Al'l'EMUX TO CUAJ'TKR A. 



attain a high velocity is small. I calculate that the surface 

 resisting forward motion is about 7 square centimetres. 



Using the same formulae (i and ii) and giving a the value of 

 '0133 x 7 = '0931, or say in round numbers o'i gramme: 



> - 1 



\Ye have i =o and v = 5 : Hence t- a-s- = 5 2 '5 = 2*5 

 10 



metres per second, and this is the maximum velocity which 

 can be attained. 



Xow 2*5 metres per second = 3,600 x 2*5 metres per hour, 

 or 9 kilometres (rather more than 5 miles per hour), is a rate 

 of progression, against a resistance of 0*1 gramme, which needs 

 25 gramme-metres of work per second. 



Therefore, if the work needed to sustain the insect during 

 flight is roS metre-gramme units, and that to urge it forwards 

 is o'25 metre-gramme units (as roS + 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 

 1 51 > times a second, assuming their surface to measure 10 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). 



