age attack, as such samples are incomplete owing to the mabruma and 

 the lost bolls being absent. The apparent percentage attack becomes 

 always lower than the true percentage, but if the assumption that 

 four worms are about the maximum usually included in pickable cotton 

 is valid, the true percentage attack can be calculated. For samples 

 containing about 81 per cent attacked bolls of picked ripe cotton, 

 the true percentage ought to be about 99 per cent. 



Table I shows the expected numbers of bolls containing no worms 

 and one to ten worms, respectively, for every third unit from three 

 to ninety-nine per cent true attack. 



Before proceeding further with calculations based on this table, 

 the following proof may be offered for the correctness of the figures. 



Ballon in his report on the Pink Boll Worm in Egypt in 1916-1917 

 on pages 42-43 gives the results of the examination of certain samples 

 of bolls which were inspected singly, and the numbers of pink boll 

 worms in which were recorded. The comparisons between Ballou's 

 observations and our calculations are found in Table II, the results 

 being a so extremely close approximation between calculated and 

 observed results as to leave no doubt as to the probability of the 

 correctness of the method of calculating the distribution of the worms 

 in the bolls. (The correlation r=O9974 0-0002 also leaves no doubt 

 that the agreement is not merely a chance one.) 



Note. The objection to util-sing Ballou's Table XIV can be made, 

 that the observations on which it was based were made during winter 

 and a long time after the bolls had been infected. Also that many 

 a worm will have had time to leave the bolls and emerge before the 

 bolls were examined. As against this can be placed that the percent- 

 ages of attacked bolls were based only on the worms actually present 

 at the time of examination, and that the emergence of the moths 

 from the bolls evidently follows the same general rules as the 

 initial infestation. The figures given by Ballou for worms present 

 would be much safer than those found by us in green bolls, as there 

 would be no chance of small ones getting overlooked by the observer 

 when dealing with dead bolls in winter. 



It will have been observed that the figures compared on Table II 

 all fall within the limit of tolerance of twelve worms. Once the limit 

 of tolerance has been exceeded, the observed boll population consists 

 only of sound bolls and bolls within the limit. This will cause a change 

 to take place in the observed percentage which will no longer coincide 

 with the true percentage, but will show a less apparent attack than 

 the true attack. It is also obvious that when the tolerance is small a 

 difference between true and apparent attack will commence early 



