li 



formably with the rule are now enormously increased, and although 

 over sufficiently large a sample considerable regularity and conformity 

 to the rule are most probable, in small samples consisting of a thousand 

 bolls only this can hardly be altogether expected. This has been 

 especially felt when working up results obtained from open bolls, 

 where samples had to be kept down in size if they were to be examined 

 at all. Examining each seed in 100 bolls one by one is a lengthy 

 process, as 1,600 seeds have to be delinted by hand to do so. 

 Increasing these samples to thousands of bolls meets with obstacles 

 other than financial. 



In 1920. with a view of studying the distribution of damage 

 within the bolls composing a sample, sixty-three samples of bolls were 

 examined lock by lock, and records were kept showing the percent- 

 age of bolls in each sample, attacked in 0, 1, 2 or 3 locks. Forty- 

 seven of these samples lie within 78 per cent apparent attack (=95 

 per cent true attack) and are usable. The remainder belong to too 

 high percentages to be used in this connection. 



If the theory of distribution of worms within the component 

 bolls of a sample is correct, it should be possible to bring the results 

 of this last examination into consonance with it. The non-entomolo- 

 gical reader must be warned, before starting on this examination, 

 that the problem is not quite on a par with throwing balls into holes, 

 where the balls remain to be counted. The worms are animate beings, 

 and the bolls, whose locks represent the holes into which the balls are 

 thrown, are also living things, and the barrier between the component 

 locks of a boll is easily broken down by a worm. 



It appears probable to the writer, that given bolls consisting of 

 three locks, and given certain numbers of worms to distribute, that 

 the distribution will follow the scheme outlined below. 



Assuming one worm only attacks one lock, and worms show no 

 preference. 



With one worm per boll there is only one chance (unless altered 

 by the insect), and that is that one lock will be attacked. 



With two worms per boll there are three chances : 



(a) Both worms will be in one lock ; one chance. 



(b) The worms will occupy two locks ; two chances. 



With three worms per boll there are nine chances. 



(a) All three worms occupy one single lock ; one chance. 



(b) The three worms are distributed over two locks ; six chances. 



(c) The worms each occupy a different lock ; two chances. 



With four worms per boll there are twenty-seven chances. 

 (a) All four in one lock ; one chance. 



