388 APPENDIX TO CHAPTER X. 
attain a high velocity is small. I calculate that the surface 
resisting forward motion is about 7 square centimetres. 
Using the same formule (i and ii) and giving a the value of 
0133 X 7="0931, or say in round numbers o*1 gramme: 
2U : 
We have 1—-—=0 and v=5: Hence v — av? = 5— 2'5 = 2'5 
10 
metres per second, and this is the maximum velocity which 
can be attained. 
Now 2°5 metres per second=3,600 x 25 metres per- hour, 
or 9 kilometres (rather more than 5 miles per hour), is a rate 
of progression, against a resistance of or gramme, which needs 
*25 gramme-metres of work per second. 
Therefore, if the work needed to sustain the insect during 
flight is 1°08 metre-gramme units, and that to urge it forwards 
is 0°25 metre-gramme units (as 1°08+0°25=1°33), the total 
energy of flight required to maintain this velocity is 1°33 metre- 
gramme units per second. 
In all the above calculations, I have entirely neglected internal 
work; my aim has been to show that the minimum work of 
flight is at least 1°33 metre-grammes per second. I have no 
doubt it is greater in reality. The estimated rate of falling is 
certainly rather less than the real rate. That the work of 
flight is very large will be manifest to all who have tried to 
climb rapidly or even to run up a staircase. Fancy doing so 
at the rate of one metre per second for any length of time! 
The work done is not however independent of the wind and of 
currents of air, but on fine evenings I think the insects gain 
and lose about the same velocity from this cause as they 
appear to fly independently of the direction of the wind. 
It can also be shown, that in order to perform 1°3 metre- 
grammes of external work, the wings must vibrate at least 
150 times a second, assuming their surface to measure Io square 
centimetres, and the arcs of vibration of their apices to be 
4 centimetres long, a result which agrees sufficiently well with 
observations already recorded (p. 207). 
