GLIDING 



11 



to drift, yet the actual amount of lift will be but 

 small. If the strongest man among the survivors 



w 



Fig. 7. 



b d is the plane, w the wind blowing horizontally against it. 

 b c is the cosine of the angle at b, d c the sine of the angle. Pro- 

 duce c d to e, making d e = b c. From d draw d p at right 

 angles to b d. From e draw e f at right angles to d e. (This 

 decides the length of the line d f). Draw f g parallel to e d 

 and d g parallel to f e. Let d f represent the force of the wind 

 acting at right angles to b d. It can be resolved into two forces, 

 f e and fg(=ed). e d we know= b c, and it can be shown 

 that f e = d c. 



In the triangles d e f, b c d, b c = d e, and the angles at e 

 and c are each right angles. If we could prove a second angle 

 = a second angle, the triangles would be equal in every respect. 

 Now the angles at d together = two right angles, and the angle 

 b d f is a right angle. Therefore b d c with f d e makes one 

 right angle. But d f e with f d e makes one right angle. There- 

 fore angle d f e = angle b d c. The triangles then are equal, 

 and the two sides f e and d e = respectively d c and b c. But 

 f e represents drift and d e lift. Therefore d c, the sine of the 

 angle at b, represents the drift, while b c, the cosine, represents 

 the lift. 



of a starving ship's crew is able to take for himself 

 nineteen-twentieths of the last biscuit, nevertheless 

 he gets but a poor meal ; and it is obvious that if 



