4 Trans. Acad. Sct. of St. Louis. 
The first term of this result is identical with the value of K. E. 
given in equation [IV ], and its value is accordingly SP, the 
wo'v? 29P 
second term, ao, when we substitute for v? its value —2— 
Aw 
from [III], becomes Pv’, which is exactly what should have been 
anticipated; viz: the work done per second in overcoming the 
resistance of the air to the motion of the ship. Accordingly 
the horse-power required for the ship when in motion is 
He eo ee bs 
The atmospheric resistance of still air upon a moving ship is 
taken to be the same as the resultant action of moving air upon 
a stationary ship, the velocity in the two cases being the same. 
The general equation for such resistance is in pounds 
P=CrRV? [TX] 
in which & is the radius of the maximum cross-section of the air- 
ship in feet; and V, as before, is the velocity of the ship in miles 
per hour. Cis a coefficient dependent upon the shape of the ship 
and the nature of its surfaces. An approximate value of C for a 
cigar-shaped air-ship with fairly smooth surfaces is 0.002. An 
exact method of determining P would be to measure the pull on 
a cable when the ship is anchored against a steady wind blow- 
ing V miles per hour. Probably no two ships would yield the 
same value of C in formula [IX]. 
3. DISCUSSION OF FoRMULA[V] FOR THE CASE OF AN ANCHORED 
Surp, with A Motor DRIvine A PROPELLER WHOSE RapIus 
IS 7. 
8P? er 
=575. = 0.0515 rT 
For a given value of P it is seen that the horse-power required 
varies inversely as the radius of the propeller. This suggests the 
economy of large propellers, or of an increase in their number. 
There are of course practical objections to very large propellers, 
and also to a large number of propellers. I venture to suggest 
for a ship three propellers, one rather low at the stern, and one 
on each side, well forward, and higher up, abreast or above the 
