May 2 1, 1903] 



NATURE 



55- 



The attenuation factor r~* in (i) does not count as dis- 

 tortion. 



The wave may go either way, and various cases can be 



laborated. If the wave is outward, the axis (r = o) is the 



>ource. The plane tf=o is a perfect electric conductor. 



I he electrification is of the same sign on its two sides. 



Other details may be got from the formuhe. 



I give an example to show the not very obvious electrical 

 meaning. Let the infinite plane conductor with the straight 

 edge be one pole of a condenser, and a straight wire placed 

 parallel to the edge, and close to it, be the other pole. Join 

 them by a battery, charging the plate and the wire. Bring 

 the wire right up to the edge, and reduce its magnitude to 

 a mere line. (This is to be done in order to attain the 

 ideal simplicity of the formulre.) Take away the battery. 

 Then the electric field is given by 



;p _ sin^fl^ -^ co%hQ r 



(3) 



where /„ is a constant and c is the permittivity. 



Finally, discharge the condenser by contact between edge 

 and wire. Then the result at time i later is that outside 

 the cylinder of radius r = vt the above field (3) persists, 

 whilst inside the cylinder there is no E or H. An electro- 

 magnetic wave separates these regions. It started from 

 the axis at the moment of contact, and as it expands 

 swallows up the whole energy of the field, and carries it 

 to infinity. Similarly, as regards the charging of the plate, 

 only the " battery " should, to have the same formulae, be 

 an impressed force acting at the axis, between the edge 

 and the wire. At time t after contact, the electric field is 

 established fully within the cylinder r=-i)t. On its boundary 

 is the impulsive wave which is laying down the remainder. 

 It also, if the contact be instantaneous, wastes an equal 

 amount of energy at infinity. 



Similarly, by varying the impressed voltage anyhow with 

 the time, the emission of an arbitrary wave of H results. 

 With a real plate and real wire, the main features would 

 no doubt be the same. The use of the line wire introduces 

 infinite voltage. 



What somewhat disguises the electromagnetics is the 

 existence of the steady electric force, or parts thereof, along 

 with the electromagnetic E and H, particularly when / is 

 arbitrary. There is a similar complication in the spherical 

 wave when the total electrification in any thin shell is not 

 zero. There is then an auxiliary internal or external electric 

 force to make continuity. 



We cannot have an undistorted wave from a simple line 

 source. But in the example the apparent line source will 

 be found to be a doublet. For the curl of e (impressed 

 force) is the source of the wave. It is double, positive on 

 one side, negative on the other. 



Solutions of the type 



^ _ ^ Ar" cos (wg + a) 



(4) 



or the same with r and vt interchanged in the denominator, 

 are not distortionless, save for the solitary term in which 

 n=—\. The above distortionless cylindrical wave (i) is 

 unique. Prove by the characteristic. 

 •^Pril 29- Oliver Heaviside. 



Seismometry and Geite. 

 Under the above heading Prof. J. Milne contributed an 

 mteresting article to Nature of April 9, p. 538, on which 

 I wish to offer some remarks. Prof. Milne seems hardly 

 to realise the significance of the enormous pressures to which 

 the earth [s deep-seated material is presumably exposed. 

 One of his objections to the hypothesis of an iron core 

 seems to be that the wave velocities for an infinite isotropic 

 medmm of the density and elasticity of iron do not accord 

 with the velocities of earthquake waves. This objection, 

 however, is not conclusive. In an infinite isotropic medium 

 there are two purely elastic wave velocities, v^ and v^, given 

 by the equations 



»i= '>J^i + n)lp, Vt=»fnjp, 



where p is the density, m and n Thomson and Tait's two 

 elastic constants. On the ordinary theory, nlnt may possess 

 any value consistent with Poisson's ratio y, or (m-n)/2m, 

 NO. 1751, VOL. 68] 



lying between o and 05. Six years ago I showed {Phil. 

 Mag., March, 1897, p. 199) that observed seismic wave 

 velocities can be accounted for by elastic waves without 

 postulating any abnormal value for Young's modulus — the 

 modulus to which Prof. Milne repeatedly refers. For in- 

 stance, we get values of 125 and 25 kilometres per second 

 respectively for v^ and v^ in a medium of density 55 with 

 a Young's modulus of only 10" grammes weight per sq. 

 cm., if we suppose n/m = i/24, or 7 = 048 approximately; 

 and the same results follow if we increase density and 

 elastic constants in the same proportion. 



In iron, as we know it, 7, of course, is not 048, but more 

 nearly 025. A material, however, which under low 

 pressures has 7 = 025, may, after prolonged exposure to 

 enormous pressures, behave as an elastic medium with 7 

 very nearly 05. In fact, if the deep-seated material acts 

 as an elastic medium, the only consistent way yet pointed 

 out for its doing so is by its behaving as if 7 were very 

 near the limiting value answering to incompressibility. 

 Neither of the elastic wave velocities, it should be noticed, 

 has anything directly to do with Young's modulus, a point 

 which cannot be too clearly emphasised. Another consider- 

 ation is the possibly appreciable influence of gravity on the 

 wave velocities. 



Coming now to the question of the behaviour of magneto- 

 graphs at times of seismic disturbance, there must un- 

 doubtedly be magnetic disturbances occasioned by earth- 

 quakes in more than one way. When a violent earthquake 

 occurs where magnetic material abounds, there may be a 

 vast movement of magnetised matter ; there may be a great 

 change in the stresses throughout adjacent magnetic 

 material ; and there may be a great change of local tempera- 

 ture. Any one of these causes will give rise to a magnetic 

 disturbance which should be practically simultaneous all 

 over the world, and should precede any seismic movement 

 at distant stations. It should also diminish very rapidly 

 as the distance from the earthquake origin increases. 



Again, as the seismic waves travel out from their source 

 they must cross volumes of magnetic matter, and the 

 mechanical effect on any such volume must necessarily pro- 

 duce changes in its magnetic field. Owing to the finite 

 velocity of seismic waves, the displacements and stresses 

 simultaneously existent in different parts of any large 

 magnetic volume must be in all kinds of phases, leading 

 to considerable interference between the magnetic disturb- 

 ances to which the different parts give rise at any con- 

 siderable distance. Thus the most plausible explanation 

 of why a magnetic disturbance of some prominence — if real 

 — -should appear at one observatory, but not at another only 

 100 miles oft, is certainly the existence of magnetic material 

 close to the former. Supposing that such local material 

 exists, the magnetic phenomena may be expected to vary 

 according to the direction in which the earthquake wave 

 is travelling. 



One of the chief difficulties in reaching definite con- 

 clusions is the contracted time scale usual in magnetograms. 

 If the true seismic and the apparent magnetic disturbances 

 occur within a few seconds of one another, it is usually 

 practically impossible to say which is the earlier. To see 

 the full force of this, one must remember that a by no means 

 improbable explanation of why apparent magnetic dis- 

 turbances accompany earthquakes at one station, but not 

 at another, is that the magnets at the former, owing to 

 pattern or site, may be much more sensitive seismographs 

 than those at the latter. 



Again, it must be remembered that whilst the so-called 

 " large waves " — rather an unfortunate term — produce in 

 general a much greater effect on a horizontal pendulum than 

 do the " preliminary tremors," it by no means follows that 

 the same will be true of either the true magnetic or the 

 purely mechanical effects on a magnet. Much may depend 

 on the method of support and the time of swing. 



The passage of the " preliminary tremors " and " large 

 waves " due to an earthquake often occupies several hours, 

 and 'during this interval several true independent magnetic 

 movements are not at all unlikely to present themselves, 

 even at times of general magnetic calm. 



For all these reasons a careful intercomparison is wanted 

 of magnetic and seismic records from a variety of stations. 

 Something might be done by running magnetographs for 

 soine time in a district where a local magnetic disturbance 



