OCR Rendition - approximate

298 Mr. Francis Gallon [Feb. 9, ppercentage of possible production, though it is usual to look on it as a simple multiple, without first multiplying and then dividing by the 100. Looking upon it as a simple multiple, the front face of each compartment in the upper heap represents the number of the parents of the same class, and the depth of the partition below compartment represents the average number that each individual of that class roduces. To sum up. We now see clearly the way in which the resemblance of a population is maintained. In the purely typical case, all the processes of heredity and selection are subject to well-defined and simple laws, which I have formulated in the appendix. Family variability, productiveness, and survival are all subject to the law of deviation, and reversion is expressed by a simple fractional coefficient. It follows that when we know in respect to any characteristic, the values of 1° in the several curves of family variability; productiveness and survival, and when we know the coefficient of reversion, we know absolutely all about the ways in which the characteristic in question will be distributed among the population at large. I have confined myself in this explanation to purely typical cases, but it is easy to understand how the actions of the processes would be modified in those that were not typical. Reversion might not be directed towards the mean of the race; neither productiveness nor survival might be greatest in the medium classes, and none of their laws may be strictly of the typical character. However, in all cases the general principles would be the same, and the same actions that restrain variability are capable of restraining the departure of average values beyond certain limits in cases where any of the above-mentioned processes are unsymmetrical in their actions. The typical laws are those which most nearly express what takes place in nature generally; they may never be exactly correct in any one case, but at the same time they will always be approximately true and always serviceable for explanation. We estimate through their means the effects of the laws of sexual selection, of productiveness, and of survival, in aiding that of reversion in bridling the dispersive effect of family variability. They show us that natural selection does not act by carving out each new generation according to a definite pattern on a Procrustean bed, irrespective of waste. They also explain how small a contribution is made to future generations by those who deviate widely from the mean, either in excess or deficiency, and they enable us to discover the precise sources whence the deficiencies in the produce of exceptional types are supplied, and their relative contributions. We see by them that the ordinary genealogical course of a race consists in a constant outgrowth from its centre, a constant dying away at its margins, and a tendency of the scanty remnants of all exceptional stock to revert to that mediocrity, whence the majority of their ancestors originally sprang. 1877.] on Typical Laws of Heredity. 299 APPENDIX. I will now proceed to formulate the typical laws. In what has been said, 1° of deviation has been taken equal to the " probable error = C x 0.4769 in the well-known formula 1 x, J= c ~V - e C' . According to this, if x = amount of deviation in feet, inches, or any other external unit of measurement, then the number of individuals in any sample who deviate between x and x + 8 x will vary as e- 7 8 x (it will be borne in mind that we are for the most part not concerned with the coefficient in the above formula). Let the modulus of deviation (c) in the original population, after the process has been gone through, of converting the measurements of all its members (in respect to the characteristic in question) to the adult male standard, be written co. 1. Sexual selection has been taken as nil, therefore the population of "parentages" is a population of which each unit consists of the mean of a couple taken indiscriminately. This, as well known, will conform to the law of deviation, and its modulus, which we will write c1, has already been shown to be equal to 2 . co. 2. Reversion is expressed by a simple fractional coefficient of the deviation, which we will write r. In the "reverted " parentages (a phrase whose meaning and purport have already been explained), 1 x, J= e r c I,;,./ 7r In short, the population of which each unit is a reverted parentage follows the law of deviation, and has its modulus, which we will write c„ equal to r c1. 8. Productiveness. We saw that it followed the law of deviation ; let its modulus be written f. Then the number of children to each parentage that differs by the amount of x from the mean of the parentages generally (i. e. from the mean of the race) will vary as X. Z. e -T ; but the number of such parentages varies as e - therefore if each child absolutely resembled his parent, the number of children W° x9 1. 1 who deviated x would vary as e - ° x e - pan , or as e - x' {7 + c,, . Hence the deviations of such children in their amount and frequency would conform to the law, and the modulus of the population of CIibPDF - www.fastio.com