NEWTON S PRINCIPIA. 301 



Bernoulli, in his dissertation, entitled &quot; Nouvelles 

 Pensees sur le Systeine de Descartes avec la Maniere d en 

 deduire les Orbites et les Aphelies de Planetes,&quot; has made 

 two objections to these investigations. First, that 

 Newton in calculating the amount of the friction between 

 two layers of fluid has not considered the pressure between 

 those layers; and, secondly, that in calculating the effect o 

 the friction, he has not taken into account the arm of the 

 lever at which it acts. Bernoulli then attempted to show 

 that the density, being supposed to vary with the distance, 

 the motion in the vortex will agree with that given by 

 Kepler s third law. 



But D Alembert* showed that this does not follow from 

 Bernoulli s own equations, for it appears that he has, in 

 integrating, omitted the lower limit ; thus he considered 



771 



m-\ j X 



x a x = , 

 o fn. 



which is true only when m is positive, whereas he after 

 wards assumes w= J. The first of Bernoulli s objections 

 has been anticipated by Newton himself. In the scholium 

 to the fifty-second proposition, he says, &quot; The matter by its 

 circular motion endeavours to recede from the axis of the 

 vortex, and therefore presses all the matter that lies be 

 yond. This pressure makes the attrition greater and the 

 separation of the parts more difficult, and by consequence 

 diminishes the fluidity of the matter.&quot; D Alembert re 

 marks that Mr. Musschenbroek in some very exact expe 

 riments, found that when the velocity is small, the friction 

 was proportional to the velocity, and not to the pressure. 

 That similar results have been obtained by later experi 

 mentalists is evident from what has been said in a pre 

 vious chapter. 



* Traite des Fluides, p. 408. 



