336 Mr. T. Tate on certain remarkable Lares 



This formula expresses the time of discharge of any liquid 

 from a small closed tube at diflfereut angles of inclination 6 to 

 the horizon, « and /3 being small constants varying slightly with 

 the section of the tube and the cohesive quality of the liquid. 



Here^x Lwill be a minimum when sin(2^—«—/3) +sin(a— /8) 

 is a maximnm, or when sin {26— a— ^) is a maximum; in this 

 case 



*^^ ,.^=45°+^, (2) 



■which expresses the angle corresponding to the minimum time 

 of descent of the liquid. 



When ^xL = oo, 6 = ^, which gives the limiting angle of 

 resistance. 



Let 6i be put for the angle of minimum time of discharge, 

 O^ + q and O^ — q for the angles of equal times of discharge j then 

 from equation (1) we get 



sin{2(^i + <7)-«-/9} = sin{2(^i-<7,)-«-/3}; 



substituting the value of 6^ given in equation (2), we get 



sin (90^ + 2(7) = sin {90°-2y,) ; 

 hence we obtain 



that is to say, the lines corresponding to equal times of discharge 

 lie on opposite sides of the line corresponding to the minimum 

 time of discharge, and are equally inclined to it. 



Putting T, for the observed time of' descent at the angle ^, of 

 minimum descent, Tg for the observed time of descent at the 

 angle of 90°, and /3 for the observed limiting angle of resistance, 

 then we find the following values of the constants in for- 

 mula (1): — 



«+/3 = 2^,-90; u = 29,-90-/3; 



^^ l+sin(a-/8) 



The experiments hereafter recorded were made with the appa- 

 ratus represented in the annexed diagram. 



