296 



NATURE 



\yan. 30, 1890 



Again, in like manner, a "resonator" was always found to 

 give the node in different positions according to the size of the 

 " vibrator " employed. This is what would be expected from 

 the principle of resonance, a resonator being able to respond 

 to any member of the " band" it would itself give out when 

 acting as a radiator, the central period of course with the greatest 



ease. Some such factor as ^"'(^"'^o) could, perhaps, express 

 this sort of thing, where \ belongs to the period of the radia- 

 tion, supposed for the moment "monochromatic," falling on 

 the resonator, and A^ belongs to the "period" of the resonator, 

 or that of the centre of its "band." 



The position of the node was also found to vary on altering 

 the character of the dielectric surrounding the resonator ; even 

 laying a piece of sealing-wax on the wire of the resonator was 

 sufficient to be observed. This might be employed to deter- 

 mine "V" in a dielectric of which only a small quantity was 

 obtainable. 



It is obviously of importance for the " central period " of the 

 resonator employed to coincide with that of the vibrator, espe- 

 cially when determining the velocity of the disturbance, for this 

 is presumably the period given by theory. This is practically 

 always done when arranging their relative sizes, so as to obtain 

 greatest intensity. So that the caution urged by M. Cornu in 

 connection with Prof. Hertz's measurements of this velocity 

 seems, from these considerations, to be to a great extent 

 unnecessary. 



It would obviously be of importance to investigate what form 

 the resonator should take, so as to give out a radiation most 

 approaching one definite period. Fred. T. Trouton. 



Bourdon's Pressure Gauge, 



As there does not seem to be in any of the more familiar text- 

 books of Physics or Engineering any satisfactory explanation of 

 the action of the Bourdon gauge, the following may be of use to 

 some of your readers. 



What we have to explain is the uncurling of the gauge under 

 internal pressure whether of gas or liquid. 



Instead of the usual flattened tube of more or less elliptical seel ion 



bent into the arc of a circle as in Fig. i, think, for convenience, 

 of one of rectangular section, such as AB of Fig. 2, in which a 



Fig. 2. 



is the fixed and B the free end, and in which we shall distinguish, 

 as indicated, the walls, roof, and floor. 



If the annulus of tube were complete, as shown in the central 

 cross-section (Fig. 3), then it is evident that under the in- 

 fluence of internal fluid pressure the outer wall would be every- 

 where in a state of tension in the direction of its length, and the 

 inner wall in a state of compression. In the immediate neigh- 

 bourhood of the ends a and b this state of compression or 



extension will be somewhat modified, but at a sufficient distance 

 from either the condition of the walls will be the same as if the 

 annulus really were complete. 



If T be the tension of the outer wall in the direction of its 

 length, P the pressure of the inner, and R the resultant fluid 

 pressure on any cross-section such as A or B (Fig. 2), then for the 

 equilibrium of the half of the annulus lying on either side of the 

 diameter ab (Fig. 3) we must have 



T = P + R. 



Consider now the equilibrium of any portion BC (Fig. 2) 

 contained between the free end B and a cross-section c at some 

 little distance from B, when the internal pressure is applied, and 

 before uncurling takes place. 



Imagine the fluid within BC to be solidified, then the externa! 

 forces acting on BC (see Fig. 4) reduce to 



(i) A tension, T, due to the action of the outer wall beyond c. 



(2) A pressure, P, ,, ,, inner ,, ,, 



(3) A resultant fluid pressure, R, acting at the centre of pres- 



sure of the cross- section c. 



and since P -f R = T, these reduce to a couple tending to un- 

 curl the tube, and the same holds for all sections sufficiently 

 removed from A and B. 



As the tube imcurls, however, new forces come into play, viz. 

 the resistance to bending of the walls, but especially of the floor 

 and roof of the tube, whose width in the direction of a principal 



Fig. 4. 



radius of the annulus, and consequently whose resistance to 

 bending, is much greater than that of the walls. Uncurling goes 

 on till the moment of the couple resisting flexure is equal to the 

 moment of the bending couple. 



It is evident from this explanation that even a tube of circular 

 section would tend to uncurl, but that it would be very insensitive 

 on account of its strength to resist flexure, and that up to a 

 certain point sensitiveness is gained by having the walls of thin 

 material, high, and very near together. 



Devonport, December 23, 1889. A. M. WoRTHiNGTON. 



Foreign Substances attached to Crabs. 



Referring to Mr. F. P. Pascoe's letter (Nature, December 

 26, p. 176), 1 cannot refrain Jrom expressing my asiouishment 

 at his inability to "see where protection comes in" in the case 

 of craLs covered with sponges, Polyzoa, &c. I should have 

 thought it obvious to everybody that slow-moving crabs, such as 

 all those he mentions and many others that 1 have seen, would 

 have a much better chance of escaping their enemies wher^ 



