OCR Rendition - approximate

292 Mr. Francis Galton [Feb. 9, which serve as representatives of a population of seeds. I will begin with showing how it expresses Reversion. In the upper stage of the apparatus the number of pellets in each compartment represents the relative number in a population of seeds, whose weight deviates from the average, within the limits expressed by the distances of the sides of that compartment from the middle point. The correct shape of the heap has been ensured by a slit of the proper curvature in the board that forms the back of the apparatus. As the apparatus is glazed in front, I have only to pour pellets from above until they reach the level of the slit. Such overplus as may have been poured in will run through the slit, to waste, at the back. The pellets to" the right of the heap represent the heaviest seeds, those to the left the lightest. I shall shortly open the trap-door on which the few representatives of the giant seeds rest. They will run downwards through an inclined shoot, and fall into another compartment nearer the centre than before. I shall repeat the process on a second compartment in the upper stage, and successively on all the others. Every shoot converges towards one standard point in the middle vertical line ; therefore the present shape of the heap of pellets is more contracted in width than it was before, and is of course more humped up in the middle. We need not regard the humping up ; what we have to observe is, that each degree of deviation is simultaneously lessened. The effect is as though the curve of the first heap had been copied on -a stretched sheet of indiarubber that was subsequently released. It is obvious from this that the process of reversion co-operates with the general law of deviation. The diagram that I annexed to Fig. 1, shows the principle of the process of reversion in a way that will be readily understood by many of those who are present. I have now to exhibit the effects of variability among members of the same family. It will be recollected that the produce of peas of the same class deviated normally on either side of their own mean weight; consequently, I must cause the pellets which were in each of the upper compartments to deviate on either side of the compartment in which they now lie, which corresponds to that of the medium weight of their produce. I open the trap-door below one of the compartments in the second stage, the pellets run downwards through the harrow, dispersing as they run, and form a little heap in the lowest compartments, the centre of which heap lies vertically below the trapdoor through which they fell. This is the contribution to the succeeding generation of all the individuals belonging to the compartment in the upper stage from which they came. They first reverted and then dispersed. I open another trap-door, and a similar process is gone through ; a few extreme pellets in this case add themselves to the first formed heap. Again I continue the process ; heap adds itself to heap, and when all the pellets have fallen through, we see that the aggregate contributions bear an exact resemblance to the heap from which we originally started. A formula (see Appendix) expresses the conditions of equilibrium. I attended to these conditions, when I 1877.] on Typical Laws of Heredity. 293 cut out the slit in the backboard of the upper compartment, by which the shape of the original heap was regulated. As an example of the results that follow from the formula, I may mention that if deviation after reversion is to deviation before reversion as 4 to 5, and if 1° of family variability is six units, then the value of 1° in the population must be ten units. It is easy to prove that the bottom heap is strictly a curve of deviation, and that its scale tends invariably to become the same as that of the upper one. It will be recollected that I showed that every variety of curve of deviation was producible by variations in the length of the harrow, and that if the pellets were intercepted at successive stages of their descent they would form a succession of curves of increasing scales of deviation. The curve in the second stage may therefore be looked upon as one of these intercepts; all that it receives in sinking to the third stage being an additional dose of dispersion. As regards the precise scale of deviation that characterises each population, let us trace, in imagination, the history of the descendants of a single medium-sized seed. In the first generation the differences are merely those due to family variability ; in the second generation the tendency to wider dispersion is somewhat restrained by the effect of reversion; in the third, the dispersion again increases, but is more largely restrained, and the same process continues in successive generations, until the step-by-step progress of dispersion has been overtaken and exactly checked by the growing antagonism of reversion. Reversion acts precisely after the law of an elastic spring, as was well shown by the illustration of the indiarubber sheet. Its tendency to recoil increases the more it is stretched, hence equilibrium must at length ensue between reversion and family variability, and therefore the scale of deviation of the lower heap must after many generations always become identical with that of the upper one. We have now surmounted the greatest difficulty of our problem; what remains will be shortly disposed of. This refers to sexual selection, productiveness, and natural selection. Let us henceforth suppose the heights and every other characteristic of all members of a population to be reduced to a uniform adult male standard so that we may treat it as a single group. Suppose, for example, a female whose height was equal to the average female height + 3° of female deviation, the equivalent in terms of male stature is the average male height + 3° of male deviation. Hence the female in question must be registered not in the feet and inches of her actual height, but in those of the equivalent male stature. On this supposition we may take the numerical mean of the stature of each couple as the equivalent of a single hermaphrodite parent, so that a male parent plant having 1° deviation, and of a female parent plant having 2° of deviation, would together rank as a single selffertilised plant of + 11°. In order that the law of sexual selection should co-operate with the conditions of a typical population, it is necessary that selection CIibPDF - www.fastio.com