26 
Again, 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 translatory velocity {v) 
along the axis. 
Time of one revolution = 
space 
velocity 
27T 
u 
H = Time x velocity = 
2ttv 
u 
Therefore, by subtraction, there results 
H'-H = 27t 1-, + ^''-- I (16) 
17. In formula (16), although the form and dimensions 
of the propeller, together with the -resistance to motion, 
might be such as to make the quantity 
rcosv V 
COSa 
equal to zero or even negative. Still, it would be surprising 
to find by experiment that (H'-H) in equation (16), was 
either negative or even zero. 
In all probability the quantity 
V rcosj/ 
— -[- 
u COSa 
would be considerably in excess of the ratio v upon u, pro- 
viding the quantities Y and v! were correctly measured by 
experiment. 
Hitherto, when negative slip has manifested itself in 
actual experiment, as in the case of the Plumper and Hanni- 
bal, it has done so only on the assumption, which is by no 
means a correct one, of V = 0. 
The foregoing investigation appears to explain clearly 
the perplexing mystery of negative slip, and it may be 
added that the arguments and conclusions with respect to 
negative slip advanced in these pages are not, in the slight- 
est degree invalidated by the circumstance of having used 
the element {a) of the propeller blade instead of the propeller 
itself. The reason of this is, that the slip of the element {a) 
is exactly the same as the slip of the ordinary screw pro- 
