SECT, x.] OF STEAM NAVIGATION. 311 



when the wind can be of service, 1 and to do this with economy, the engines should 

 work expansively (see art. 419.) ; hence, the arrangement of the engine should be 

 such as would answer to work at full pressure in a calm. This condition enables 

 us to fix the power of the engine by the rate for still water ; and if the vessel has 

 sails sufficient to maintain the speed with about half the power of the engines, 

 when the wind is fair, it will be as much as can be usefully employed. The 

 greatest attention should be given to keep the centre of effort on the sails as low as 

 possible, and to arrange them so that the angle of the vessel's inclination may be 

 inconsiderable, that the wheels may not dip unequally. 



647. The average speed in still water, beyond which it does not seem to be 

 desirable to go, is ten feet per second ; that is, seven common miles, or six nautical 

 miles per hour : and at this velocity, when the wind is as powerful as it is prudent 

 to carry all the canvas, the direct effect will be only one horse power for each 

 thirty-two yards superficial. 2 



648. A fair wind also contributes to the motion of a vessel, by giving motion 

 to the sea itself; a head wind opposes its motion, and a current has a similar effect. 

 If v be the velocity a vessel is impelled at in still water by the power P, and the 

 velocity of the current be H^ n v, using the upper sign when it is with the vessel, 

 then P (1 +_ nf = the power the boat will require. 



If the stream be in the direction of the vessel's motion, and half its velocity in 

 still water, then n = '5 and P (1 '5) 2 = '25 P ; or the vessel will require only 

 one-fourth of the effective power. 



If the vessel move against the stream, the stream being half its velocity in still 

 water, then P (1 + *5) 2 = 2'25 P ; or the vessel will require 2i times the power to 

 preserve its velocity. 



649. But in ascending a stream the difference must be in the velocity, and it 



1 It is a common notion, that the sails should be used in addition to the steam power, to gain 

 greater velocity ; but this is not desirable, except for post-office packets and the like, because an 

 immense extent of canvas affords only a very small power when the vessel moves at a considerable 

 velocity ; hence, economy directs to saving fuel, rather than increasing speed. 



2 To find the effect of the wind in any other direction, and with any other velocity, let V be the 

 velocity of the wind in feet per second, a = the angle it makes with the direction of the vessel's 

 motion, v = the velocity of the vessel in feet per second, b = the angle a perpendicular to the 

 surface of the sail makes with the direction of the motion of the vessel ; then it is nearly, 



3200 cos. b 



,-^f - = the yards ot canvas, 



(V cos. (a + b) v cos. 6) 2 



equivalent to a horse power or 550 Ibs. raised one foot per second. 



