EMERSION AN ELEMENT OF RESISTANCE. 59 



only at low velocities, and at higher velocities it will increase very slowly, 

 and will even diminish as the velocity is increased. 



4. The Resistance increases very slowly from about 25 to 29 miles an hour, at 



which point the velocity being - of that which is the measure of the force 



of gravity for a given point of the earth's surface, or about 43 feet per se- 

 cond, and 29 miles an hour ; the resistance has attained a maximum, and 

 rapidly decreases, and continues to do so. 



5. At 43.8 miles an hour (when v = 2g), the floating body emerges wholly from 



the fluid, and skims its surface. 



It should be observed, that the phenomena corresponding with these results 

 will be modified when the depth of the fluid is small, by the wave and other ele- 

 ments of resistance, upon the consideration of which we are to enter in another 

 part of this paper. 



It is also to be observed, that the form of the floating body is no element in 

 the formula of emersion — that the law is a general one. This caution is the 

 more necessary, because Mr Challis has given a formula of emersion for a sphere, 

 derived from the summation of all the elementary forces acting upwardly upon 

 the sphere, which are obtained from resolving the obhque forces on each point of 

 the sphere into co-ordinates of vertical and horizontal action. The particular 

 case treated by Mr Challis, although true for a sphere, does not apply to an 

 elongated body, so as to diminish its emersion, but merely changes its position, 

 and in such a manner as to increase, instead of diminishing, the resistance of the 

 fluid. The effect he refers to is a gi-eat evil incident to a certain form of vessel, 

 which otherwise possesses considerable advantages. The law of Diminished Re- 

 sistance and Immersion which I have developed, is perfectly general in its apph- 

 cation, and wholly independent of casual form. It has for its foundation merely 

 the simple principle. That gravity, acting on a soUd body during a given unit of 

 time, is a constant quantity, and that the displacement of the fluid by the weight 

 of the body, being a quantity that increases both with the velocity and the quan- 

 tity of that displacement, must ultimately be equal in quantity, as it is opposite 

 in direction, to the pressure of the soUd downwards by gravity. 



Section IL— On the Motions that are communicated to the Particks of a Fluid by 



the Motion of a Floating Body. 



Many of the attempts which have been made to verify by experunent, or to 

 discover empirically, the laws of the motion of floating bodies, have been defeated 



