23 
(a) is equal to zero. Let v’ be the angular velocity, the 
velocity in the direction of the axis AB, respectively, which 
will produce the above described effect, then 
tw'qq^v - v'cosa = 0. 
From which. 
V 
7 
Vj 
rcosj^ 
cosa 
( 9 ) 
It now remains to find the distance H' traversed along 
the axis of the element {a) viz. AB during one revolution, 
then 
space _ 27 t 
u' 
27rrcosi/ 
Time of one revolution = 
velocity 
,-r# • 1 • 27T27 
H' = time X velocity = 
u 
cosa 
( 10 ) 
Again, to find the distance H traversed along the axis 
AB during one revolution of the element (a), when it moves 
with an angular velocity (u) and a velocity {y) in the direc- 
tion of its axis, then 
m- ^ w space 2 ttv 
Time 01 one revolution = — ~ — r— = — 
velocity 
u 
H = Time x velocity = 
2ttv 
u 
,( 11 ) 
13. The quantity H' is usually described as the measure 
of the speed of the element (a) of the propeller blade, and 
H as the measure of the speed of the vessel propelled. 
When H' is equal to H, then the element (a) of tlie pro- 
peller is said to move as fast as the vessel. 
When H' is less than H, then the element (a) is moving 
faster than the vessel. 
When H' is greater than H, then the element (cC) is not 
moving so fast as the vessel. 
The quantity (H' — H) has been usually designated by 
naval architects the sli]) of the element (ct). 
The value of this sliy> is readily found from equation (10) 
and (11) as follows; 
= - j (12) 
I cosa U ) ' ' 
