622 



NATURE 



[April 2 s, 1889 



If a vessel is to remain at rest for a considerable period, an anti- 

 fouling composition which exfoliates rapidly, and which also 

 contains poisons known to act on germ life, must be used, the 

 amount of such poison depending on the seasons and the waters 

 in which the ship is to be ; whilst if a vessel is to be continually 

 running, then a slowly exfoliating composition must be employed, 

 and a very small percentage of poison is all that is required, as 

 skin friction and the comparative absence of the germs and spores 

 in deep water will do the rest. 



Our ships represent an enormous capital, and any trouble or 

 care which will prolong their existence is well worth taking and 

 will be amply repaid, and at the present time a heavily corroded 

 and foul vessel means either ignorance or negligence on the part 

 of those who have the responsibility of deciding on the composi- 

 tions to be used ; and, finally, it must be clearly borne in mind 

 that there is no anti-fouling composition which ever has been 

 made, or probably ever will be made, that will answer for all 

 cases, and that, until this is clearly recognized, the present un- 

 satisfactory condition of the question will exist. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, March 28. — "The Diurnal Variation of 

 Terrestrial Magnetism." By Arthur Schuster, F.R.S., Professor 

 of Physics ; with an Appendix by H. Lamb, F.R.S., Professor 

 of Mathematics, Owens College, Manchester. 



In the year 1839, Gauss published his celebrated memoir on 

 " Terrestrial Magnetism," in which the potential on the earth's 

 surface was calculated to twenty-four terms of a series of surface 

 harmonics. It was proved in this memoir that if the horizontal 

 components of magnetic force were known all over the earth the 

 surface potential could be derived without the help of the vertical 

 forces, and it is well known now how these latter can be used to 

 separate the terms of the potential which depend on internal 

 from those which depend on external sources. 



The use of harmonic analysis to separate internal from ex- 

 ternal causes has never been put to a practical test, but it seems 

 to me to be specially well adapted to inquiries on the causes of 

 the periodic oscillations of the magnetic needle. 



If the magnetic effects can be fairly represented by a single 

 term in the series of harmonics as far as the horizontal forces are 

 concerned, there should be no doubt as to the location of the 

 disturbing cause, for the vertical force should be in the opposite 

 direction if the origin is outside from what it should be if the 

 origin is inside the earth. 



In any case, the differences between the two results will be of 

 the same order of magnitude as the vertical force itself. If it 

 were then a question simply of deciding whether the cause is 

 outside or inside, without taking into account a possible combina- 

 tion of both causes, the result should not be doubtful even if we 

 have only an approximate knowledge of the vertical forces. 



Two years ago I showed that the leading features of the hori- 

 zontal components for diurnal variation could be approximately 

 represented by the surface harmonic of the second degree and 

 first type, and that the vertical variation agreed in direction and 

 phase with the calculation on the assumption that the seat of the 

 force is outside the earth. The agreement seemed to me to be 

 sufficiently good to justify the conclusion that the greater part of 

 the variation is due to causes outside the earth's surface. Never- 

 theless, it seemed advisable to enter more fully into the matter, 

 as in the first approximate treatment of the subject a number of 

 important questions had to be left untouched. I now publish 

 the results of an investigation which has been carried out as far 

 as the observations at my disposal have allowed me to do. My 

 original conclusions have been fully confirmed, and some 

 further information has been obtained, which I believe to be of 

 importance. 



I have made use of the observations taken at Bombay, Lisbon, 

 Greenwich, and St. Petersburg. The horizontal components of 

 the diurnal variation during the year 1870 were in the first place 

 reduced to the same system of co-ordinates and to the same units. 

 If we remember that experience has shown the diurnal variation 

 to be very nearly the same for places in the same latitude, except 

 near the magnetic pole, and also that it is symmetrical north and 

 south of the equator, we may for a given time of day assume the 

 horizontal components known over eight circles of latitude, four 

 of which are north and four south of the equator. 



From the horizontal components, the potential was calculated 

 in terms of a series of surface harmonics. It was found that in 



order to represent both the summer and the winter effect with 

 sufficient accuracy thirty-eight terms were necessary. In this 

 calculation the vertical forces were not made use of at all. 



FrojQ the potential, as calculated from the horizontal com- 

 ponents, we can deduce the vertical force, either on the assump- 

 tion that the variation is due to an outside cause, or that it is 

 due to an inside cause ; and compare the vertical forces thus 

 found with the vertical forces as actually observed. 



If we put both into the form 



Tn cos n(t-t„^, 



we can obtain an idea of the agreement as regards amplitude 

 and phase for each harmonic term. The following tables give 

 the results for n — 1 and n — 2 — that is, for the diurnal and 

 the semi-diurnal variation : — 



Table I. 

 Observed and calculated Values of the Coefficients t^ and i^ of 

 Vertical Force, when expressed in the form r^ cos {t - jfj> 

 + Tn COS 2{t - i.j), on the supposition that the Disturbing 

 Force is inside the Earth. 



Bombay 



Lisbon 2; 



Greenwich 



St. Petersburg, 1870 

 „ 1878 



Table II. 

 Observed and calculated Values of the Coefficients t and t.^ 

 when expressed in the form r^ cos {t — i^ -f r^ cos 2{l - t.^), 

 on the supposition that the Disturbing Force is outside the 

 Earth. 



Bombay 



Lisbon _ 



Greenwich 



St. Petersburg, 1870 



Calc. Obs. Diff. 



Calc. ! Obs. ! Diff. 



h m. 



- o 36 



- o 04 



- o iS 



- 2 27 



- I 34 



In Table I. the comparison of the observed phases is made 

 with the values calculated on the assumption that the disturbing 

 force is inside the earth. In Table II. the same comparison is 

 made on the alternative hypothesis. There is complete dis- 

 agreement in Table I. between the observed and calculated 

 values, and nearly complete agreement in Table II. It is seen, 

 how both at Lisbon and Bombay the time of maximum dis- 

 placement agrees within three minutes of time for the diurnal 

 variation, and at Lisbon within four minutes of time also for the 

 semi-diurnal variation. Considering that Lisbon is the most 

 important station, not only on account of its geographical 

 position, but also because the observed vertical forces apply to 

 the same year as the calculated ones, the result is strikingly in 

 favour of the outside force. The results for Greenwich argue 

 in the same direction. As regards St. Petersburg, the results 

 for 1870 neither agree with one nor with the other hypothesis. 

 The observations for 1870 are, however, doubtful, but the results 

 for 1878 agree well with the hypothesis of an outside disturbing 

 force. 



The observed amplitudes are found in all cases to be 

 considerably smaller than the calculated ones. 



If we then take it as proved that the primary cause of this 

 variation comes to us from outside the earth's surface, we are 

 led to consider that a varying magnetic potential must cause 

 induced currents within the earth, if that body is a sufficiently 

 good conductor. These induced currents might be the cause 

 of the apparent reduction in amplitude. As my colleague. 

 Prof. Lamb, has given considerable attention to the problen> 

 of currents in a conducting sphere, I consulted him, and he 



