532 



NA TURE 



YApril 19, 1877 ^ 



7 YPICAL LA WS OF HEREDITY 1 

 III. 



IF a g^raphic representation is desired, which will give the 

 absolute number of survivors at each degree, we must 

 shape the rampart which forms nature's target so as to be 

 liighest in the middle and to slope away at each side 

 according to the law of deviation. Thus Fig. 6 represents 

 the curved rampart before it has been aimed at ; Fig. 7, 

 j;fterwards. 



1 have taken a block of wood similar to Fig. 4, to repre- 

 sent the rampart ; it is of equal height throughout. A 

 cut has been made at right angles to its base with a fret- 

 saw, to divide it in two portions — that which would 

 remain after it had been breached, Fig. 5, and the cast 

 of the breach. Then a second cut with the fret-saw has 

 been made at right angles to its face, to cut out of the 

 rampart an equivalent to the heap of pellets that repre- 

 sents the original population. The gap that would be 

 made in the heap and the cast that would fill the gap are 

 curved on two faces, as in the model. This is sufficiently- 

 represented in Fig. 7. 



The operation of natural selection on a population 

 already arranged according to the law of deviation is 

 represented more completely in an apparatus, Fig. 8, 

 which I will set to work immediately. 



It is faced with a sheet of glass. The heap, as shown 

 in the upper compartment of the apparatus, is three inches 

 in thickness, and the pellets rest on slides. Directly below 

 the slides, and running from side to side of the apparatus, 

 is a curved partition, which will separate the pellets as 

 they fall upon it, into two portions, one that runs to waste 

 at the back, and another that falls to the front, and forms 

 a new heap. The curve of the partition is a curve of 

 deviation. The shape of this heap is identical with the 

 cast of the gap in Fig. 7. It is highest and thickest in 

 the middle, and it fines away towards either extremity. 

 When the slide upon which it rests is removed, the pellets 

 run down an inclined plane that directs them into a frame 

 of uniform and shallow depth. The pellets from the deep 

 central compartments (it has been impossible to represent 

 in the diagram as many of these as there were in the 

 apparatus) will stand very high from the bottom of the 

 shallow frame, while those that came from the distant 

 compartments will stand even lower than they did before. 

 It follows that the selected pellets form, in the lower 

 compartment, a heap of which the scale of deviation is 

 n-juch more contracted than that of the heap from which 

 il was derived. It is perfectly normal in shape, owing to 

 an interesting theoretical property of deviation (see for- 

 mulae at er,d of this memoir). 



Productiveness follows the same general law as sur- 

 vival, being a percentage of possible production, though 

 it is usual to look on it as a simple multiple, without 

 oividing by the 100. In this case 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 parti- 

 tion below that compartment represents the average num- 

 ber that each individual of that class produces. 



To sum up. We now see clearly the way in which the 

 resemblance of a population is maintained. In the purely 

 typical case, each of the processes of heredity and selec- 

 tion is subject to a v/ell-defined and simple law, which 

 1 have formulated in the appendix. It follows that when 

 v/e know 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 that characteristic will be dis- 

 tributed among the population at large. 



I have confined myself in this explanation to purely 

 typical cases, but it is easy to understand how the factions 

 of the processes would be modified in those that were 



I Lecture delivered at the Royal Institution, Friday evening, February 

 9 , by Franas Gallon, F.R.S. Continued from p. 514. 



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. How- 

 ever, in all cases the general principles would be the same. 

 Again, the sarrie actions that restrain variability would 

 restrain the departure of average values beyond certain 

 limits. 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 pro- 

 ductiveness, 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 hov/ small a contribution is made to future gene- 

 rations by those who deviate widely from the mean, either 

 in excess or deficiency, and enable us to calculate whence 

 the deficiency of exceptional types is supplied. We see 

 by them that the ordinary genealogical course of a race 

 consists in a constant outgrowth from its centre, a con- 

 stant 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 origin- 

 ally sprang. 



Appendix. 



I will now proceed to formulate the typical , laws. In 

 what has been written, 1° of deviation has been taken 

 equal to the " probable error " = C X o'4769 in the well- 



According to this, if 



known formula y = ■ — — . e 



C sjlT 



X — amount of deviation in feet, [inches, or any other 

 external unit of measurement, then the number of indi- 

 viduals in any sample who deviate between x and x -{-hx 



will vary as <? '^^ hx (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 popula- 

 tion, after the process has been gone through, of convert- 

 ing 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 «//, 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 con- 

 form to the law of deviation, and its modulus which 

 we will write r^ has already been shown to be equal to 



I 



2. Reversion is expressed by a fractional coefficient of 

 the deviation, which we will write r. In the " reverted " 

 parentages (a phrase whose meaning and object have 

 already been explained) 



-y = 



rc sj-n 



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 rc-^^. 



3. 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 £ 



f^ 



mean of the race), will vary as e 



_£! 

 such parentages varies as e '^^ , therefore if each chil^ 



but the number of ^ 



A 



