THE METAMORPHOSIS OF INSECTS 173 



Head measurements of larvae. It was demonstrated by Dyar ('go) 

 that the widths of the head of a larva in its successive instars follow 

 a regular geometric progression in their increase. The head was 

 selected as a part not subject to growth during a stadium; and the 

 width as the most convenient measurement to take. By means of 

 this criterion, it is possible to determine, when studying the transfor- 

 mations of an insect, whether an ecdysis has been overlooked or not. 

 Experience has shown that slight variations between the computed 

 and the actual widths may occur; but these differences are so slight 

 that the overlooking of an ecdysis can be readily discovered. The 

 following example will serve to illustrate the method employed. 



A larva of Papilio thoas was reared from the egg ; and the widths 

 of the head in the successive instars was found to be, expressed in 

 millimeters, as follows: .6; i.i; 1.6; 2.2; 3.4. 



By dividing 2.2. by 3.4 (two successive members of this series), the 

 ratio of increase was found to be .676+ ; the number, .68 was taken, 

 therefore, as sufficiently near the ratio for practical purposes. By 

 using this ratio as a factor the following results were obtained : 



Width found in fifth instar= ..................... 3.4 



Calculated width in fourth instar (3.4 X .68) = ..... 2.312 



" " third " (2.312 X .68) ==.... 1.57 



" " second " (1.57 X .68) = .... 1.067 



" " first (1.067 X .68) - ..... 725 



By comparing the two series, as is done below, so close a correspond- 

 ence is found that it is evident that no ecdysis was overlooked. 

 Widths found: .6; i.i; 1.6; 2.2; 3.4 



calculated: .7; i.i-; 1.6-; 2.3. 



The reproduction of lost limbs. The repro- 

 duction of lost limbs has been observed in many 

 insects ; but such reproduction occurs here much 

 less frequently than in the other classes of the 

 Arthropoda. The reproduction takes place dur- 

 ing the period of ecdysis, the reproduced part 

 becoming, larger and larger with each molt; 

 hence with insects, and with Arachnida as well, 

 the power of reproducing lost limbs ceases with 

 I the attainment of sexual maturity; but not so 



with the Crustacea and the "Myriapoda" which 

 molt after becoming sexually mature. In none 



Fig. 193- A spider in o f t ^ e observed examples of the reproduction 

 which lost legs were j j 



being reproduced. of appendages has an entire leg been reproduced. 



