352 MR. P. 0. PEDERSEN ON THE SURFACE-TENSION OF LIQUIDS 



in B will keep itself practically constant, independently of the quantity used in the 

 jet apparatus. This is, of course, on the understanding that the diameter of the 

 syphon is sufficiently large. 



Experiments have shown that with this arrangement, and for jets not exceeding 

 2 mm. in diameter, the water surface in B will vary at most 0'2 mm., and the 

 apparatus can stand and operate by itself day and night. 



The above-mentioned arrangement is especially convenient for investigation of a jet 

 produced from ordinary tap-water, and was used in practically all the preliminary 

 investigations for judging the exactness and practicability of the methods of 

 measuring. As these investigations take, as a rule, a long time, it is very important 

 that the pressure be kept constant. 



For other fluids that are available only in limited quantities this method cannot, of 

 course, be used. In these cases the author has, as a rule, employed the usual modus 

 operandi with decreasing pressure. This will be more fully explained under the 

 description of the experiments. 



Determination of the Cross -section of the Jet. 



5. When using the present method for determination of the surface-tension it is 

 necessary besides the wave-length to know two of the three following quantities : 

 velocity of the jet, the sectional area of the jet, and the discharge. This last named 

 is easiest to determine with sufficient exactness, and will, therefore, in every case be 

 measured. The choice then remains between measuring the velocity of the jet or the 

 cross-sectional area, but before making this choice I will give a short summary of the 

 methods that are available at this moment to determine the velocity and sectional 

 area of a jet. 



The velocity V can be determined by use of TORRICELLI'S formula V = ay/^H), 

 where H is the pressure, g the acceleration of gravity and a a coefficient. Many 

 experiments have been made to investigate the exactness of TORRICELLI'S formula. 

 The results of these investigations are, mainly : for fluids with little viscosity, with 

 not too high pressure, and, lastly, with holes the diameter of which exceeds 5 mm., 

 the formula is practically correct, as the coefficient a is very nearly equal to 1 ; for 

 water a = - 97 to 0'99. Special reference can be made here to TH. VAUTIER'S* 

 careful investigations on this subject. 



With this in view, it was the author's original intention to determine the velocity 

 of the jet in this manner ; it, however, soon appeared that, just in the circumstances 

 which have especial interest in the present instance, the deviations from TORRICELLI'S 

 formula are very important. It is for this reason that, so as not to use too great a 

 quantity of fluid, it is necessary to use thin jets, for example with a diameter of 



* TH. VAUTIER, ' Compt. Rend.,' 103, p. 372, 1886; ' Th^se pn's. a la Fac. de Science d. Paris,' 1888; 

 'Ami. China. Phys.,' (6), 15, p. 433, 1888; ' Journ. d. Phys.,' (2), 8, pp. 301, 396, 1889. 



