1879.] 



the Capillary Phenomena of Jets, 



75 



Table I. — November 11, 1878. 

 Pressure. Wave -length. */ (Pressure). 



253 104 91 



216 91 84 



178 81 76 



144 70 69 



113* 61* 61* 



83 51 52 



58 42 43 



39 33 36 



21 24 26 



The agreement of the second and third columns is pretty good on 

 the whole. Small discrepancies at the bottom of the table may be 

 due to the uncertainty attaching to the zero point of pressure, and 

 also to another cause, which will be referred to later. At the higher 

 pressures the observed wave-lengths have a marked tendency to in- 

 crease more rapidly than the velocity of the jet. This result, which 

 was confirmed by other observations, points to a departure from the 

 law of isochronous vibration. Strict isochronism is only to be expected 

 when vibrations are infinitely small, that is, in the present application 

 when the section of the jet never deviates more than infinitesimally 

 from the circular form. During the vibrations with which Table I is 

 concerned, however, the departures from circularity are very con- 

 siderable, and there is no reason for supposing that such vibrations 

 will be executed in exactly the same time as vibrations of infinitely 

 small amplitude. Nevertheless, this consideration would not lead to 

 an explanation of the discrepancies in Table T, unless it were the fact 

 that the amplitude of vibration increased with the pressure under 

 which the jet issues. 



As a matter of observation the increase of amplitude is very ap- 

 parent, and was noticed by Magnus. It is also a direct consequence 

 of theory, inasmuch as the lateral velocities to which the vibrations 

 are due vary in direct proportion to the longitudinal velocity of the 

 jet. Consequently the amplitude varies approximately as the square 

 root of the pressure, or as the wave-length. The amplitude here 

 spoken of is measured, of course, by the departure from circularity, 

 and not by the value of the maximum radius itself. 



The law of the square root of the pressure thus applies only to small 

 amplitudes, and unfortunately it is precisely these small amplitudes 

 which it is difficult to experiment upon. Still it is possible to approach 

 theoretical requirements more nearly than in the experiments of 

 Table I. 



The next set of measurements (Table IT) refer to an aperture in the 

 form of an ellipse of moderate eccentricity. Two wave-lengths were 



