6i4 



NA TURE 



\_April 2(), 1886 



sented by one carrying positive electricity down or negative 

 jClectricity up, whereas that at the North Magnetic Pole might be 

 one carrying positive electricity up or negative electricity 

 down. We say probably, because it is exceedingly difficult to 

 imagine that either of these vertical currents goes through 

 the lower regions of the atmosphere into the earth, and it is 

 likewise very difficult to imagine that the system of currents is 

 an open one. They must, therefore, somehow close themselves 

 in the upper atmospheric regions, and we may thus perhaps 

 imagine that, while we have an ascending current at the North 

 Magnetic Pole, we liDve a series of descending positive currents 

 at the equator. 



Or, if we prefer to render the analogy between the meteoro- 

 logical and magnetical systems more verbally complete, we 

 should say ascending negative currents at the equator and 

 descending negative currents at the pole. 



These vertical currents being supposed to be confined to the 

 upper regions of the atmosphere, we might imagine that they 

 ought to render themselves visible at the magnetic pole, where 

 they are most concentrated. If so, they would appear as a 

 luminous vertical curtain or fringe suspended in mid-air. This 

 at once suggests to us that the well-known form and nearly con- 

 tinuous appearance of the aurora in these regions may be due to 

 this cause, and may represent to us the vertical component of 

 those currents which we have here supposed to be the causes of 

 the solar diurnal magnetic variations. It must not, however, be 

 supposed that in making this suggestion we imply that pheno- 

 mena of an auroral nature are not likewise connected with 

 magnetic disturbances. 



It is to be remarked in conclusion that 'a system of atmo- 

 spheric currents will act inductively on the terrestrial magnetic 

 system, so that the final effect on the needle will be the conjoint 

 effect of the currents above and of the magnetic change below. 

 In the case of the declination it is our inability to express the 

 force that acts near the equator or near the magnetic pole in 

 terms of any conceivable general change in the magnetic system 

 that induces us to look to atmospheric currents as affording us a 

 simpler mode of expiessing observed facts. This, however, 

 does not hold for the horizontal force near the equator. A set 

 of airrents moving east in both hemispheres will produce by 

 induction a definite and well-understood effect upon the ter- 

 restrial magnetic system. We do not, therefore, know how far 

 the change produced by the sun upon this element is due to a 

 cause above the needle or how much to magnetic change below ; 

 and in this respect the conclusions we have deduced may require 

 modification. 



ON THE DIURNAL PERIOD OF TERRESTRIAL 



MAGNETISM^ 

 'X'HE explanation of the daily variation of the magnetic forces 

 -^ observed on the surface of the earth will, in all probability, 

 lead to the explanation of the mysterious connection between 

 solar phenomena and terrestrial magnetism. For the increase 

 in amplitude of the diurnal variation of the horizontal compo- 

 nents of magnetic force forms one of the most striking effects 

 accompanying the increase in sunspot activity. The daily 

 variation, then, seems a most important symptom of solar in- 

 influence, and its investigation becomes a matter of great 

 interest. 



In the remarks which I wrote out for the Report of the Com- 

 mittee appointed by the British Association for the purpose of 

 considering the best means of comparing and reducing magnetic 

 observations, I pointed out the importance of adopting a sugges- 

 tion, made already by Gauss, to apply the analysis of surface 

 harmonics to the diurnal oscillations. It is well known that 

 such an analysis would allow us to decide the question whether 

 the immediate cause of the disturbance was inside or outside the 

 surface of the earth ; nor can there be t\^■o opinions as to the 

 importance of definitely .settling that question. At the time I 

 wrote out my suggestions, however, it seemed to me that, as the 

 causes of the disturbance had their seat in all probability close 

 to the surface, whether outside or inside, that we should require 

 a large number of terms in the expansion before we could arrive 

 at a definite result. 



In this I was mistaken, and it is one of the principal objects 

 of this paper to show that the periodic variations adapt them- 

 selves with great facility to the analysis, and that even with the 



1 Abstract of ,i Paper read before the Mancliester Literary and Philo- 

 sophical Society, by Arthur Sclnister, F. R.S. 



very limited quantity of material at our disposal we shall be 

 able to arrive at most important results ; results which within a 

 short time might be made absolutely certain if additional obser- 

 vations at a few well-selected stations are taken. My results, as far 

 as they go, point definitely to the region outside tht surface of the 

 ea!-th as the locality of the periodic cause of the variation. It 

 is easy to see that, if electric currents parallel to the earth's sur- 

 face produce any disturbance, we can readily find out whether 

 these currents are outside or inside the earth. As we pass 

 through any current-sheet, the normal magnetic force remains 

 continuous, but that tangential component which is at right 

 angles to the current suffers a discontinuity depending on the 

 intensity of the current. For a spherical current-sheet these 

 components will always be of opposite sign. If we then find 

 the distribution of magnetic potential on the surface of the earth 

 from the horizontal components only, we should get by calcula- 

 tion a vertical component of different sign according as the 

 cause is inside or outside. A comparison with the observed 

 values will at once decide the question. A more careful analysis 

 is necessary, if tlie causes are partly outside and partly inside, 

 and we wish to determine their relative importance. 



I believe that few practical magneticians at the present day read 

 Gauss's memoir "On the General Theory of Terrestrial Magnet- 

 ism," and the loss which cosmical physics has suffered in conse- 

 quence is, as far as ourgeneration is concerned, quite irretrievable. 

 The memoir is a model of scientific reasoning, and full of sugges- 

 tions which are as valuable now as they were fifty years ago. 

 The investigations of Gauss are founded on the assumption of a 

 magnetic potential on the surface of the earth, but that assump- 

 tion requires justification in the case of magnetic disturbances. 

 There will be no potential if there is a discharge of electricity 

 through the earth's surface, and a variation of electric charge 

 would be equivalent to a current. Calculation shows that 

 electrostatic experiments on the surface of the earth would have 

 shown before now if there was a sufficiently rapid change in 

 electric potential to cause a disturbance of the magnetic needle. 

 As regards an actual discharge, it is difficult to form an estimate, 

 and we have therefore to fall back on magnetical observations, 

 and see whether or not they seem to show that the line-in- 

 tegral of magnetic force taken round a closed curve vanishes. 

 The calculations of the author, made on the assumption that it 

 does vanish, seem to show a general agreement with fact ; but 

 some observations of Sabine, taken near the magnetic pole, 

 would, if confirmed, point to a discharge in the Arctic regions. 



The determinations of the diurnal variation of the magnetic 

 variations show such a remarkable regularity everywhere 

 except in the Arctic regions, and especially in latitudes between 

 20° and 60°, that we may as a first approximation express the 

 westerly force (measured as change in declination) as the product 

 of two quantities, one changing with local time, the other with 

 latitude only. This assumption leads to the conclusion that the 

 northerly com]5onent of force ought to be a maximum or minimum 

 when the declination-needle passes through its me.an position. 

 This is very nearly true at Greenwich, Bombay, Lisbon, and 

 Hobart. The agreement is not quite so good at the Cape of 

 Good Hope and in St. Helena, but the observations at these 

 places show some marked anomalies. It is found by observa- 

 tion that the variation in declination increases with the latitude, 

 and we may as a first approximation put it proportional to the 

 sine of the latitude. Writing 7 for the westerly, % fo'' ^'^ 

 northerly component of force, u for the co-latitude, K for the 

 longitude reckoned towards the east, and t for the local time, we 

 may put 



7 = cos 71 cos {t -I- X). 



It follows from this, on the assumption of the existence of a 

 potential, that 



X = cos 2« sin (t 4- A). 



The important point here is the factor cos z«, which changes 

 sign at a latitude of 45°. If our equation is approximately 

 right, the northerly force ought to be a maximum in the morn- 

 ing, a ininimum in the afternoon in the equatorial regions where 

 cos 2tt is negative, while in latitudes above 45° the minimum 

 ought to take place in the morning. This is exactly what 

 happens, with the exception that the change seems to take place 

 in latitudes smaller than 45°. At Bombay the maximum of 

 horizontal force takes place at 11 o'clock a.m. At Greenwicli 

 the minimum takes place a little after that time. 



At Lisbon {ii = 51°) the phase agrees in summer with Green- 

 wich, and in winter with Bombay, the Greenwich type pre- 



