July 31, 1913] 



NATURE 



3, 



effect that such a device increases the number of 

 degrees of freedom of the apparatus with an accom- 

 panying increase in the number of possible oscilla- 

 tions and of conditions necessary for stability is, I 

 believe, incontrovertible. One form of dynamical 

 instability that may result in such cases is the setting 

 up of violent oscillations, ever increasing in ampli- 

 tude, in the pendulum itself, accompanied by flapping 

 of the control planes, in which case this particular 

 method of control becomes worse than useless. 



The remedy which naturally suggests itself, in such 

 circumstances, is to damp down the oscillations of the 

 pendulum by means of frictional or other resistances, 

 and it is probable that few university graduates who 

 have taken first-class honours in mathematics would 

 think that such a contrivance could possibly be wrong. 

 The following test case will show how very dangerous 

 it is to attempt to draw conclusions from general 

 considerations. 



For the aeroplane or torpedo, we substitute a heavy, 

 rigid body POR, free to rotate without resistance 

 about a horizontal axis through its centre of gravity 

 O, perpendicular to the plane of the paper, and there- 

 fore, in the absence of other causes, in neutral 

 equilibrium, and we assume that the moment of 

 inertia of this body is considerable. 



We next imagine a light, small pendulum OQ to 

 be fixed in bearings in the body POR, so that it can 

 turn about the same axis, but we suppose that a 

 frictional couple is called 

 into play between the large 

 body and the pendulum at 

 these bearings. The pen- 

 dulum being light, this fric- 

 tional couple exerts no ap- 

 preciable effect on the large 

 body POR, but the friction 

 is sufficient rapidly to damp 

 out the oscillations of the 

 pendulum itself. The effect 

 of a rudder plane controlled 

 by the pendulum we repre- 

 sent by the assumption that 

 the pendulum operates some 

 mechanism which impresses 

 on the large body a 

 couple proportional to the angle QOP, tending to 

 make it revolve towards OQ, the object of this couple 

 being to bring that body into a position of rest in 

 which OP is pointing vertically downwards. 



When the large body is rotating in the counter- 

 clockwise direction (as in the figure) the small pen- 

 dulum assumes a position of equilibrium OQ on the 

 right-hand side of the vertical, and inclined to the 

 vertical at a certain angle a, the moment of its 

 weight then just balancing the frictional couple. 

 When the body begins to swing backwards the pen- 

 dulum swings with it until both have described an 

 angle 2a, so that the pendulum occupies the position 

 OQ', now making an angle <* on the opposite side of 

 the vertical. During this portion of the motion the 

 controlling mechanism impresses on the body a con- 

 stant angular acceleration, because the angle QOP 

 remains constant. Consequently in the new position 

 the body is rotating with a certain angular velocity 

 set up by this acceleration. In the subsequent motion 

 the pendulum remains at rest in the position OQ', 

 and the body performs a simple harmonic rotation 

 about OQ', but owing to its initial angular velocity 

 it does not come to rest until its ansrular distance 

 from OQ' is greater than the angle OOP. It follows 

 by this reasoning that the oscillations increase in 

 amplitude, and this effect owes its existence to the 

 frictional couple. 



G. H. Bryan. 



The Structure of the Diamond. 



We have applied the new methods of investigation 

 involving the use of X-rays to the case of the diamond, 

 and have arrived at a result which seems of consider- 

 able interest. The structure is extremely simple. 

 Every carbon atom has four neighbours at equal dis- 

 tances from it, and in directions symmetrically related 

 to each other. The directions are perpendicular to 

 the four cleavage or |(m) planes of the diamond; 

 parallel, therefore, to the four lines which join the 

 centre of a given regular tetrahedron to the four 

 corners. The elements of the whole structure are four 

 directions and one length, the latter being, in fact, 

 1-52 x io -8 cm. There is no acute angle in the figure. 

 These facts supply enough information for the con- 

 struction of a model which is easier to understand 

 than a written description. 



If we proceed from any atom, using only standard 

 directions, to the next but one, the straight line join- 

 ing the first to the last is a diagonal of a face of the 

 cubical element of structure ; if we move in the same 

 way through four stages, using all four standard 

 directions in turn, the straight line joining the first 

 and the last is a cube edge. Starting from any atom 

 we can return to it after six stages, using three 

 standard directions twice each. In this way we 

 always link together rings of six carbon atoms. 



If the structure is looked at along a cleavage plane 

 it is seen that the atoms are arranged in parallel 

 planes containing equal numbers of atoms, but 

 separated by distances which alternate and are in the 

 ratio 3 : 1 (actually 1 =;2 x io -8 cm. and 051 x io -8 cm.). 

 It is a consequence of this arrangement that no second 

 order spectrum is reflected by the (m) planes, 

 although spectra of the first, third, fourth, and fifth 

 orders are found. It was this fact that suggested 

 the structure described above. Several other tests, 

 however, may be applied, and all are satisfied. 



Zincblende appears to have the same structure, but 

 the (m) planes contain alternately only zinc and only 

 sulphur atoms. In this way the crystal acquires 

 polaritv and becomes hemihedral. 



W. H. Bragg. 



Leeds, July 28. W. L. Bragg. 



Artificial Hiss. 



Replying to the inquiry of Lord Rayleigh (in 

 Nature of May 29, vol. xci., p. 319) as to the way in 

 which an artificial hiss may be produced with a 

 moderate pressure of air, I suggest that a current of 

 air directed against a sharp edge of a knife held 

 somewhat obliquely may answer his purpose. 



In this connection it is interesting to note that for 

 the formation of the hissing sound in our mouth the 

 presence of saliva seems necessary. If I dry the 

 tongue and the other parts which are needed for the 

 pronunciation of the hissing "s," it is almost impos- 

 sible to produce an audible "s," and the tongue — 

 instinctively, as it were — makes an effort to gather 

 some saliva and to wet itself. 



I would therefore suggest that Lord Rayleigh wet 

 the end of the rubber tube with which he experi- 

 mented. Fred J. Hiixig. 



Kioicho 7, Kojimachi, Tokyo, July 1. 



It had occurred to me also that the moisture of the 

 mouth might play a part in the production of a hiss, 

 but I do not find that such drying as I can give 

 makes an important difference. 



I have to thank several correspondents for sugges- 

 tions. In particular, Mr. G. Beilby sent me two pipes 

 suitable for a 4 in. water pressure, which gave a 

 better effect than anything I had then tried, but 

 still, in my estimation, much short of a well-developed 



NO. 2283, VOL. 91] 



