June 2S, 1888] 



NATURE 



211 



in the bright spot. If I make a small motion of the disk, I shall 

 move the bright spot and the effect will disappear. I am push- 

 ing the disk away now, and the flaring has stopped. The flame 

 is still in the shadow of the disk, but not at the centre. I bring 

 the disk back again, and when the flame comes into the centre 

 it flares again vigorously. That is the phenomenon which was 

 discovered by Delisle and confirmed by Arago and Fresnel, but 

 mathematically it was suggested by Poisson. 



Disc 



Flame 



Source 



Fig. 4. 



r Poisson's calculation related only to the very central point in 

 the axis of the disk. More recently the theory of this experi- 

 ment has been very thoroughly examined by a German mathe- 

 matician, Lommel ; and I have exhibited here one of the curves 

 given by him embodying the results of his calculations on the 

 subject (Fig. s). 



The abscissas, measured horizontally, represent distances 

 drawn outwards from the centre of the shadow o ; the ordinates 

 measure the intensity of the light at the various points. The 

 maximum intensity o A is at the centre. A little way outwards, 

 at B, the intensity falls almost, but not quite, to zero. At C there 

 is a revival of intensity, indicating a bright ring ; and further out 

 there is a succession of subordinate fluctuations. The curve on 



QT =28 INCHES 

 &== 10 > > 

 A-= -6 » ? 

 37' = 15 »» 



B 



Fig. 



the other side of o A would of course be similar. This curve cor- 

 responds to the distances and proportions indicated, a is the 

 distance between the source of sound and the disk ; b is the dis- 

 tance between the disk and the flame, the place where the 

 intensity is observed. The numbers given are taken from the 

 notes of an experiment which went well. If we can get our 

 flame to the right point of sensitiveness, we may succeed in 

 bringing into view not only the central spot, but the revived 

 sound which occurs after you have got away from the central 

 point and have passed through the ring of silence. There is the 



loud central point. If I push the disk a little, we enter the ring 

 of silence, B ; l a little further, and the flame flares again, being 

 now at C 



Although we have thus imitated the optical experiment, I 

 must not leave you under the idea that we are working under the 

 same conditions that prevail in optics. You see the diameter of 

 my disk is 15 inches, and the length of my sound-wave is about 

 half an inch. My disk is therefore about thirty wave-lengths in 

 diameter, whereas the diameter of a disk representing thirty 

 wave-lengths of light would be only about toVt inch. Still, the 

 conditions are sufficiently alike to get corresponding effects, 

 and to obtain this bright point in the centre of the shadow 

 conspicuously developed. 



I will now make an experiment illustrating still further the 

 principle of Huygens' zones, which I have already roughly 

 sketched. I indicated that the effect of contiguous zones was 

 equal and opposite, so that the effect of each of the odd zones 

 is one thing, and of the even zones the opposite thing. If we 

 can succeed in so preparing a screen as to fit the system of zones, 

 allowing the one set to pass, and at the same time intercepting 

 the other set, then we shall get a great effect at the central 

 point, because we shall have removed those parts which, if they 

 remained, would have neutralized the remaining parts. Such a 

 system has been cut out of zinc, and is now hanging before you. 

 When the adjustments are correct, there will be produced, under 

 the action of that circular grating, an effect much greater than 

 would result if the sound-waves were allowed to pass on without 

 any obstruction. The only point difficult of explanation is as to 

 what happens when the system of zones is complete, and extends 

 to infinity, viz. when there is no obstiuction at all. In that case 

 it may be proved that the aggregate effect of all the zones is, in 

 ordinary cases, half the effect that would be produced by any one 

 zone alone, whereas if we succeed in stopping out a number of the 

 alternate zones, we may expect a large multiple of the effect of 

 one zone. The grating is now in the right position, and you see 

 the flame flaring strongly, under the action of the sound-waves 

 transmitted through these alternate zones, the action of the other 

 zones being stopped by the interposition of the zinc. But the 

 interest of the experiment is principally in this, that the flame is 

 flaring more than it would do if the grating were removed alto- 

 gether. There is now, without the grating, a very trivial 

 flaring ; 2 but when the grating is in position again — though a 

 great part of the sound is thereby stopped out — the effect is far 

 more powerful than when no obstruction intervened. The 

 grating acts, in fact, the part of a lens. It concentrates the 

 sound upon the flame, and so produces the intense magnification 

 of effect which we have seen. 



[The exterior radius of the «th zone being x, we have, from 

 the formula given above — 



1 1 _ n\ 



a + b~x*' 



so that if a and b be the distances of the source and image from 

 the grating, the relation required to maintain the focus is, as 

 usual, 



I 1 1 



a + b=f> 



where/, the focal length, is given by — 



J n\ 



In the actual grating, eight zones (the first, third, 

 fifth, &c.) are occupied by metal. The radius 

 of the first zone, or central circle, is 3 inches, 



_ t so that x^/n — g. The focal length is neces- 

 sarily a function of X. In the present case \ = 4 



inch nearly, and therefore f= 18 inches. If a and b are the 



same, each must be made equal to 36 inches.] 



SCIENTIFIC SERIALS. 



Revue d'Anthrofologie, troisieme serie, tome iii., 1888 

 (Paris). — Stratigraphic palaeontology in relation to man, by M. 

 Marcellin Boule. Rejecting as unauthenticated all evidence of 

 human existence in the Tertiary age, the author considers the 



1 With the data given above the diameter of the silent ring is two-thirds of 

 an inch. 



2 Under the best conditions the flame is absolutely unaffected. 



