Oct, 21. 1875J 



NATURE 



537 



earth's rotation, which diverts these currents from the 

 direction of the meridians, we have there the true cause 

 of the trade winds of the high regions, of which the 

 lower trade winds are only the counterpart and the 

 result. The lower trade winds are ordinarily attri- 

 buted to an equatorial rarefaction and to the indraught 

 which results from it. On this account, the indraught 

 being direct and ceasing with the day, the lower trade 

 winds ought to show, just as sea and land breezes, an 

 alternation from day to night, of which there exists no 

 trace. In considering the trade winds, on the contrary, 

 as the indirect result of the draining effected in the region 

 of the upper strata, we see that the intermediate mass 

 plays the part of the air receiver of a hydraulic machine, 

 which, by annihilating differences of velocity, produces a 

 steady flow, but which placed under the direct action of 

 the motive power would have been intermittent. 



The theory of indraught or aspiration represents, on 

 the contrary, vast regular currents of the atmosphere as 

 shown by Fig. 12. We here see at the equator a sort of 



chimney towards which the air is drawn, and up which it 

 ascends, and thereafter takes a course to north and to 

 south. The proof that matters do not take place alto- 

 gether in this way, and that the expansion of the air on 

 all sides in the zone most highly heated by the sun does 

 not there upset the order and the statical superposition of 

 the strata, is astronomical refraction, whose laws are the 

 same at the equator as in temperate regions ; there is in 

 addition the perfect regularity and the smallness of the 

 barometric oscillations — conditions little compatible with 

 those of a colossal updraught, or even with the behaviour 

 of the trade winds, which no one has ever seen at the 

 confines of the zone of calms begin to assume a vertical 

 direction. 



If we have at length succeeded in dispelling the idea of 

 vertical aspiration from which has been deduced the direct 

 cause of all aiirial currents and all tempests, and the idea 

 of electricity considered as the chief agent in the mecha- 

 nics of the atmosphere, and lastly the confounding, so 

 frequently, of statical pressure in a fluid mass in repose 

 with dynamical pressure in a medium traversed through- 

 out by movements the most capricious, we shall have no 

 difficulty in accepting the following considerations, for 

 the subject being in this way simplified, the result is a 

 simple question of pure mechanics. 



Vortices or Eddies with their Axes vertical to the Current 

 of Water. — If the question exclusively concerned pure 

 mechanics or mathematics, we should be stopped at the 

 very threshold of the inquiry, because mechanics does 

 not yet embrace the study of gyratory movements in 

 liquids or fluids. We have not up to the present moment 

 succeeded in submitting to analysis exact problems of 

 hydrodynamics, unless in very special cases in which 

 we may consider fluids as composed of elements of 

 volume containing always the same molecules, of such 

 sort that their masses are invariable and that the mole- 

 cules situated at the surface or on any of the sides will 

 always remain at the surface or at the same side. Be- 

 sides, the trajectories of the liquid filaments ought never 

 to present those re-entering or spiral-like curves which we, 

 however, so frequently remark. If we set out with these 

 restrictive hypotheses, the question cannot be attacked 



by analysis. In other words, we are forced absolutely to 

 exclude all that relates to the movements with which we 

 are now dealing. 



But where analysis is still powerless, experiment and 

 observation remain for our guidance. Whirling move- 

 ments make their appearance not only in gases ; they are 

 equally found in liquids, where they are more manageable, 

 since they can be followed by the eye and even produced 

 at pleasure. We shall therefore commence with the 

 movements which are observed in liquids after we have 

 drawn a vital distinction between tlie different whirling 

 movements with which we are dealing. Air and water 

 present in fact very complicated gyrations, some ebullient 

 transitory, and without any stability of figure, others' 

 perfectly regular and persistent. They are distinguished 

 by a very simple geometrical figure : the second class 

 have their axis always vertical ; the others turn round 

 axes diversely inclined. A moment's reflection will enable 

 us to account for the difference. In the case of a hori- 

 zontal gyration the spires keep clear of the surround- 

 ing layers past which they whirl, or only very slightly 

 graze them in their course. In the first case all motion of 

 the layers disappears ; that of the surface even no more 

 exists ; because at the surface of separation between the 

 water and the air the eddying spires issue from the liquid 

 mass and cut through or carry away to the interior the air 

 placed above so as to produce the phenomena of spray, 

 froth, foam, and emulsion. 



Let us then confine ourselves to whirling movements 

 round a vertical axis, which the student of hydraulics 

 knows and observes, and which can be reproduced at will 

 and studied experimentally. These are, in truth, regular 

 persistent movements which obey laws very simple and 

 precise. The general law which embraces all these phe- 

 nomena is as follows : — When there exists in a current of 

 water differences of velocity between the filaments in 

 lateral juxtaposition, there tends to be generated, by 

 reason of these inequalities, a regular gyratory move- 

 ment round a vertical axis. The spires described by the 

 molecules are sensibly circular, with their centres about 

 the axis. These are, speaking more exactly, the spires of 

 a helix, slightly conical and descending, so that in follow- 

 ing a molecule in its movements it is seen to turn rapidly 

 in a circle round the axis, which it imperceptibly ap- 

 proaches, descending with a velocity very much less than 

 the linear velocity of rotation. Evidently the centrifugal 

 force which results from this gyratory movement must be 

 everywhere counterbalanced by the pressure of the sur- 

 rounding liquid ; there is then inside these eddying spires, 

 at least at their upper orifice, a slight lowering of the 

 pressure which discloses itself at the surface of the liquid 

 by a feeble conical depression centered about the axis of 

 rotation. 



The two following characteristic properties are demon- 

 strated by analysis : — (i) The entire whirl may be regarded 

 as separated from the surrounding fluid, which remains 

 immoveable, by a surface of revolution whose meridian 

 curve has its concavity turned downwards. In other words, 

 the exterior figure of the whirling mass is in the form 

 of an inverted cone pointing downwards. (2) The angular 

 velocity of a molecule increases in proportion as it ap- 

 proaches the axis ; it is inversely proportional to the square 

 of its distance from the vertical axis. Hence the linear velo- 

 city increases in simple inverse proportion to its distance 

 from the axis. If we consider how great the breadth of 

 the whirling cone in the current of the water occasionally 

 is, relatively to the size of the lower orifice, we shall 

 understand how a gyration which appears sluggish at the 

 surface and at the circumference becomes violent at the 

 base of the funnel-shaped eddy. 



These two laws, it must be here observed, are appli- 

 cable not only to liquids but also to gases. They are 

 easily verified by the experiment of throwing a little dust 

 into water in which an eddy has been formed, when the 



