The Problem of the Sirex 



horizontal position. In order to pass from 

 the former to the latter, the insect veers 

 round by describing the arc of a circle. 

 When this turn has been effected, the distance 

 Is completed in a straight line. 



Let us consider the Sirex at his starting- 

 point. His stiffness of necessity compels him 

 to turn gradually. Here the insect can do 

 nothing of its own initiative ; everything is 

 mechanically determined. But, being free 

 to pivot on its axis and to attack the wood on 

 either side of the sheath, it has the option of 

 attempting this reversal in a host of different 

 ways, by a series of connected arcs, not in 

 the same plane. Nothing prevents it from 

 describing winding curves by revolving upon 

 itself: spirals, loops constantly changing 

 their direction, in fact, the complicated route 

 of a creature that has lost its way. It might 

 wander in a tortuous maze, making fresh at- 

 tempts here, there and everywhere, groping 

 for ever so long without succeeding. 



But it does not grope and it succeeds very 

 well. Its gallery is still contained within 

 one plane, the first condition of the minimum 

 of labour. Moreover, of the different 

 vertical planes that can pass through the 

 eccentric starting-point, one, the plane which 

 passes through the axis of the tree, cor- 



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