INSECT EVOLUTION CHETVERIKOV. 447 



and some of them are already approaching the end of their earthly 

 existence. 



What cause, then, what factor, started the vertebrates and insects 

 on these two diametrically opposite roads of evolution? What pecu- 

 liarity of structure of their organism in one case (in the vertebrates) 

 hinders their excessive diminution, admitting at the same time almost 

 unlimited external increase, while in the other case (in insects) 

 diminution is almost unlimited ? 



However great the difference and variation in the body structure 

 between vertebrates and insects, still the majority of their organs 

 give us no clue to the solution of the problem we proposed. Neither 

 the differences in structure of the alimentary canal, nor of the mus- 

 culature, the heart, the nervous system, nor any of the other soft 

 internal organs, can explain to us why evolution in the direction of 

 such external diminution was possible in insects and entirely inac- 

 cessible to the vertebrates. Only on passing over to a study of the 

 skeleton do we find in the two groups such sharp, characteristic, and 

 common differences which give a key to the understanding of the dia- 

 metrically opposite paths of their evolution. Saying nothing about 

 the chitin of insects which, owing to its simultaneous hardness and 

 elasticity, represents an ideal skeletal material, the very fact of the 

 transfer of the skeleton of insects to the surface, the perifera of their 

 bodies, appears, in my opinion, to be the most essential moment which 

 determined their evolution. 



I will not dwell on the fact that a continuous external skeleton is 

 the best means of protection against the influence of the external 

 medium, which is especially important for small forms, since the rela- 

 tion of the circumference of their body to its surface is in them par- 

 ticularly unfavorable. The purely mechanical peculiarities of the 

 internal as well as the external skeleton are of great importance to us. 



In order to explain this question more precisely we will turn to 

 the accompanying illustration (fig. 1). Above is represented a 

 graph of the exoskeleton of, let us say, some extremity, when the 

 diameter of the inner area is 4/5 of the outer diameter. Below we 

 have two graphs with an internal skeleton arranged along the axis 

 of the extremities. If we now turn to the theory of resistance of mate- 

 rials, we will find there the following data : The modulus (i. e., the 

 power) of resistance to bending (and in the given instance it is just 

 this form of resistance that interests us) in a solid cylinder, and in 

 a hollow one is expressed by the following two formulae : 



vv 32 ana vv x ^^ 



W and W x are the respective moduli ; 



D is the diameter of the cross section of the cylinder; 



