April 12, 1877] 



NATURE 



513 



small seeds, all of — 3° of deviation. The intermediate 

 packets corresponded severally to the intermediate de- 

 grees ± 2° ± 1° and 0°, As the seeds are too small to 

 exhibit, 1 have cut out discs of paper in strict proportion 

 to their sizes, and strips in strict proportion to their 

 weights, and have hung below them the foliage produced 

 by one complete set. Many friends and acquaintances 

 each undertook the planting and culture of a complete 

 set, so that I had simultaneous experiments going on in 

 various parts of the United Kingdom. Two proved 

 failures, but the final result was this : that I obtained the 

 more or less complete produce of seven sets, that is of 

 7 X 7 X 10, or 490 carefully weighed seeds. 



It would be wholly out of place if I were to enter into 

 the details of the experiments themselves, the numerous 

 little difficulties and imperfections in them, or how I 

 balanced doubtful cases, how I divided returns into 

 groups, to see if they confirmed one another, or how I 

 conducted any other of the well-known statistical opera- 

 tions. Suffice it to say that I took immense pains, which 

 if I had understood the general conditions of the problem 

 as clearly as I do now, I should not perhaps have cared 

 to bestow. The results were most satisfactory. They 

 gave me two data, which were all that I required in order 

 to understand the simplest form of descent, and so I got 

 at the heart of the problem at once. 



Simple descent means this, The parentage must be 

 single, as in the case of the sweet peas which were not 

 cross-fertilised, and the rate of production and the inci- 

 dence of natural selection must both be independent of 

 the characteristic. The processes concerned in simple 

 descent are those of Family Variability and Reversion. It 

 is well to define these words clearly. By family varia- 

 bility is meant the departure of the children of the same 

 or similarly descended families from the ideal mean type 

 of all of them. Reversion is the tendency of that ideal 

 mean type to depart from the parent type, ''reverting" 

 towards what may be roughly and perhaps fairly described 

 as the average ancestral type. If family variability had 

 been the only process in simple descent, the dispersion of 

 the race would indefinitely increase with the number of 

 the generations, but reversion checks this increase, and 

 brings it to a standstill, under conditions which will now 

 be explained. 



On weighing and sorting large samples of the produce 

 of each of the seven different classes of the peas, I found 

 in every case the law of deviation to prevail, and in every 

 case the value of i° of deviation to be the same. I was 

 certainly astonished to find the family variability of the 

 produce of the little seeds to be equal to that of the big 

 ones, but so it was, and I thankfully accept the fact, for if 

 it had been otherwise I cannot imagine, from theoretical 

 considerations, how the problem could be solved. 



The next great fact was that Reversion followed the 

 simplest possible law ; for the proportion was constant 

 between the deviation of the mean weight of the produce 

 generally and the deviation of the parent seed, reckoning 

 in every case from one standard point. In a typical case, 

 that standard must be the mean of the race, otherwise the 

 deviation would become unsymmetrical, and cease to 

 conform to the law. 



I have adjusted an apparatus (Fig. i) to exhibit the action 

 of these two processes. We may consider them to act not 

 simultaneously but in succession, and it is purely a matter 

 of convenience which of the two we suppose to act the 

 first. I suppose first Reversion then Family Variability. 

 That is to say, I suppose the parent first to revert and 

 then to tend to breed his like. So there are three stages : 

 (i) the population of parents, (2) that of reverted parents, 

 (3) that of their offspring. In arranging the apparatus I 

 have supposed the population to continue uniform in 

 numbers. This is a matter of no theoretical concern, as 

 the whole of this memoir relates to the distinguishing 

 peculiarities of samples irrespectively of the absolute 



number of individuals in those samples. The apparatus 

 consists of a row of vertical compartments, with trap- 

 doors below them, to hold pellets which serve as repre- 

 sentatives 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 dis- 

 tances of the sides of that compartment from the middle 

 point. The correct shape of the heap has been ensured 

 by my having cut a slit of the proper curvature in the 

 board that forms the back of the apparatus. As it is 

 glazed in front I have only to pour pellets in 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 ; thus the pre- 

 sent 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 india-rubber that was subsequently released. It 

 is obvious from this that the process of reversion co- 

 operates with the general law of deviation. Fig. 6 shows 

 the principle of the process of reversion clearly, 



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 ; that is to 

 say, I must make 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 trap-door through which 

 they fell. This is the contribution to the succeed- 

 ing 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- do or, 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 re- 

 semblance to the heap from which we originally started. 

 A simple formula (see Appendix) expresses the conditions 

 of equiUbrium. I attended to these, when 1 cut out the 

 slit in the back board of the upper compartment, by which 

 the shape of the original heap was regulated. Thus it 

 follows from the formula that if deviation after reversion 

 was to deviation before reversion as 4 to S, and if 1° of 

 family variability was 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 suc- 



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