THE MEASUREMENT OF VARIATION. 11 



the laws of chance. Supposing a group of developing 

 organisms be taken, of which the growth can be affected 

 in a favourable or an unfavourable manner by their 

 surroundings. Let us suppose that there are twenty 

 different agencies, each of which would produce an 

 equal, favourable effect on growth, and twenty which 

 would produce just as great an effect in the opposite 

 direction. Suppose also that each organism is sub- 

 jected to only half of these forty different agencies; 

 then it would follow, according to the laws of chance, 

 that a larger number of the organisms would be acted 

 upon by 10 favourable and 10 unfavourable agencies, 

 than by any other combination; i. e., they would, on our 

 hypothesis, remain absolutely unaffected in their 

 growth. A somewhat smaller number would be acted 

 upon by 11 favourable and 9 unfavourable agencies, or 

 on the whole, would have their growth slightly in- 

 creased. A still smaller proportion would be acted on 

 by 12 favourable and 8 unfavourable agencies, or would 

 have their growth rather more increased. Finally the 

 number of organisms acted on by 20 favourable and 

 unfavourable agencies would be extraordinarily small, 

 but in this case the effect on growth would be extremely 

 large. Similar relationships, only in the reverse direc- 

 tion, would of course be found in those cases in which 

 the number of unfavourable agencies exceeded the 

 number of favourable. If desired, the proportional 

 numbers of organisms acted on by all the different com- 

 binations of agencies may be readily determined by ex- 

 panding the binomial (J + |) 20 . It is found, for in- 

 stance, that for each single time the organisms are 

 acted on by the whole 20 favourable agencies, they are 



