248 
Mr T. Tredgold on Steam-Boats. 
sumption of fuel to produce a given effect, is much greater than 
in engines on land ; and, perhaps, much in consequence of the 
imperfection of the draught of the chimney, and the limited 
space for the boiler. The former might be easily remedied by 
an artificial blast, directed so as to force the flame to expend its 
heat on the boiler. And, while on this subject, it well deserves 
the attention of those who wish to improve steam-boats, to adopt 
some more effective methods of confining the heat to its proper 
object, and particularly where the engineer and firemen are ex- 
posed to it. 
When the paddles of a steam-boat are in action, there is a 
point in each paddle, wherein, if the whole reaction of the fluid 
was concentrated, the effect would not be altered ; this point 
may be called the centre of reaction. Tt has not been determin- 
ed for the case under consideration, but may perhaps form a 
subsequent object of research. 
We suppose the fluid to be at rest, and the velocity of the 
centre of re-action to be V, and the velocity of the boat to be v ; 
then V — v is the velocity with which the paddles strike the 
water. Or, the difference between the velocity of the paddles 
and the velocity of the boat is equal to the velocity with which 
the paddles act on the water ; hence, when these velocities are 
equal, the paddles have no force to impel the boat ; and, if the 
paddles were to move at a slower rate, they would retard it. 
Now, as (V — tt) is the velocity, the force of the reaction will 
be as (V — tt ) 2 , for this quantity is proportional to the pressure 
which would produce the velocity V — tt. But, during the ac- 
tion of the paddle, the water yields with a velocity V — v , and 
since the velocity of the boat is tt ; the effective power is as 
V — v : v : : (V — tt) 2 : v (V — tt). And the effect of this 
power in a given time, is a maximum when tt 2 (V — tt) is a 
maximum, that is, when 2 V = 3 tt, or when the velocity of the 
centre of reaction of the paddles is 1J times the velocity of the 
boat. 
It is desirable that the action of the paddles should be as 
equable and continuous as possible, unless they be arranged so 
that the variation of the power of the engine may coincide with 
the variation in the action of the paddles. But, in attempting 
to render the action of the paddles equable, their number ought 
