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XLIII. On Discontinuous Movements of Fluids, 

 By Professor Helmiioltz*. 



IT is well known that thehydrodynaraic equations give exactly 

 the same partial differential equation for the interior of an 

 incompressible fluid free from friction, and the particles of which 

 do not rotate, as obtains for stationary currents of electricity or 

 heat in conductors of uniform conductivity. It might be ex- 

 pected, therefore, that, for the same shape of the space traversed 

 and for like conditions of boundary, the form of the stream for 

 fluids would be the same as that for electricity and heat, with 

 the exception of trifling differences caused by secondary condi- 

 tions. In fact, however, the differences in many cases are very 

 evident and profound between the arrangement of the current of 

 a fluid and that of the above-mentioned imponderables. 



Such differences are especially obvious if the current enters 

 through an opening with sharp edges, into a wider space. In 

 such cases the radiant lines of electricity separate from one an- 

 other in all directions immediately on passing the opening ; while 

 a fluid current, whether water or air, moves forwards at first 

 from the orifice in a compact stream, which is then usually dis- 

 sipated in gyrations at a greater or less distance. The parts of 

 the fluid of the larger vessel which lie in the neighbourhood of 

 the orifice, but at the sides of the current, may, on the contrary, 

 remain completely at rest. Every one is acquainted with this 

 sort of motion, which is shown clearly by a current of air im- 

 pregnated with smoke. In fact in these phenomena the com- 

 pressibility of the air is of little influence ; and air shows, with 

 very few deviations, the same forms of motion as water. 



Such great differences between what actually takes place and 

 the deductions from the theoretical analysis hitherto accepted, 

 must cause physicists to regard the hydrodynamical equations as 

 a practically very imperfect approximation to the truth. The 

 cause of this discrepancy might be supposed to lie in the internal 

 friction of the fluid, although the divers strange and saltatory 

 irregularities which every one has encountered who has experi- 

 mented upon the motions of fluids can in no wise be accounted 

 for by the continuous and uniform action of friction. 



The investigation of the case where periodical motions result 

 from a continuous air-current, as, for instance, in organ-pipes, 

 convinced me that such an action could only arise by a discon- 

 tinuous motion of the air, or at least by an approximately dis- 

 continuous one. Hence I was led to the discovery of a condi- 



* Translated by Frederick Guthrie, F R.S.E., from the Monatsbericht 

 der koniglich preussischen Akademie der Wissenschaften zu Berlin. April 

 1868, p. 215. 



Phil. Mag. S. 4. Vol. 36. No. 244. Nov. 1868. Z 



