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L. On certain remarkable Laws relating to the Cohesion of Fluids. 

 By T. Tate, Esq."^ 



IP a small glass tube, closed at one extremity and filled with 

 liquid, be inverted, the liquid will remain suspended by the 

 pressure of the atmosphere, provided the cohesion of the particles 

 of the liquid at the lower extremity remains unbroken ; but if 

 the cohesion .of these particles be broken, the liquid will be dis- 

 charged from the tube with a velocity depending upon the dia- 

 meter of the tube and its inclination to the horizon. From au 

 extensive series of experiments with tubes varying from -3 inch 

 diameter to -12 inch diameter, I have found that for all tubes 

 within these limits, the minimum time of descent of the liquid 

 takes place at, or very nearly at, 50 degrees inclination to the 

 horizon. 



When the tube is held in a horizontal position, the liquid, 

 from the combined action of cohesion and the lateral pressure of 

 the liquid, assumes the form shown in the 



annexed diagram. Now when the tube ^,^^^j==^^^ 



is inclined to the horizon, this pressure 



approximately varies with the cosine of the angle of inclina- 

 tion ; but at the same time the tendency of the liquid to run 

 down the plane varies with the sine of its inclination, so that, 

 irrespective of the resistance of friction, the force accelerating 

 the descent of the liquid will approximately vary in the com- 

 pound ratio of these functions. Hence it follows that the mini- 

 mum time of descent of the liquid must take place at an inclina- 

 tion lying somewhere between the horizontal and vertical posi- 

 tions of the tube. 



Let L = the length of the column of the liquid in the tube i 

 inches. 

 t = the time of descent of the liquid in seconds for each 



unit of length of the tube. 

 T = ^ X L the time of descent of the whole column. 

 d = the corresponding inclination of the tube to the 

 horizon. 

 a, b = constants to be determined from the results of ex- 

 periment. 

 u,^ = constant angles, also to be determined from the results 

 of experiment. 

 Then we assume 



m __^ , T a - d 



~^ '~8in(^-yS)cos(^-a)'^sin(2^-«-;8)+sin(a-/3) +*•(!) 



* Communicated by the Author. 



