905 



WHIRLING-MACHINE. 



WHIRLPOOL. 



936 



iug the reaistance experienced by military projectiles ill passing 

 through the air ; and the objects which this mathematician applied at 

 the extremity of the revolving arm were hemispheres of pasteboard. 

 Any one of these he could at pleasure dispose so that either its con- 

 vex or plane surface might be resisted by the air : there was also 

 provided a flat plate of lead equal in weight to the hemisphere 

 employed, which could be fixed to the arm when the hemisphere was 

 removed, for the purpose of ascertaining the resistance opposed by the 

 air to the motion of the arm itself. 



The radius of the circle described by each hemisphere in its revolu- 

 tion is measured from the axis of the cylinder to the centre of the 

 sphere, of which the revolving object is the half, and the radius of the 

 cylinder is measured from the same axis to the middle of the silk line 

 passing round the surface : let the latter radius be represented by /, 

 and the former, when any one of the hemispheres is applied, by it. 

 The time is marked by a stop-watch at the end of each revolution, and 

 the differences between them are taken for the times of the revolu- 

 tions. After a few revolutions the differences are very nearly constant ; 

 and a mean of ten or twelve of these nearly constant differences may be 

 considered as the time of revolution, when the motion is uniform in 

 consequence of the equality of the resistance and inertia to the weight 

 of the descending body ; let this weight be represented by w. 



In order to discover the resistance due to the inertia of the machine 

 and the action of the air upon the arm (the plate of lead, with its 

 plane in a horizontal position, being fixed at the end of the arm), 

 different weights are attached to the silk line, till some one is found 

 which causes the arm to revolve uniformly in the same time as the 

 hemisphere may have been observed to revolve when its motion was 

 uniform. This weight, which may be represented by w, is evidently 

 the equivalent of that reaistance and inertia ; and the difference w v> 

 is the value of the air's resistance against the anterior surface of the 

 revolving hemisphere only. The velocity of the latter is measured by 

 the length, in feet, of the arc described by its centre in one second, and 

 the weight or resistance w w is supposed to be applied at the cir- 

 cumference of the cylinder, to which the silk line is a tangent. This 



term must consequently be multiplied by -, in order to reduce it to 



R 



the value of that which would be equivalent to it if applied at the 

 centre of the revolving object. 



From a mean of numerous experiments with a hemisphere whose 

 diameter was 6'375 inches, and which revolved with velocities varying 

 from 3 feet to 20 feet [>er second, Dr. Huttou found that the resistance 

 of the air against the flat side was to the resistance against the convex 

 M 2'48 to 1 : by theory it should be as 2 to 1 only. From experi- 

 ments made with hemispheres of different magnitudes, also with a 

 whole sphere, a cone, and a very short cylinder, it was found that the 

 .nee experienced by similar surfaces (the velocities varying from 

 In ii-et to 20 feet per second) were nearly proportional to the surfaces, 

 increasing a little above that proportion with the greater surfaces ; and 

 that the resistances on the game surface varied, at a mean, with the 

 'J'Hl ]jwer of the velocity, gradually increasing with the increasing 

 velocities. When a hemispherical or conical surface was acted on by 

 the air, the resistance was less than that which was experienced by a 

 plane surface of equal diameter ; but the sharper surface had not 

 always less resistance than one which was round : the convex surface 

 of a hemisphere, for example, experienced less resistance than that of 

 a cone, contrary to the result of theory. The resistance on the base of 

 a cone was to the resistance on the convex surface as 2'3 to 1 : by 

 theory it should be as 4 to 1. The resistance on the base of a short 

 cylinder was less than that on the base of a cone, though the areas 

 were equal ; also, on account of the different manner iu which air acts 

 on the posterior surfaces, the base of a hemisphere experienced less 

 resistance than that of a cone, and the convex surface of a hemisphere 

 less than that of a whole sphere of equal diameter. 



The whirling-machine invented by Ferguson is a frame or box of 

 wood, containing a wheel about 2 feet in diameter, on each tide of which 

 is .1 pulley about 6 inches in diameter; the axes of all are in vertical 

 positions, and, by strings passing over the wheel and pulleys, the latter 

 are made to revolve on turning the wheel by means of a handle. The 

 in hine was intended to exhibit, in a popular manner, the principal 

 effects of centripetal or centrifugal forces, when bodies revolve in the 

 circumferences of circles. 



On the axle of each pulley there is fixed, at its middle point, a bar 

 of wood iu a horizontal position, and on this a small plate or carriage 

 of brass is made to slide easily along two horizontal wires extending 

 from the centre to one extremity of the bar : a silk line attached to 

 this plate passes under a small brass pulley near the centre of the bar, 

 and over a similar pulley fixed in a brass frame, about 6 inches above 

 the first pulley ; the line is afterwards attached to a brass plate or 

 carriage, which is capable of sliding up or down in the brass frame, 

 according as the first plate moves from or towards the centre, along 

 the wires on the horizontal bar. A given weight is placed on this first 

 carriage at any distance from the centre, and the pulley, to whose axle 

 r is fixed, is made to revolve by turning the handle on the axle 

 of the wheel : then, on placing such a weight on the carriage in the 

 brans frame as will just allow the former weight to recede in conse- 

 quence of the centrifugal force which that weight with its carriage 



acquires by the revolution, the weight in the frame, including that of 

 its carriage, is to be considered as the equivalent of the centrifugal 

 force. 



For example, let the two pulleys be of equal diameters, and let each 

 be made to carry on its axle a horizontal bar with a sliding plate or 

 carriage : then, if a weight of 6 ounces, including the carriage, be placed 

 at 3 inches from the centre of motion on one bar, and 2 ounces, 

 including the carriage, on the other bar, at 9 inches from its centre of 

 motion ; upon making the two bars revolve rapidly, the centrifugal 

 forces will cause any equal weights on the carriages in the two brass 

 frames to rise to the tops of those frames at the same instant. Here 

 the velocities of rotation are represented by 3 and 9, and the weights 

 by 6 and 2, so that the ratio compounded of the velocities and masses 

 is one of equality ; and this is considered as verifying the proposition 

 that if bodies revolve in circular orbits, the centrifugal forces are equal 

 when the products of the masses and velocities are equal. Again, let 

 the diameter of one of the pulleys be twice as great as that of the 

 other, so that when the bars are placed on the axles and are made to 

 revolve by turning the wheel, the angular velocity of oue may be half 

 the angular velocity of the other : then, if any equal weights, for 

 example, be fixed ou the carriages which slide on the two bars, at equal 

 distances from the centres of motioupaud if there be placed ou the 

 carriages in the brass frames above tnose centres, weights, including 

 those of the carriages, such that the weight above the larger pulley 

 may be one-fourth of that which is above the smaller pulley ; the cen- 

 trifugal forces arising from the revolutions will allow these weights to 

 be raised at the same instant, proving that both the revolving bodies 

 are retained in circular orbits. Here the angular velocities of the 

 revolving bodies are as 1 to 2, and the weights in the frames, which 

 represent the centrifugal forces, are as 1 to 4 ; and the experiment 

 shows that when equal bodies revolve in equal circular orbits, the 

 centrifugal or centripetal forces are to one another as the squares of 

 the angular velocities. 



It is easy to understand that such experiments may be varied so as 

 to exhibit all the phenomena of circular movements. 



WH IKLPOOL, a place in a river, or iu the sea, where in con- 

 sequence of obstructions from banks, rocks, or islands, or the oppo- 

 sition of winds and currents, the waters acquire a revolving motion. 



The agitation of the waters which is constantly observed near 

 Messina, and which is usually designated the whirlpool of Charybdis, 

 is now well known to be unaccompanied by any vortiginous motion by 

 which vessels might be absorbed, and is, rather, an incessant undula- 

 tion of the water. The agitation is said to exist iu several different 

 places at the same time, within the circumferences of circles whose 

 diameters, when the wind is moderate, do not exceed 100 feet, and is 

 caused by the wind acting obliquely on the rapid current which sets 

 towards the faro, or lighthouse, from the north during six hours, and 

 from the south during the next six hours, and so on alternately ; the 

 changes taking place respectively with the rising and setting of the 

 moon. Spallanzani, who wa.-j rowed over the spot when the wind was 

 light, experienced no danger, though the boat was much tossed by the 

 waves : he was informed however that when the wind is high, the 

 swelling of the waves is more violent and extensive, so that small 

 vessels which are driven within the limits of the agitation may be sunk 

 by the waves breaking over them, and large ones may be driven on the 

 1 talian shore, where they are sometimes wrecked on the rock of Scylla. 

 The dashing nf the waves on the hollow rocks about Cape 1'eloro 

 produces a noise which is said to resemble the barking of dogs ; and it 

 is probable that these sounds gave rise to the fable that a female 

 monster surrounded by ferocious doga and wolves lay there in wait to 

 devour the mariners who might be wrecked on the coast. 



Home of the descriptive particulars of the Galofaro, the supposed 

 Charybdis [CALABRIA, col. 23(i, in GEOG. Div.], juat given, are derived 

 from Captain (now Admiral) W. H. Smyth's account of Sicily and its 

 islands. We now add the following, as given, from that work, in the 

 author's subsequent memoir on the Mediterranean, pp. 181, 182 : 

 " To the undecked boats of the lihegiana, Locrians, Zanoleans, and 

 Greeks it must have been formidable ; for even in the present day 

 small craft are sometimes endangered by it, and I have seen several 

 men-of-war, and even a 7-4-guu ship (the Queen, bearing t/iejtay of Rear- 

 Admiral Kir Charles Penrvsc), whirled round on its surface; but by 

 using due caution there is generally very little danger or inconvenience 

 to be apprehended. The Galofaro appears to be an agitated water, of 



from 70 to 90 fathoms in depth It is owing probably to the 



meeting of the harbour and lateral currents with the main one, the 

 latter being forced over in this direction by the opposite point of Pezzo. 

 Thia agrees in some measure with the relation of Thucydides, who calls 

 it a violent reciprocation of the Tyrrhene and Sicilian seas ; and he ia 

 the only writer of remote antiquity I remember to have read who has 

 assigned thia danger its true situation and not exaggerated its effects. 

 Many wonderful stories are told respecting this vortex, particularly 

 some said to have been related by the celebrated diver, Colas, who at 

 last lost his life here. I have never found reason, however, during my 

 examination of thia spot, to believe one of them. The formation of 

 the Tangdora shoals, stretching out on each aide of the little kind of 

 bay off which the Galofaro is situated, is probably owing to the eddies 

 of Charybdis." 



The Maelstrom, between the islands of Mosker and Warae on the 



