352 Raymond Pearl 



shown graphically in Fig. 2. The plan of this- diagram is the same 

 as that of Fig. I. 



From this diagram it is apparent that the increase in the breadth 

 of the eggs which occurs with successive laying follows, on the 

 whole, a straight line. The actual observations zigzag up and 

 down, but the underlying steady tendency appears to be for the 

 breadth of the eggs to increase at a slow, but uniform rate, or, in 

 other words, in a straight line. This is in marked contrast to 

 what has been seen for the length. 



Turning now to the index (lOO X breadth 4- length) which may 

 be taken as measuring shape we have the discussion of a series of 

 values which have been seen to follow a straight line divided by a 

 dimension which follows a decided curve. It would be expected 

 that the quotient (index) so obtained would exhibit a decided 

 curve when plotted. That this is in fact the case is shown in 

 Plate II, where the zigzag line represents the observed indices of 

 the successively laid eggs. Examining this diagram it is seen that 

 to a more pronounced degree the statements made regarding the 

 change in the length of the eggs apply to the index, if "increase" 

 is in each case substituted for "decrease." The index increases 

 in value very rapidly at first and the rate of increase becomes 

 progressively slower with successive eggs. In the case of the index 

 the whole 87 eggs are included in the plotted curve. 



Now since the length-breadth index is a better measure of the 

 shape of the egg as a whole than either the length or breadth alone 

 it is desirable to deal with this character in the further analytical 

 study of this case. It was decided to graduate the index curve. 

 Now the shape of the curve, rising sharply at the beginning, curv- 

 ing smoothly and quickly and then running off nearly horizontal, 

 only curving very gradually, suggests at once to the eye that it is 

 a logarithmic curve. Furthermore, previous experience with 

 similar data suggested a logarithmic as the proper curve. Accord- 

 ingly a curve of the type 



y = a + bx + c log x 



was fitted to the observations, as a first trial. In obtaining the 

 constants of this equation a table of values of S (log x) S (log x\ 



