SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 307 



between the summits. These distances can be directly put equal to the wave-lengths 

 sought, for, considering the jet-axis as a straight line, the wave-profile can, apart 

 from possible irregularities, be expressed with great approximation by (see p. 296) 



r = a + be~" cos kz-\ --- e~ 2e * cos 2kz-\ --- e~ 2 '~. 

 24 a 8 a 



Finding the summits z n of this curve by putting 3r/3z = 0, we get approximately 



TT 



The first term on the right side is a constant, and with the values of e, k, and />/, 

 which correspond to the experiments carried out, the second term is quite negligible 

 as compared with the accuracy of the experiments. 



P. O. PEDERSEN has also measured the wave-length on a jet with very small wave- 

 amplitudes. The author mentions* that it has not been possible for him to produce 

 jets with such regular vibrations that he could use a method for the determination of 

 the wave-lengths which he describes and which in the, main features is of the same 

 nature as that described above. He therefore employed another method, which is, in 

 the main, as follows : Illuminating the jet with a parallel beam of light, the rays 

 twice refracted and once reflected form a wave-like image on a photographic plate, 

 and as the amplitude of the image is much larger than that of the jet, the wave- 

 length could be measured directly on the image. By this method the wave-length is 

 determined as mean wave-length on a longer jet-piece. As however will appear 

 from experiments, which will be described later, it is of the greatest importance to be 

 able to determine the single wave-length with great enough accuracy for the 

 variations of the wave-lengths to be examined. 



The image -format ion of the jet was also used in the examination of the jets 

 mentioned on p. 299. If the tube was turned around its axis at the same time as the 

 ' images were observed in the telescope, the appearances of these changed as the 

 curvature of the profile of the jet seen from above gradually varied, the points 

 A and B being displaced. The variations in the appearance of the images were most 

 rapid in the moments in which the curvature of the profile was near to O. Every 

 time the curvature became O, the points A and B fell together and a regular elliptic 

 luminous spot without structure was seen in the telescope. To the tube was fastened 

 a disk with a graduation, and every time the luminous spot mentioned appeared in 

 the telescope during the revolution of the tube the graduation was read oft'. If the 

 jet were symmetrical with respect to two perpendicular planes, the places read off 

 must lie symmetrical on the circumference of the circle and also be the same at 

 different distances from the orifice. This examination was very sensitive and it 

 showed, too, that not all of the tubes examined satisfied the conditions to a sufficient 



* PEDERSEN, foe. cit., p. 368, 

 2 R 2 



