354 Raymond Pearl 



and iS" {x log x) calculated in this laboratory^ was used with great 

 saving of labor. The resulting curve was 



y = 49.0241 — .0910 X + 11.7669 log X 



where y denotes the length-breadth index and x the ordinal num- 

 ber of the egg in the whole series laid. 



Calculating the ordinates of this curve we have the set of values 

 shown graphically by the smooth curve in Plate II. 



It is clear that this curve is a wonderfully good graduation of 

 the observations. It is so good, in fact, that it is apparent that 

 this logarithmic curve is the analytical expression of the manner in 

 which the change in the shape of the eggs of No. l8^ occurred. It 

 is possible now summarily to state the facts regarding the shape of 

 the eggs of hen No. 183 as follows: The first egg laid by this hen 

 was abnormally long and narrow; the eggs subsequently laid ap- 

 proached more and more to the normal in shape. This change in 

 shape was in accordance with a logarithmic curve of the type 



y = a + bx + c log x 



wherein y denotes the length-breadth index of the egg, x its ordinal 

 number in the series laid, and a, b and c are constants. 



It will be noted that the smooth curve shows a tendency for the 

 index as observed to decrease after reaching a maximum along in 

 the region of the 50th to 60th eggs. The turning downward of the 

 theoretical curve comes about from the fact that the term .0910 x 

 in the equation is negative. This decrease is not to be interpreted 

 as due to any tendency for the eggs to change from the normal to- 

 wards the abnormal after a number have been laid. On the con- 

 trary there is every reason to believe that it is merely a chance result 

 due to ending the observations at the particular point where they 

 were ended. The observation line fluctuates up and down as the 

 result of chance factors. It happened by chance that towards 

 the end of the series the "down" fluctuations predominated to an 

 extent sufficient to change the sign of the line term {x term) in the 

 equation and turn the fitted curve slightly downward. There is 



* This table, which is very useful in fitting logarithmic curves to any sort of data by the method of 

 least squares, will shortly be published. 



