264 NEWTON S PRINCIPIA. 



a sphere, and a spheroid, of equal breadth be placed suc 

 cessively in the middle of a cylindric canal, so that their 

 axes may coincide with the axis of the canal, these bodies 

 will equally hinder the passage of the water through the 

 canal. The resistances will then be equal. The resistance, 

 therefore, on a sphere will be C v 2 p, where C is the area 

 of one of its great circles. 



3. The investigation of this question, as given by Newton 

 in his first edition, was very erroneous. He had totally neg 

 lected the contraction of the vein after the fluid had passed 

 the orifice ; hence he had deduced that the velocity of the 

 efflux was that due to only half the height of the water in 

 the vessel. This mistake he afterwards corrected, but the 

 investigation still remains open to very serious objections. 

 For it is quite certain that the first case considered by 

 Newton in which the water descends by a funnel bears no 

 resemblance to the actual state of the motion. The water 

 is not found to flow out in a cataract, leaving a mass of 

 unmoved water supported by the bottom. Each particle, 

 whether vertically over the hole or near the circumference 

 of the cylinder, descends in a nearly vertical direction, 

 acquiring or losing velocities in nearly the same ratio. 

 Those particles which are once in a horizontal section 

 remain very nearly in the same horizontal plane. When 

 the particles approach very close to the bottom, they acquire 

 a considerable horizontal motion, and, in consequence, the 

 issuing stream continues to contract after it leaves the 

 orifice. The manner in which Newton deduces the law 

 of resistance from the velocity of efflux is also erroneous. 

 It is very ingenious and wonderful, but at the same time 

 very uncertain. The proposition being false in principle, 

 we cannot expect a corollary founded on that principle to 

 be altogether correct. The reasoning by which the resis 

 tances to a sphere and cylinder are shown to be equal can 



