TRANSACTIONS OF THE SECTIONS. 533 



by a further increase to 9 miles, '205 = i nearly. The im- 

 mersion goes on diminishing at superior velocities in a con- 

 tinuous ratio, the emersion becoming at 20 miles -456 = | ; at 

 30, "684 = f ; at 40 miles an hour, only y'^ of the whole section 

 will be immersed ; and at 43-859 miles the elevating force will 

 exactly balance the gravitation of the vessel, and she will rise 

 entirely on the top of the water, descending to skim its sur- 

 face and again rising above it at alternate intervals of equal 

 duration. 



4. The law may be generally expressed thus : If any float- 

 ing body he put in motion with a given velocity^ the pressure 

 which it exerts downwards upon the fluid in virtue of gravity 

 is diminished by a quantity proportional to the weight of a 

 column of the fluid having the height due to the velocity; 

 and the ratio of the height of such a column to the velocity it 

 represents will express the ratio of the dynamical section of 

 immersion to the statical one, and the resistance will be that due 

 to this diminished section. 



5. Although the author has not verified this law experi- 

 mentally to higher velocities than 20 miles an hour, yet from 

 its perfect coincidence with observation up to that point, he 

 has sufficient confidence in its correctness to predict that it 

 will hold rigorously in the higher velocities ; and if either this 

 theory or a more accurate one substituted for it should be 

 found to hold, we may yet save our science from some imputa- 

 tion of sluggishness. 



Let S = section of statical immersion. 

 V = velocity of motion. 

 g = measure of gravity. 

 s' = dynamical section of immersion. 

 vs = displacement of statical section. 



— = height due to velocity. 



When s = 0, v = 2g = 64! feet per sec. 



Table showing the relation of the dynamical section of immer- 

 sion due to a given velocity, the statical section being consi- 

 dered as unity. 



Miles per hour. Feet per second. Amount of Emersion. 



1 1-46 -0228125 



2 2-92 -0456250 



3 4-38 0684375 



4 5-84 0912500 



