240 



above the statical immersion, and the resistance diminished, — the 

 reverse of the fact. It is farther proved by experiment, that when 

 the emergence which Professor Challis has examined takes place 

 to the greatest extent, the resistance is at its maximum, whereas, 

 according to him, it should be a minimum. 



Whatever use, therefore, practical men may be induced to make 

 of the reasoning of Mr Challis, it may be expected to lead them to 

 results the reverse of what they intended. 



The kind of emergence of a floating body from the surface of a 

 fluid, which Professor Challis states that he wa^ the first to explain 

 on mechanical principles, is therefore of a diflFerent nature from 

 that which he intended to explain, and is due only to the peculia- 

 rity of the form of the body. It is not the kind of emergence to 

 which any of the phenomena he wished to explain are due- 



The essential principle on which Mr Russell has explained the 

 tendency to emergence of all bodies at high velocities, indepen- 

 dent of their figure, is this : The gravity of a body is the cause and 

 measure of its displacement. This gravitation, during a given in- 

 terval of time, is a given constant quantity. The quantity of fluid 

 displaced by a floating body in motion, in virtue of the gravitating 

 force, is variable, increasing with the velocity. The gravitating 

 force of the body during a second is a given quantity, acting down- 

 wards. The pressure of all the fluid displaced in a second is ano- 

 ther force opposed to the former, and acting upwards on the bottom 

 of the vessel. From these two forces an equation is formed, which 

 gives the amount of emergence depending only on velocity, and 

 an expression results, into which the former does not enter : this 

 result was afterwards confirmed by experiment. 



It is only necessary, in conclusion, to state, that these discussions 

 have nothing to do with the phenomena of the wave, to which alone 

 the chief anomalies of resistance are due. 



