98 MECHANICAL RECREATIONS [CH. V 



proportions is not simple, but the above argument will serve 

 to illustrate the fact that the working of a machine may not 

 be similar to that of a model of it. 



Leaving now these elementary considerations I pass on to 

 some other mechanical questions. 



Sailing quicker than the Wind. As a kinematical 

 paradox I may allude to the possibility of sailing quicker than 

 the wind bloius, a fact which strikes many people as curious. 



The explanation* depends on the consideration of the 

 velocity of the wind relative to the boat. Perhaps, however, 

 a non-mathematician will find the solution simplified if I con- 

 sider first the effect of the wind-pressure on the back of the 

 sail which drives the boat forward, and second the resistance to 

 motion caused by the sail being forced through the air. 



When the wind is blowing against a plane sail the resultant 

 pressure of the wind on the sail may be resolved into two 

 components, one perpendicular to the sail (but which in general 

 is not a function only of the component velocity in that direc- 

 tion, though it vanishes when that component vanishes) and 

 the other parallel to its plane. The latter of these has no 

 effect on the motion of the ship. The component perpen- 

 dicular to the sail tends to move the ship in that direction. 

 This pressure, normal to the sail, may be resolved again into 

 two components, one in the direction of the keel of the boat, 

 the other in the direction of the beam of the boat. The 

 former component drives the boat forward, the latter to lee- 

 ward. It is the object of a boat-builder to construct the boat 

 on lines so that the resistance of the water to motion forward 

 shall be as small as possible, and the resistance to motion in 

 a perpendicular direction (i.e. to leeward) shall be as large as 

 possible ; and I will assume for the moment that the farmer 

 of these resistances may be neglected, and that the latter is 

 so large as to render motion in that direction impossible. 



Now, as the boat moves forward, the pressure of the air 

 on the front of the sail will tend to stop the motion. As 



* Qzanam, 1803 edition, vol. m, pp. 359, 367 ; 1840 edition, pp. 540, 543. 



