12 THE FLIGHT OF BIRDS 
the plane were not inffined 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. 
Fia. 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. 2-6. 
The question is well dealt with in Prof. Langley’s Haperiments 
in Aero-dynamics ; see especially pp. 24 and 25. 
