516 president's address. — section gi. 



nature of the case.t In other words, the numerical solution of a 

 formula, which, starting with a given number of people, and assum- 

 ing any simple law for births and deaths, gives values which are non- 

 unifomi in their progression with time. That appreciable oscillations 

 actually exist is shown in the birth and death rates of all countries, 

 and I have found that these follow sensibly the normal law of fre- 

 quency. 



This oscillation must have been repeated on a larger scale in 

 secular history. For example, if we suppose the rate of population 

 increase for the decade 1881-1901 for several countries to apply con- 

 tinuously we find that, starting even with a single couple, only a 

 relatively small number of years are necessary to attain to the woi'ld's 

 total existing population. Hence, the characteristic rates of increase 

 CI last century ma}' be merely a phase-value in a secular cycle of 

 changes. 



It is evident that for a complete theoiy of population we shall 

 need to know what are the amplitudes of the oscillations of all periods, 

 mensual, annual, and secidar. Tlie science of statistics is too recent 

 for a sufficient accumulation of data, but enough has been obtained 

 t ) draft the first outline of an adequate theory. 



I-. Regression towards Average Values. — Quetelet, a man of 

 versatile attainments and able as a mathematician, was practically 

 the first to apply rigorous methods to the study of man and his 

 faculties. More recently ]\Ir. Francis Galton, in his " Hereditary 

 Genius'' (1869) and his "Natural Inheritance*' (1887) made a begin- 

 ning in the statistical treatment of the phenomena of variation, a 

 field in which so much brilliant work has been done by Professor Karl 

 Pearson, and some of his co-v:orkers in the Philosophical Transactions 

 of the Eoyal Society and in '"' Biometrika." This latter journal and the 

 " Archiv fiir Rassen unci Gesellschafts-Biologie " of Berlin, are devoted 

 to the publication of investigations of the type under consideration. 



Some of the well-ascertained results are as important as they 

 are striking. For example, if one take any variable character, its 

 " average value in offspring" can be related to its value in a parenii 

 by a simple linear equation. J This, equation really expresses what 

 has been called filial regression. In general terms, this may be 

 described as the tendency obsen^ed by Mr. Francis Galton for off- 

 spring to approximate to the mean or average of the stock- — that is, 

 towards ?nediocrity. For example, the average height of sons of 

 fathers below average height will approximate more closely to such 

 average; or, again, the average for the intelligence of sons of excep- 

 tionally talented fathers will more closely approximate to the general 

 average. Galton examined data relating to stature, eye colour, 

 temper, artistic faculty, and some fonns of disease. He supplemented 

 his observations on human beings by others on sweet-peas and moths, 

 obtaining confirmatory evidence. One may describe the law by saying 

 that any peculiarity in an individual is shared by his kinsfolk, but in 



t I shall show in another place that the oscillations or deviations fo'low the 

 ordinary law of frcciuency. 



X For example, if //„ be its average value in the nffspring-, and r the vnlue in a 

 parent //„ = a + fSx 



hence, if x' has the value a (1-^); yi„ will equal x'; that is, in that case alone the 

 average for the offspring will equal the value for the parent. 



