102 NATURAL SCIENCE [August 1898 



APPENDIX III 



Resistance and Horse Power 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. 



IfH.P.=*(PW)- « = !* %?"?*"? = 2-5. 

 log 421 - log 321 



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 x where V = velocity, 

 Horse-power =JcV x x. V= k F"*+l. 



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 x , again 



H.P. = IVx+l + mV' ix - * where I and m are constants. 

 So that unless x = 2, the H.P. required no longer varies as Vx+1. 



I have nowhere seen this pointed out, and should be glad of any information on the 

 subject. 



