4 Trans. Acad. Sci. of St. Louis. 



The first term of this result is identical with the value of A'. E. 



1 f* 



given in equation [IV], and its value is accordingly — P'; the 



r 



second term, — - — , when we substitute for v^ its value -|— 

 ^9 ^ Aw 



from [III], becomes Pv', which is exactly w^hat 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 



fl. = 4(i6^ + ?2y)^ P(y^) 



550 \ r 15 / 550 



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 = CirW^V [IX] 



in which R 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. C is 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 ofIan Anchored 

 Ship, with a Motor Driving a Propeller Whose Radius 

 IS r. 



opi pi 



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 



