Sept. is, 1916 Dwarf Eggs 987 



Pearl and Miner (17) have published a table showing, for each value of 

 the ratio of the probable error to the deviation, the probable occurrence 

 in a hundred trials of a deviation as great or greater than the observed, 

 provided chance alone is operating, and also the odds against its occur- 

 rence. From this table we see that the odds against a deviation due to 

 chance alone, which is 3.0 times its probable error, is 22.26 to 1. We 

 also see that above 3.0 the increase in odds is very rapid. At 4.0 it is 

 142.26 to 1 ; at 5.0 it is 1,350.35 to 1 ; at 8.0 it is 1,470,588,234 to 1. In 

 the present discussion a deviation less than twice its probable error is 

 considered insignificant. The significance of a deviation between two 

 and three times the probable error is considered doubtful. A deviation 

 between three and four times its probable error is considered probably 

 significant. A deviation four or more times its probable error is con- 

 sidered almost certainly significant, with the understanding that when 

 the odds against the occurrence of a given deviation being due to chance 

 alone are as great or greater than 142.26 to 1, the deviation is almost 

 certainly due to some other cause than error of sampling. 



From Table V we see that small-yolked dwarf eggs are significantly 

 smaller than normal eggs and larger than the other classes of dwarf eggs. 

 These significant differences are seen in length, breadth, and weight 1 — 

 that is, the small-yolked egg is nearer the size of a normal egg than are 

 dwarf eggs with little or no yolk. The average length, breadth, and 

 weight are all slightly higher for dwarf eggs which contain some free yolk 

 than for yolkless dwarf eggs. These slight differences may be due to 

 errors in sampling, since in no case is the deviation three times its probable 

 error — that is, although the mean size of the observed dwarf eggs with 

 some free yolk is slightly greater than the mean size of the observed 

 yolkless dwarf eggs, this difference is not certainly significant. 



These results are in line with the results from other investigations on 

 the size of eggs. First, Pearl (12) showed that the relation of the weight 

 of the entire egg to the number of yolks contained (zero, one, two, or 

 three) is very accurately described by a parabola. He concluded that, 

 while the size of eggs is not directly proportional to the number of yolks 

 they contain, a definite relation probably exists between the amount of 

 albumen secreted and the amount of yolk present in the duct in a given 

 case. Second, Curtis (5) showed that within the eggs of an individual 

 bird the actual weight of both albumen and shell is higher in triple-yolked 

 than in double-yolked and higher in double-yolked than in single-yolked 

 eggs. The increase in these accessory parts is not, however, proportional 

 to the increase in yolk weight, since the yolk which formed only 24.37 

 per cent of the normal eggs formed 33.91 per cent of the double-yolked 

 and 35.52 per cent of the triple-yolked eggs. Third, Curtis (4) showed 

 that in the normal eggs of each individual bird there is a significant 



1 The weight of each egg part is also significantly smaller in small-yolked dwarf than in normal eggs. 



