380 



NOTE VII. 



MOTION OP FLUIDS RUNNING OUT OP SMALL ORIFICES. 



(3.) MANY attempts were made by the mathematicians 

 who followed Newton to improve and extend the theory of 

 the motion of water running out of vases. But though 

 the results were often correct, yet the principles on which 

 their solutions were founded did not possess a character 

 sufficiently elementary to entitle them to be called axioms. 

 Maclaurin gave an extension of Newton s theory in his 

 &quot; Traite des Fluxions,&quot; liv. i. chap. 12. He argues that 

 the weight of water must be divided into three parts : the 

 first, which accelerates the motion of the surface, and is 



equal to A h -y (following the preceding notation), the 

 d&amp;gt; t 



second, which presses on the base of the vessel, and the 

 third which in the little time 8 1 communicates a velocity 

 V U to the mass V B t of fluid that flows out of the 

 vessel in that time. He assumes that these last two 

 forces are always in a constant ratio, which he supposes to 

 be that of the mass of solidified fluid to the mass of water 

 in Newton s cataract. 



Daniel Bernoulli * gave a theory founded on the prin 

 ciple that the fluid may be divided into horizontal strata 

 which remain horizontal throughout the motion and de 

 scend with a velocity reciprocally proportional to the area 



* Traite d Hydrodynamique. 



