By Alfred J. Lotka
In the 50 years that experience handed on the grounds that Alfred Latka's dying in 1949 his place because the father of mathematical demography has been safe. together with his first demographic papers in 1907 and 1911 (the latter co authored with F. R. Sharpe) he laid the principles for good inhabitants concept, and over the subsequent many years either principally accomplished it and located handy mathematical approximations that gave it useful applica tions. given that his time, the sector has moved in numerous instructions he didn't foresee, yet mostly it's nonetheless his. regardless of Latka's stature, besides the fact that, the reader nonetheless must hunt throughout the previous journals to find his valuable works. As but no exten sive collections of his papers are in print, and for his half he by no means as sembled his contributions right into a unmarried quantity in English. He did so in French, within the half Theorie Analytique des institutions Biologiques (1934, 1939). Drawing on his components of actual Biology (1925) and such a lot of his mathematical papers, Latka provided French readers insights into his organic idea and a concise and mathematically available precis of what he known as fresh contributions in demographic analy sis. we'd be exact in additionally calling it Latka's contributions in demographic analysis.
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We disguise our ignorance with words. We extinguish our curiosity without satisfying it. Nerve energy, vital force, and all similar terms, are names which introduce error into research on the subjects to which they attach themselves. It is not in this way that science advances. t Is it not strange that a truth easily seized by the whimsical spirit of a Moliere would have escaped the more serious thoughts of certain philosophers? RECAPITULATION Before considering more definitively the specific problems which will occupy us in subsequent chapters, it will be useful to briefly recapitulate the general principles we have noted thus far.
In place of a game of cards we will make use of a quantity of black and white balls. Fifty black balls are found in urn A, and fifty white balls in urn B. We draw at random one ball from urn A and another from urn B, and we return to urn B the ball coming from urn A, and vice versa. We mix the contents of both urns well, and repeat the operation of taking one ball at random from each urn and returning it to the opposite urn. After each draft we note the contents of the two urns. The diagram in Figure 1 represents the number of black balls in urn A after successive drafts.
The fact is that they were introduced in the course of one hundred drafts resembling the series already described, this latter simply forming the continuation of an earlier series. Only before commencing the first series, the balls were all numbered, from 1 to 100, and throughout both series a protocol was followed to record the numbers of the balls contained in the two urns. 10 10 10 :10 100 ORDER OF DRAWING Figure 1. Curve representing the number of black balls in urn A after n drawings, beginning from a time zero taken as the hundredth draft.
Analytical Theory of Biological Populations by Alfred J. Lotka