354 MR. P. 0. PEDERSEN ON THE SURFACE-TENSION OP LIQUIDS 



Thus the difference shown in the time of outflow is wholly explained in this 

 manner. 



ISARN himself explains the difference mentioned as originating from different 

 contractions, and calculates on the basis of such measurements the coefficient of 

 contraction. There can be no doubt, however, that this is incorrect, as the influence 

 of the surface-tension on the coefficient of contraction certainly is not great, as will be 

 shown later. 



If this reduction of the velocity on account of the capillary-pressure in the jet were 

 the only deviation from TORRICELLI'S formula, it could be corrected and the velocity 

 accordingly calculated ; but as the diameter of the jet becomes smaller the value of a 

 is also reduced and this coefficient becomes to a great degree dependent upon the 

 nature of the edge of the hole, so that in every case it is necessary to determine the 

 value of a, or, in other words, determine the velocity of the jet in another manner. 



Lord RAYLEIGH*, who used this method to determine the velocity of the jet, says 

 with regard to it : " The pressure at any moment of the outflow could be measured 

 by a water manometer read with a scale of millimeters. Some little uncertainty 

 necessarily attended the determination of the zero point ; it was usually taken to be 

 the reading of the scale at which the jet ceased to clear itself from the plate on the 

 running out of the water." 



According to the above, this method can not be taken as a satisfactory solution of 

 the question. 



Direct measurement of the velocity of the jet can be made in several manners. 

 TH. VAUTlERf added small drops of another fluid and determined the velocity of the 

 drops by taking photographs on a plate moving with a known speed. The method 

 seems to be good so long as the diameter of the jet is ' not too small (in VAUTIER'S 

 experiments the diameter of the hole was 576 mm.), but with small diameters the 

 method is useless on account of the risk of noticeable change both in the surface- 

 tension and in the coefficient a on account of the additional alien liquid. 



Another and simpler method J is to determine the velocity by help of the geometric 

 form of the jet. This method can also give satisfactory results for thick jets, but for 

 thin ones it is of no value. 



Besides the previously mentioned reduction of velocity on account of the capillary 

 pressure in the jet, the surface-tension produces other differences in the velocity. 

 The presence of the jet is inseparably connected with a continual production of new 

 fluid surface, and the requisite energy is essentially taken from the kinetic energy of 

 the jet as its horizontal velocity reduces. The loss of pressure, h t , corresponding to 

 this reduction is easily found to be ,m 



h-f. (2). 



dpg 



* Lord RAYI.EIGH, 'Roy. Soc. Proc.,' 29, p. 71, 1879 ('Papers I,' p. 375). 



t TH. VAUTIER, loc. tit. 



} See WINKELMANN, ' Handbuch d. Phys.,' I., "Ausfluss uud Strahlbildung," F. AuERBACH, 1891. 



