38 
PITCH OF THE SCREW. 
that up to a certain point we may, by reducing the pitch, decrease the angular 
loss without increasing the surface friction to a serious extent; and so, vice versa, 
we may decrease the surface friction without our having an angular loss equal 
to the power thus saved. When so much is yet to be ascertained by practice, 
it is a most encouraging feature in the trials with the screw of the Archimedes, 
the proportions of which were given without any data derived from experience, 
that the results have been so satisfactory as they have proved. 
PITCH OF THE SCREW. 
In ascertaining the pitch of the screw it is obviously necessary that the following 
circumstances should be considered, namely, 
The proposed velocity of the vessel; 
The best velocity of the screw; 
The amount of slip or recession. 
If we suppose the vessel to be moved through the water a given distance, say 
from a to b, fig. 29, and the screw be allowed to revolve without friction, any point 
Fig. 29. 
in its periphery would describe an angular line, which, if generated upon a plane 
surface, may be represented by a c. In this case the pitch is equal to the motion, 
and we have no slip. But if we suppose the vessel to be propelled by the screw, 
and the slip to be equal to one-fifth of the vessel’s motion, then as the latter 
advances, the water is displaced to an extent equal to the space contained between 
the parallel lines a c and d e. Hence, in order to find the true pitch, draw the