INVESTIGATED HY THE METHOD OF JET VIBRATION. 349 



The equation of the jet Ijecomes then 



r = 07746 . 0'1647 /Vl318 + 0'1440 cos 2<j> . cos J^L+0'0138 cos 4<. cos -22L+ ...) 



= 0-1444 + 0-01837 cos 2<. cos 



3*932 



. cos 4<. cos 



1 ' 



+ 0-0001913 cos 6<A. cos - 



' 



0'04G 



(10), 



from which the co-ordinates for every point of the surface of the jet can l>e calculated. 

 The profile line resulting from < = in (10) has special interest. This line is shown 

 in fig. 1. In order better to judge the form of the curves the height is enlarged 



10crr\. 



Fig. 1. 



fifty times in relation to the length. It can be seeu that the form of the curve is 

 mainly determined by the original vibration corresponding to n = 2, but that at the 

 same time also the other vibrations cause perceptible deviations. 



In the measurements made by Lord RA.YLEIGH, PICCARD, and MEYER the wave- 

 length X, is determined as the length between two successive summits of the profile 

 line of the jet. It can be seen in fig. I, that this length can vary and deviate 

 somewhat from the wave-length X. In order to illustrate the size of these 

 deviations for the jet corresponding to (10), drawings of the summits of the profile 

 line are shown in fig. 2. By calculation it is found that r is maximum for 

 z = 0, 2 = 3-932-0-109 cm., z = 2. 3'932-0'171 cm., and z = 3. 3'932 + 0'211 cm. 



As above stated, X, = 3 '932 cm. 



The wave-lengths measured in this manner are 



X -' = 3-823 cm. ; X 1 '" = 3'870 cm. ; X 11 '"' = 4'314 cm. 



The errors stated in per cent, of X 3 are respectively 2'6, T6, and +97. 



The error can be reduced by taking the mean value of several lengths. On the 

 other hand, the amplitudes of the supplementary vibrations have been greater in 

 proportion to the fundamental vibration with almost all the measurements up to now 

 than in the instance mentioned here. 



Even with relative measurements as those made by MEYER* these reasons can 



* MEYBR, for, eii. 



