2g8 



VHILOSOPHICAL TRANSACTIONS. 



[anno 1739. 



Essay on the Measure and Motion of Effluent Water. By Dr. James Jurin, 

 F.R.S. W 453, p. 65. Translated from the Latin. Part 11, being the 

 Continuation from p. 284 of this volume. 



Of the Resistance of the Parts of Water among themselves arising from a Want 



of Lubricity. 



We must now consider that resistance of fluids whicli arises from the mo- 

 tion of its parts among themselves, and is called, by Sir I. Newton, a resist- 

 ance arising from a want of lubricity. He makes this of two sorts ; one aris- 

 ing from the tenacity of the fluid, the other from the mutual attrition or friction 

 of its parts. 



The former he thinks is uniform in a given surface, or that it produces an 

 effect proportional to the time ; and this opinion is agreeable to experiments. 

 The latter he considers as increasing in proportion to the velocity, or but little 

 less. About this however he determines nothing, for want of experiments. 



Hypothesis. — The resistances arising from the want of lubricity in water. 

 Dr. Jurin considers as in a ratio compounded of the three following. 1. Of 

 the ratio of the surface of the parts moved ; 2. Of the ratio of the relative 

 velocity with which the parts of water are moved among themselves ; 3. Of 

 the subduplicated ratio of the altitude of the fluid. All which are allowed by 

 Sir I. Newton, and most other philosophers. 



Prob. 8. — To explain the Resistance of the Parts of the Cataract which arises 



from the Want of Lubricity. 



Let r denote the radius of the hole, A the altitude of the cataract, y the 

 radius of any horizontal section, :r the altitude of the cataract above that section, 

 z the radius of any circle in that section, and v the velocity of the water in the 

 centre of the hole. 



Then uv'- will be the velocity of the water in the centre of the section 



having the radius y ; and 



fi/- the velocity in the circumference of the 



circle of the radius z; also -Z)/- the relative velocity, and Imzi the surface of 

 the nascent cylinder, to the radius z and altitude x : then, by the above 3 posi- 

 tions, the resistance of cylindric surface, is as 

 9,mzx X -2 V - X yoc = — -—xz. 



Now let <v, x, and y be considered as constant quantities, while z flows till 



