34 



Prof. J. J. Thomson. 



3p-2 Sp -16 



and i£ the molecule is so complex that a. and /3 may be regarded as 

 independent, then the limits of a, and (3 are zero and infinity. 

 The quantity p is at present undetermined. 



Let us apply this result to find the pressure of a gas on the 

 sides of the vessel which contains it. To do this we must consider 

 what takes place at the sides of the vessel. The general 

 nature of this action was described by Sir William Thomson 

 ("Nature," vol. xxiv, p. 47). As the vortex rings move up to the 

 sides of the vessel they swell out and move slowly up the bounding 

 surface, where they form a layer of swollen vortices sticking to the 

 sides of the vessel. A vortex ring coming up to the surface tends 

 to wash off the vortex rings attached to the surface on either side of 

 it, so that when things have got into a state of equilibrium there is a 

 vortex ring washed off for each one that comes up. Thus the 

 pressure on the surface of the vessel will be the same as if the vortex 

 ring struck against the surface and was reflected away again with 

 its velocity reversed, if we assume, as seems natural, that the average 

 velocity of the rings leaving the surface is the same as of those 

 approaching it. Thus each ring that comes up may be looked upon 

 as communicating twice its momentum to the surface, and we can 

 explain the pressure of a gas, just as in the ordinary theory. We 

 have to remark here, however, that the phrase momentum of the 

 vortex ring is ambiguous, as there are two different momenta con- 

 nected with the ring ; there is (1) the momentum of the ring and the 

 fluid surrounding it ; and (2) the momentum of the fluid forming the 

 ring alone ; this is proportional to the velocity of the ring, while (1) 

 is not only not proportional to the velocity, but in the single ring 

 decreases as the velocity of the ring increases ; in a very complex ring- 

 it does not necessarily do this, but even in this case it is not propor- 

 tional to the velocity. 



Now, when a vortex ring gets stopped by a surface the question 

 arises whether the momentum communicated to the surface is the 

 momentum (1) or (2). The answer to this question depends on what 

 we consider the nature of the surface to be. If the surface stops the 

 fluid as well as the ring, then no doubt (1) is the momentum which is 

 communicated to the surface. If, however, the surface stops the ring 

 but allows the greater part of the fluid to flow on, then the momen- 

 tum communicated to the surface is evidently approximately equal to 

 (2). If we consider that the surface is formed of vortex rings the 

 latter supposition seems the more probable, as the fluid in which the 

 rings move can hardly be supposed to be stopped by such a porous 

 surface. We may illustrate this by a mechanical analogy. Let us 

 suppose that we have a number of anchor rings with circulation 



