1879.] the Capillary Phenomena of Jets. 87 



of the note, though not absolutely definite, cannot differ much from 

 that which corresponds to the division of the jet into wave-lengths of 

 maximum instability ; and, in fact, Savart found that the frequency 

 was directly as the square root of the head, inversely as the diameter 

 of the orifice, and independent of the nature of the fluid — laws which 

 follow immediately from Plateau's theory. 



From the pitch of the note due to a jet of given diameter, and issuing 

 under a given head, the wave-length of the nascent divisions can be at 

 once deduced. Reasoning from some observations of Savart, Plateau 

 finds in this way 4*38 as the ratio of the length of a division to the 

 diameter of the jet. The diameter of the orifice was 3 millims., from 

 which that of the jet is deduced by the introduction of the coeffi- 

 cient "8. Now that the length of a division has been estimated a priori, 

 it is perhaps preferable to reverse Plateau's calculation, and to exhibit 

 the frequency of vibration in terms of the other data of the problem. 

 Thus 



frequency= iSl5- • v • • (9) - 



But the most certain method of obtaining complete regularity of 

 resolution is to bring the reservoir under the influence of an external 

 vibrator, whose pitch is approximately the same as that proper to the 

 jet. Magnus* employed a Neef's hammer, attached to the wooden frame 

 which supported the reservoir. Perhaps an electrically maintained 

 tuning-fork is still better. Magnus showed that the most important 

 part of the effect is due to the forced vibration of that side of the 

 vessel which contains the orifice, and that but little of it is propagated 

 through the air. With respect to the limits of pitch, Savart found 

 that the note might be a fifth above, and more than an octave below, 

 that proper to the jet. According to theory, there would be no well- 

 defined lower limit ; on the other side, the external vibration cannot 

 be efficient if it tends to produce divisions whose length is less than 

 the circumference of the jet. This would give for the interval defining 

 the upper limit tt : 4' 508, which is very nearly a fifth. In the case of 

 Plateau's numbers (jr : 4" 38) the discrepancy is a little greater. 



The detached masses into which a jet is resolved do not at once 

 assume and retain a spherical form, but execute a series of vibrations, 

 being alternately compressed and elongated in the direction of the axis 

 of symmetry. When the resolution is effected in a perfectly periodic 

 manner, each drop is in the same phase of its vibration as it passes 

 through a given point of space ; and thence arises the remarkable 

 appearance of alternate swellings and contractions described by Savart. 

 The interval from one swelling to the next is the space described by 



* "Pogg. Ann.," bd. cvi, 1859. 



