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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 Xv’, so that the pressure on 
17 centimetres="2331 grammes. Now, the pressure causing 
downward motion is 1 gramme, the weight of the insect, and 
the pressure resisting the motion is @=*233I grammes per 
metre of velocity, therefore the maximum rate of falling (x) is 
the velocity (v) acquired under gravity—av?, when v—av?=x 
is a maximum. 
Since if x =v—av? (i) 
dx 
—~ =1— 2a (ii 
a (ii) 
And this is a maximum, when 
dx 
-=0, and I—2av=0; 
dv 
Then as 2a=} nearly, v=2, nearly: 
Putting this value of v into v—av’=x, where x is the 
maximum velocity of falling, we have, 2—4x‘23=2-—0'92, 
or in round numbers, 1 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 1 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 
