THE METAMORPHOSIS OF^ INSECTS 173 



Head measurements of larvae. — It was demonstrated by Dyar ('90) 

 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 measiu-ement 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; 1.1-; 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 

 the attainment of sexual maturity; but not so 

 with the Crustacea and the "Myriapoda" which 

 molt after becoming sexually mature. In none 



Fig-'f93-— A spider in of the observed examples of the reproduction 

 which lost legs we: e . . , . , , j j 



being reproduced. of appendages has an entu-e leg been reproduced. 



