12 THE FLIGHT OF BIRDS 



the plane were not inclined at all, but presented 

 its edge to the air, there would be practically no 

 support. There is, therefore, beyond all dispute 

 a limit somewhere to the possible reduction in the 

 incline of the aeroplane. The question is where, 

 for practical purposes, that limit comes in. Newton 

 formulated a law with regard to this, a law which 

 is now quoted only to be condemned, and some- 

 times quoted with expressions of contempt for 

 him and mathematicians in general.* Newton 

 held that the resistance of the air increases as the 

 square of the sine of the angle of inclination. 



Fig. 8. 



Thus, if we take angles of 5°, 10°, 20°, the resistance 

 would increase, from 25 to 100, to 400. Instead of 

 being grateful to Newton for his great contribution 

 to our understanding of flight, his discovery that 

 the resistance of the air increases as the square 

 of the velocity of bodies moving through it, some 

 writers have depreciated him and his work because 

 he has come to a wrong conclusion on this further 

 question. As a matter of fact the resistance of 

 the air varies as the angle, i.e. as its sine, not as 

 the square of its sine. Therefore, as you diminish 

 the angle, you still have a considerable amount of 

 resistance, and it is divided up largely in favour 



* See Sir H. Maxim's Artificial and Natural Flight, pp. 2-G. 

 The question is well dealt with in Prof. Langley's Experiments 

 in Aero-dynamics ; see especially pp. 24 and 25. 



