360 MR. P. O. PEDERSKN ON THE SURFACE-TENSION OF LIQUIDS 



TABLE I. 



In these evolutions it is supposed that /, = 1 2 (see fig. 7), a condition easy to satisfy 

 with great exactness. 



It can easily be seen that all the foregoing continues to be true in the main, even if 

 the velocity of the jet is not the same over the whole cross-section. With use of the 

 method on jets that are not cylindrical there are some complications. Reference will 

 only be made here to the jets investigated in this paper, the equation of which is 

 r = a + b cos n<f> . cos kz. 



When n is an even number, the oblique sections produced by the edges k can, 

 without appreciably altering the volume of -the piece cut out, be replaced by the 

 normal sections through the points where the axis meets the oblique sections. Ifn 

 is uneven, this will not be the case, but the deviation will be small for all the jets 

 investigated in this work. The only error to be considered will thus result from the 

 circumstance that the volume of the jet which is cut oft' by two normal sections, at a 

 constant distance from each other, will vary a little with the position in relation to 

 the stationary waves of the jet. To investigate the amount of this error the volume 

 of the jet V L between the planes z = and z = L is determined : 



f$=2ir (V=I, 

 ^ 

 4=0 J*=ii 



= 77-L 



4/ 



If X is the wave-length, then k = 27T/X and 



V L = 7T . L . 



~ X sin L 



4 / 16 X 



(9). 



(10). 



If X is equal to the distance between the edges (this distance is always greater, the 

 actual error consequently smaller than that calculated), then equation (10) shows 

 that the greatest volume that can be cut out is 



whilst the average value is 



= XTT (a 2 



