By (xiv) -- - ^-er i ${j**} where e= ~ 2 ^- . 4 26 KAEL PEAESON Transfer the differentiations from /3 to o- 2 and we have : = (- 1 ^)^ ^ or, all the w-functions can be found by differentiating the first w-function with regard to the standard-deviation squared.
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