188 THE STRUCTURE AND LIFE OF BIRDS cuap. 
if the problem is to be tackled at all. Every one is 
familiar with the pipes of different dimensions in 
arithmetic books which are opened at various times, 
some of them filling, some of them emptying a cistern, 
the problem being to discover at what precise time 
the cistern will be full or empty. Such problems give 
healthy exercise to the brain, but we must not suppose 
that the behaviour of water passing through pipes is 
a thing that can be absolutely predicted. The present 
calculation shows us general principles. But, since it 
does not take into account the resistance of the air to 
such an irregular surface as that of a bird’s wing, it 
does not enable us, in the case of a particular bird, to 
fix the exact angle at which he must set himself, if he 
wishes, having attained a certain velocity, to glide 
onward and maintain his level. 
Though the resistance offered by the air to surfaces 
like those of a wing cannot be accurately measured, 
yet it is possible to obtain some notion of its amount. 
If you hold an umbrella so that the inside faces a 
strong breeze, it feels a great strain, and is likely to 
give at every point. If, on the other hand, the out- 
side meets the blast, the air passes harmlessly off its 
slippery convexity. Herr Lilienthal, the German 
engineer, who has sailed through the air a distance of 
over 500 yards with only a slight descent, once, as he 
was carrying his wings to the place of trial, was 
cheered by the fact that the air gathered in their 
curved under-surfaces and relieved him of all the weight. 
If we take a single big wing feather and wave it 
through the air, we feel that the resistance varies 
according as we turn the concave or convex surface to 
