366 ON THE FORCE OF THE RUDDER, &C. 



above quoted, as 840 is to 729 (for 60), so is 2205 to 1Q13 pounds, 

 the perpendicular force. 



This effort will no doubt appear very inconsiderable when coin, 

 pared with the effect it produces, which is to turn a mass of 900 

 tons ; but it must be observed that this effort is applied at a very 

 great distance from the point of rotation and from the vessel's centre 

 of gravity ; for this centre is a little beyond the middle of the vessel 

 towards the prow, as the anterior part swells out, while the poste- 

 rior tapers towards the lower works in order that the action of tlje 

 rudder may not be interrupted. On the other hand, it can be 

 shewn that what is called the spontaneous centre of rotation, the 

 point round which the vessel turns, is also a little beyond the mid- 

 dle and towards the prow; hence it follows, that the effort applied 

 at the extremity of the keel, towards the stern, acts to move the" 

 vessel's centre of gravity, by an arm of a lever 12 or 15 times as 

 long as that by which this centre of gravity, where the weight of the 

 vessel is supposed to be united,, exerts its action. And lastly, there 

 is no comparison between the action exercised by this weight when 

 floating in water, and that which it would exert if it were required 

 to raise it only one line. It needs therefore excite no surprise, that 

 the weight of one ton, applied with this advantage, should make 

 the vessel's centre of gravity revolve around its centre of rotation. 



If the ship, instead of going at the rate of two leagues per hour 

 sails at the rate of three, the force applied to the rudder will be to 

 that applied in the former case, in the ratio of nine to four; conse- 

 quently, if the position of the rudder be as above supposed, the 

 actual force will be 3719 pounds, or rather 4304 pounds: if the 

 velocity of the vessel were four leagues per hour, this force, in the 

 same position of the rudder, would be four times as much as at 

 first, or 6612 pounds, or rather 7652 pounds. 



Hence it is evident why a vessel, when moving with rapidity, is 

 more sensible to the action of the helm ; for when the velocity is 

 double, the action is quadrupled ; this action then follows the 

 square or duplicate ratio of the velocity. 



If the water moves in a direction parallel to the keel when it 

 impels the rudder, it will be found that this angle ought to be 54 

 degrees 44 minutes j but, as already observed, the water is carried 

 along in an angular manner towards the, direction of the keel con- 



