102 NATURAL SCIENCE [August 1898 
APPENDIX III 
RESISTANCE AND Horsk Powkr AS A FuNCTION OF VELOCITY 
In the experiment referred to in the article, the H.P.’s in the two cases were ‘294 and 
151 respectively, while the velocities were in ratio 421 to 321. 
fF ce 009 294—log 151, 
Comparing this with examples of towing vessels this would appear rather low. 
There is, however, a difference between towing, and propelling with internal 
mechanism. 
In former case if Resistance=kV* where V = velocity, 
Horse-power=kV2% x V=kVe+, 
In the latter case, in which the vessel is propelled, for example, with a screw or oar, 
the force of propulsion is obtained by generating momentum in the water. Making the 
apparently legitimate assumption that the mass of water encountered by the propeller 
varies as the velocity of the vessel (probably more correct in the case of the screw than 
with an oar), since the rate at which the propeller is passing the main body of water 
is V. 
If Resistance=kV~, again 
H.P. =/V2+1+4+mV22-1 where 7 and m are constants. 
So that unless 7=2, the H.P. required no longer varies as V7+1. 
I have nowhere seen this pointed out, and should be glad of any information on the 
subject. 
