APPENDIX TO CHAPTER X. 



CALCULATION OF THE WORK DONE IN FLIGHT. 



ACCORDING to numerous experiments the pressure of the air 

 is '0133 grammes per centimetre x v 2 , so that the pressure on 

 17 centimetres = '2331 grammes. Now, the pressure causing 

 downward motion is i gramme, the weight of the insect, and 

 the pressure resisting the motion is a = '2^i grammes per 

 metre of velocity, therefore the maximum rate of falling (x) is 

 the velocity (v) acquired under gravity av 2 , when v av 2 = x 

 is a maximum. 



Since if x = v av 2 (i) 

 dx 



,..-. 

 (11; 



dv 

 And this is a maximum, when 



dx 

 - = o, and i 2av = o; 



dv 



Then as 2.a = \ nearly, v = 2, nearly: 



Putting this value of v into v av z = x, where x is the 

 maximum velocity of falling, we have, 2 4 x '23 = 2 0*92, 

 or in round numbers, i metre per second, as the maximum 

 rate of falling. 



If one metre per second is the maximum rate of fall, the 

 work done in sustaining its weight by a creature like the 

 Cockchafer, having 17 centimetres of surface and i gramme 

 weight, will be i metre-gramme per second, or more accurately 

 1*08 metre-grammes per second. 



As the surface presented to the air, in forward movement, is 

 much less, and the only work to be done in progressing for- 

 ward is that against the resistance of air, the work needed to 



