258 



NEWTON S PRINCIPIA. 



height through which a body must fall to acquire this 

 velocity, 



Let there be a hole E F in the centre of the bottom, and 

 let the whole cavity of the vessel which encompasses the 

 falling water be full of ice, so that the water may pass 

 through the ice as through a funnel. The particles of 

 water are supposed to cohere a little, that in falling they 

 may approach each other, and thus instead of being 

 divided into several, they will form a single cataract. We 

 shall also suppose the form of the 

 funnel such that the particles of 

 water fall freely down. The lines of 

 motion will form surfaces of re 

 volution whose axis is the axis of the 

 funnel, and the forces of cohesion act 

 ing on any particle have a resultant 

 normal to these surfaces. The velocity 

 of the particle will not therefore be 

 affected by this force, and if z be the 

 depth of any particle below the plane 

 A B and v its velocity we have 



E G 



each particle arrives with the same velocity at the aperture 

 E F. The form of the funnel was supposed such as to 

 admit of this motion; hence the area of any section must 

 be inversely as the mean vertical velocity of the fluid for 

 all parts of that section. 



Now, if the particles of water did not exert any action 

 on the icy funnel through which it flows we might suppose 

 this funnel dissolved into water without changing the cir 

 cumstances of the motion. But the descending fluid does 

 act on the dissolved ice, and the whole nature of the motion 

 is changed. But Newton argues that nevertheless the 



