36o 



NA TURh 



{August 1 8, 1 88] 



the seventh, the ratio being 8:15. When this disk is 

 rotated rapidly, and wind is blown through a flat nozzle 

 held with its opening radially at the edge, two notes are 

 heard giving this exact interval. If the vibration is slow, 

 beats are heard : if the inbratioti be rapid, the beat-note is 

 heard. In order to compare these notes the more 

 accurately with a true combinational tone, the same 

 disk is pierced by three concentric rings of holes, 

 one with 64, another with 120, giving the ratio 8:15, 

 and another, with 8 holes only, corresponding to the 

 number of beats between 120 and the octave of the 

 64 set (12S), that is to say, to the upper beat-not; of tlie 

 interval 8 : 15. When air is blown through the rings of 

 64 and 120 holes in the rotating siren-disk, exactly the 

 same notes and same bests or beat-notes are produced as 

 by the wave-curve at the edge. Here there can surely be 

 no partial tones present to complicate the phenomenon. 

 For greater convenience in comparing several combina- 

 tions, the wave-forms are cut upon cylindrical rims 

 mounted upon one a.xis as in the first figure, a flat disk 

 pierced with holes being added above for comparison. 

 In every case slow rotation gives beats, and rapid rotation 

 the beat-note exactly as Konig's theory requires. 



It remains yet to be seen what answer Helmholtz and 

 the mathematical acousticians will give to the challenge 

 thrown down by Konig in this beautiful and ingenious 

 piece of mechanism. Meantime we may mention that 

 Mr. Bosanquet of Oxford has just been examining the 

 very same question, though by different means. He finds 

 that all Konig's higher beat-tones can be accounted for 

 by the assumption that the terms of higher orders become 

 important in the mechanism of the ear when the dis- 

 placements are considerable, and that therefore " by 

 transformation" in this sense the variations of maximum 

 displacement in the resultant wave give rise to to-and-fro 

 vibrations of simple form having the same frequency as 

 these variation?, and therefore evoke in the ear a note 

 whose frequency is the same as the number of beats. He 

 is also positive that such tones exist only in the ear, and 

 are inaudible in resonators. Lastly, he has satisfied him- 

 self that in all the cases of beats between mistuned con- 

 sonances in which the higher note is (nearly) 2, 3, 4, . . . 

 &c., times as rapid as the lower, the beat consists of vari- 

 ations of intensity of the lower of the two primary tones. 



S. P. T. 



HYDRODYNAMIC ANALOGIES TO ELEC- 

 TRICITY AND MAGNETISM 



FROM a scientific and purely theoretical point of view 

 there is no object in the whole of the Electrical 

 E.xhibition at Paris of greater interest than the remark- 

 able collection of apparatus exhibited by Dr. C. A. 

 Bjerkncs of Christiania, and intended to show the funda- 

 mental phenomena of electricity and magnetism by the 

 analogous ones of hydrodynamics. I will try to give a 

 clear account of these experiments and the apparatus 

 empluyed ; but no description can convey any idea of the 

 wonderful beauty of the actual experiments, whilst the 

 mechanism itself is also of most exquisite construction, 

 Every result which is thus shown by experiment had been 

 previously predicted by Prof Bjerknes as the result of his 

 mathematical investigations. 



It has long been known that if a tuning-fork be struck 

 and held near to a light object like a balloon it attracts it. 

 This is an old experiment, and the theory of it has been 

 worked out more than once. Among others Sir William 

 Thomson gave the theory in the Philosophical Magazine 

 in 1S67. In general words the explanation is that the air 

 in the neighbourhood of the tuning-foik is rarefied by the 

 agitation which it experiences. Consequently the pressure 

 of the air is greater as the distance from the tuning-fork 

 increases. Thus the pressure on the far side of the 



balloon is greater than that on the near side, and the 

 balloon is attracted. 



Dr. Bjerknes has followed out the theory of this action 

 until he has succeeded in illustrating most of the funda- 

 mental phenomena of electricity and magnetism. He 

 causes vibrations to take place in a trough of water about 

 six inches deep. He uses a pair of cylinders fitted with 

 pistons which are moved in and out by a gearing which 

 regulates the length of stroke and also gives great 

 rapidity. These cylinders simply act alternately as air- 

 compressers and expanders, and they can be arranged so 

 that both compress and both expand the air simulta- 

 neously, or in such a way that the one expands while the 

 other compresses the air, and vice versa. These cylin- 

 ders are connected by thin india-rubber tubing and fine 

 metal pipes to the various instruments. A very simple 

 experiment consists in communicating pulsations to a 

 pair of tambours, and observing their mutual actions. 

 They consist each of a ring of metal faced at both sides 

 with india-rubber and connected by a tube with the air- 

 cylinders. One of them is held in the hand ; the other is 

 mounted in the water in a manner which leaves it free 

 to move. It is then found that if the pulsations are of the 

 same kind, i.e. if both expand and both contract simulta- 

 neously, there is attraction. But if one expands while the 

 other contracts, and vice versd, there is repulsion. In 

 fact the phenomenon is the opposite of magnetical and 

 electrical phenomena, for here like poles attract, and 

 unlike poles repel. 



Instead of having the pulsation of a drum we may 

 use the oscillation of a sphere ; and Dr. Bjerknes has 

 mounted a beautiful piece of apparatus by which the 

 compressions and expansions of air are used to cause a 

 sphere to oscillate in the water. But in this case it must 

 be noticed that opposite sides of the sphere are in oppo- 

 site phases. In fact the sphere might be expected to act 

 like a magnet ; and so it does. If two oscillating spheres 

 be brought near each other, then, if they are both moving 

 to and from each other at the same time, there is attrac- 

 tion ; but if one of them be turned round, so that both 

 spheres move in the same direction in their oscillations, 

 then there is repulsion. If one of these spheres be 

 mounted so as to be free to move about a vertical axis, it 

 is found that when a second oscillating sphere is brought 

 near to it, the one which is free turns round its axis and 

 sets itself so that both spheres in their oscillations are 

 approaching each other or receding simultaneously. Two 

 oscillating spheres, mounted at the extremities of an arm, 

 with freedom to move, behave with respect to another 

 oscillating sphere exactly like a magnet in the neighbour- 

 hood of another magnetic pole. I believe that these 

 directive effects are perfectly new-, both theoretically and 

 experimentally. The professor mounts his rod with a 

 sphere at each end in two ways : (i) so that the oscilla- 

 tions are along the arm, and (2) so that they are perpen- 

 dicular. In all cases they behave as if each sphere was a 

 little magnet with its axis lying along the direction of 

 oscillation. 



Dr. Bjerknes looks upon the water in his trough as 

 being the analogue of Faraday's medium ; and he looks 

 upon these attractions and repulsions as being due, not to 

 the action of one body on the other, but to the mutual 

 action of one body and the water in contact with it. 

 Viewed in this light, his first experiment is equivalent to 

 saying that if a vibrating or oscillating body have its 

 motions in the same direction as the water, the body 

 moves away from the centre of disturbance, but if in the 

 opposite direction, towards it. This idea gives us the 

 analogy of dia- and para-magnetism. If, in the neigh- 

 bourhood of a vibrating drum, we have a cork ball, 

 retained under the water by a thread, the oscillations of the 

 cork are greater than those of the water in contact with 

 it, owing to its small mass, and are consequently relatively 

 in the same direction. Accordingly we have repulsion, 



