13 



nature, and that a single weighting, if introduced, allows for the 

 movements of the worms. It will be found that if one subtracts one- 

 fourth from the calculated number of bolls attacked in one lock, that 

 the number calculated for the bolls attacked in one lock approaches 

 vary closely to the observed facts. Carrying the remainders over and 

 adding them to the figure giving the calculated numbers attacked in 

 two locks, and then subtracting one quarter from the sums obtained, 

 serves to bring the figures calculated for bolls attacked in two locks 

 extremely close to the observed figures. These quarters remaining 

 over added to the calculated numbers of bolls atacked in three locks 

 completes the calculation and brings once more observation and calcula- 

 tion extremely close together. The correlation between the observed 

 numbers and the calculated and weighted numbers is r=0-9557 

 0-0038. This examination was made on Sakellarides cotton. 



These results cannot possibly be ascribed to chance, seeing that 

 forty-seven observations enter into the calculation, and seeing that 

 fifty-four pairs of figures were compared for correlation. 



We are publishing in another paper all the statistics colledcd 

 hitherto concerning infestation of green bolls by the pink boll worm 

 and by Earias. No attempt is being made by us to reduce those figures 

 to statements of percentage damage comparable from one year to 

 another. With the information given here it ought to be apparent 

 that great care must be used before lightly drawing conclusions, and 

 that it is not permissible to use means of percentages indiscriminately, 

 although it might be allowed to use averages after translating percent- 

 ages of infestation into terms of numbers of worms per hundred bolls. 

 From this, percentages of attack might be calculated again. This 

 would, however, require a knowledge of the average maximum worm 

 population per boll which we do not yet possess. An example will 

 make the preceding more clear. Supposing the average maximum 

 number of worms per boll be limited to ten. Given two samples 

 of 100 bolls each, one attacked to 3 per cent, the other to 99 per 

 cent. If these two are averaged, the attack would appear to be 51 per 

 cent. But the internal composition of the 200 bolls would be very 

 different from that of a normal sample with 51 per cent attack. We 

 would now have (see Table III) three worms+946 worms in 200 bolls 

 or 475 worms per 100 bolls, which number of worms would belong more 

 properly to an attack between 84 per cent and 87 per cent, though their 

 distribution would be different. The damage being proportionate to the 

 number of worms, the figure 51 per cent attack would no longer corre- 

 spond to the normal damage expected at that intensity of attack, any 

 argument based on averages of this kind would be fallacious. In fact, 

 in the extreme case used as illustration, we would really have about 47 

 per cent damage to record, instead of about 12 per cent which would be 

 expected in a normal sample with 51 per cent attack. 



