of the total possible chance of attack. It will be seen, therefore, that 

 as long as the complete boll population including setting, maturing and 

 ripe bolls is examined, there will be a proportion of sound ones as long 

 as boll production is proceeding. It is also evident that, unless the 

 attack has increased to 100 per cent there must be some sound bolls 

 present of each age, and that finally some sound bolls will mature. 



Perhaps it is also well to bear in mind that as long as boll produc- 

 tion is proceeding the attack as expressed in percentages is being kept 

 low, by the presence of the young bolls which are not or scarcely 

 attacked. As soon as the production of new bolls ceases, or slackens, 

 the percentage of attack is no longer kept down in this way, and the 

 resulting increasing rise in percentages becomes very evident. To this 

 the steep rise at the end of the season is to a great extent due in a 

 record of percentage attack of green bolls only. 



Having shown the considerations which have to be remembered 

 when trying to work out a formula, it is perhaps only necessary to 

 remark that more than one plan of distribution of worms into bolls 

 was studied, whereby the method now to be described was found to 

 fit the observed facts best. 



Presuming, that, as is a fact, more than one worm can infest a 

 single boll, and for the moment presuming that the number per boll 

 is not limited in any way (which however is not the case), the distribu- 

 tion of 1 , 2 , 3 or further multiples of worms per boll appears to be 

 regulated as follows : 



In each 100 bolls with n per cent attack there will be (100-n) per 

 cent bolls free from worms. Of the n bolls containing worms (100-w) 

 per cent will contain one worm only. Of the remaining bolls (IQO-n) 

 per cent will contain two worms, of the remainder (100-n) per cent will 

 contain three worms, and so further until the figures representing the 

 number of bolls containing 0, 1, 2, 3, etc., worms when added together 

 gives 100, by which time the last figure obtained (for the largest 

 number of worms per boll) will have become a negligible fraction. 



The number of worms in a given sample can be calculated with 

 ease from the figures thus obtained. For example : 



Given 30 per cent attack, the expectations are : 



70 '00 bolls with no worms. 

 21-00 



TOTAL 



6-30 

 1-89 

 0-57 

 0-17 

 0.05 

 0-02 



100-00 



or 21 '00 worms. 



all 



42-84 



